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Answer test results

This page exposes the results of running answer tests on STACK test cases. This page is automatically generated from the STACK unit tests and is designed to show question authors what answer tests actually do. This includes cases where answer tests currentl fail, which gives a negative expected mark. Comments and further test cases are very welcome.

Answer test	Passed?	Student response	Teacher answer	Options	CAS errors	Raw mark	Expected mark	Feedback	Answer note
AlgEquiv	Expected failure	1/0	1		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATAlgEquiv_STACKERROR_SAns.
AlgEquiv	Expected failure	1	1/0		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATAlgEquiv_STACKERROR_TAns.
AlgEquiv	Expected failure		(x-1)^2		The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question.	0	-1	The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question.	ATAlgEquivTEST_FAILED-Empty SA.
AlgEquiv	Expected failure	x^2			The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty teacher answer, probably a CAS validation problem when authoring the question.	0	-1	The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty teacher answer, probably a CAS validation problem when authoring the question.	ATAlgEquivTEST_FAILED-Empty TA.
AlgEquiv	Expected failure	x-1)^2	(x-1)^2		The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question.	0	-1	The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question.	ATAlgEquivTEST_FAILED-Empty SA.
AlgEquiv	Pass	x1	x_1			0	0
AlgEquiv	Pass	x_1	x[1]			0	0
AlgEquiv	Pass	x[1]	x1			0	0
Predicates
AlgEquiv	Pass	integerp(3)	true			1	1		ATLogic_True.
AlgEquiv	Pass	integerp(3.1)	true			0	0
AlgEquiv	Pass	integerp(3)	false			0	0
AlgEquiv	Pass	integerp(3)	true			1	1		ATLogic_True.
AlgEquiv	Pass	lowesttermsp(x^2/x)	true			1	1		ATLogic_True.
AlgEquiv	Pass	lowesttermsp(-y/-x)	true			1	1		ATLogic_True.
AlgEquiv	Pass	lowesttermsp((x^2-1)/(x-1))	true			0	0
AlgEquiv	Pass	lowesttermsp((x^2-1)/(x+2))	true			1	1		ATLogic_True.
Case sensitivity
AlgEquiv	Pass	X	x			0	0		ATAlgEquiv_WrongCase.
AlgEquiv	Pass	exdowncase(X)	x			1	1
AlgEquiv	Pass	exdowncase((X-1)^2)	x^2-2*x+1			1	1
Permutations of variables (To do: a dedicated answer test with feedback)
AlgEquiv	Pass	Y=1+X	y=1+x			0	0		ATEquation_default
AlgEquiv	Pass	v+w+x+y+z	a+b+c+A+B			0	0
Numbers
AlgEquiv	Pass	4^(-1/2)	1/2			1	1
AlgEquiv	Pass	4^(1/2)	sqrt(4)			1	1
Mix of floats and rational numbers
AlgEquiv	Pass	0.5	1/2			1	1
AlgEquiv	Pass	0.33	1/3			0	0
AlgEquiv	Pass	5.1e-2	51/1000			1	1
AlgEquiv	Pass	0.333333333333333	1/3			0	0
AlgEquiv	Pass	(0.5+x)*2	2*x+1			1	1
Complex numbers
AlgEquiv	Pass	sqrt(-1)	%i			1	1
AlgEquiv	Pass	%i	e^(i*pi/2)			1	1
AlgEquiv	Pass	(4sqrt(3)%i+4)^(1/5)	8^(1/5)(cos(%pi/15)+%isin(%pi/15))			1	1
AlgEquiv	Pass	(4sqrt(3)%i+4)^(1/5)	rectform((4sqrt(3)%i+4)^(1/5))			1	1
AlgEquiv	Pass	(4sqrt(3)%i+4)^(1/5)	polarform((4sqrt(3)%i+4)^(1/5))			1	1
AlgEquiv	Pass	%i/sqrt(x)	sqrt(-1/x)			1	1
Infinity
AlgEquiv	Pass	inf	inf			1	1
AlgEquiv	Pass	inf	-inf			0	0
AlgEquiv	Pass	2*inf	inf			0	0
AlgEquiv	Pass	0*inf	0			1	1
Powers and roots
AlgEquiv	Pass	x^(1/2)	sqrt(x)			1	1
AlgEquiv	Pass	x	sqrt(x^2)			0	0
AlgEquiv	Pass	abs(x)	sqrt(x^2)			1	1
AlgEquiv	Pass	1/abs(x)^(1/3)	(abs(x)^(1/3)/abs(x))^(1/2)			1	1
AlgEquiv	Pass	sqrt((x-3)*(x-5))	sqrt(x-3)*sqrt(x-5)			0	0
AlgEquiv	Pass	1/sqrt(x)	sqrt(1/x)			1	1
AlgEquiv	Pass	x-1	(x^2-1)/(x+1)			1	1
AlgEquiv	Pass	2^((1/5.1)*t)	2^((1/5.1)*t)			1	1
AlgEquiv	Pass	2^((1/5.1)*t)	2^(0.196078431373*t)			0	0
AlgEquiv	Pass	a^b*a^c	a^(b+c)			1	1
AlgEquiv	Pass	(a^b)^c	a^(b*c)			0	0
AlgEquiv	Pass	(assume(a>0),(a^b)^c)	a^(b*c)			1	1
AlgEquiv	Pass	(assume(x>2),6*((x-2)^2)^k)	6(x-2)^(2k)			1	1
AlgEquiv	Pass	signum(-3)	-1			1	1
AlgEquiv	Pass	6*((x-2)^3)^k	6(x-2)^(3k)			1	1
AlgEquiv	Pass	(4sqrt(3)%i+4)^(1/5)	6^(1/5)cos(%pi/15)-6^(1/5)%i*sin(%pi/15)			0	0
AlgEquiv	Pass	2+2*sqrt(3+x)	2+sqrt(12+4*x)			1	1
AlgEquiv	Pass	6e^(6(y^2+x^2))+72x^2e^(6*(y^2+x^2))	(72x^2+6)e^(6*(y^2+x^2))			1	1
Expressions with subscripts
AlgEquiv	Pass	a1	a_1			0	0
AlgEquiv	Pass	rhozV/(4piepsilon[0]*(R^2+z^2)^(3/2))	rhozV/(4piepsilon[0]*(R^2+z^2)^(3/2))			1	1
AlgEquiv	Pass	rhozV/(4piepsilon[1]*(R^2+z^2)^(3/2))	rhozV/(4piepsilon[0]*(R^2+z^2)^(3/2))			0	0
AlgEquiv	Pass	sqrt(k/m)*sqrt(m/k)	1			1	1
AlgEquiv	Pass	(2*pi)/(k/m)^(1/2)	(2*pi)/(k/m)^(1/2)			1	1
AlgEquiv	Pass	(2pi)(m/k)^(1/2)	(2*pi)/(k/m)^(1/2)			1	1
AlgEquiv	Pass	sqrt(2*x/10+1)	sqrt((2*x+10)/10)			1	1
AlgEquiv	Pass	((x+3)^2*(x+3))^(1/3)	((x+3)(x^2+6x+9))^(1/3)			1	1
Need to factor internally.
AlgEquiv	Pass	((x+3)^2*(x+3))^(1/3)	((x+3)(x^2+6x+9))^(1/3)			1	1
Polynomials and rational function
AlgEquiv	Pass	(x-1)^2	x^2-2*x+1			1	1
AlgEquiv	Pass	(x-1)*(x^2+x+1)	x^3-1			1	1
AlgEquiv	Pass	(x-1)^(-2)	1/(x^2-2*x+1)			1	1
AlgEquiv	Pass	1/(4*x-(%pi+sqrt(2)))	1/(x+1)			0	0
AlgEquiv	Pass	(x-a)^6000	(x-a)^6000			1	1
AlgEquiv	Pass	(a-x)^6000	(x-a)^6000			1	1
AlgEquiv	Pass	(4*a-x)^6000	(x-4*a)^6000			1	1
AlgEquiv	Pass	(x-a)^6000	(x-a)^5999			0	0
AlgEquiv	Pass	(k+8)/(k^2+4*k-12)	(k+8)/(k^2+4*k-12)			1	1
AlgEquiv	Pass	(k+7)/(k^2+4*k-12)	(k+8)/(k^2+4*k-12)			0	0
AlgEquiv	Pass	-(2k+6)/(k^2+4k-12)	-(2k+6)/(k^2+4k-12)			1	1
AlgEquiv	Pass	1/n-1/(n+1)	1/(n*(n+1))			1	1
AlgEquiv	Pass	0.5x^2+3x-1	x^2/2+3*x-1			1	1
AlgEquiv	Pass	14336000000x^13+250265600000x^12+1862860800000x^11+7623925760000x^10+18290677760000x^9+24744757985280x^8+14567212351488x^7-3267871272960x^6-6408053107200x^5+670406720000x^4+1179708800000x^3-429244800000x^2+56696000000*x-2680000000	512(2x+5)^7(5x-1)^5(70x+67)			1	1
AlgEquiv	Pass	14336000000x^13+250265600000x^12+1862860800000x^11+7623925760000x^10+18290677760000x^9+24744757985280x^8+14567212351488x^7-3267871272960x^6-6408053107200x^5+670406720000x^4+1179708800000x^3-429244800000x^2+56696000000*x-2680000001	512(2x+5)^7(5x-1)^5(70x+67)			0	0
AlgEquiv	Pass	14336000000*x^13	512(2x+5)^7(5x-1)^5(70x+67)			0	0
Trig functions
AlgEquiv	Pass	cos(x)	cos(-x)			1	1
AlgEquiv	Pass	cos(x)^2+sin(x)^2	1			1	1
AlgEquiv	Pass	cos(x+y)	cos(x)cos(y)-sin(x)sin(y)			1	1
AlgEquiv	Pass	cos(x+y)	cos(x)cos(y)+sin(x)sin(y)			0	0
AlgEquiv	Pass	cos(x#pm#y)	cos(x)cos(y)-(#pm#sin(x)sin(y))			1	1		ATLogic_True.
AlgEquiv	Pass	sin(x#pm#y)	sin(x)cos(y)#pm#cos(x)sin(y)			1	1		ATLogic_True.
AlgEquiv	Pass	sin(x#pm#y)	cos(x)sin(y)#pm#sin(x)cos(y)			0	0
AlgEquiv	Pass	2*cos(x)^2-1	cos(2*x)			1	1
AlgEquiv	Pass	1.0cos(1200%pi*x)	cos(1200%pix)			1	1
AlgEquiv	Pass	diff(tan(10*x)^2,x)	cos(6*x)			0	0
AlgEquiv	Pass	exp(%i*%pi)	-1			1	1
AlgEquiv	Pass	2cos(2x)+x+1	-sin(x)^2+3*cos(x)^2+x			1	1
AlgEquiv	Pass	(2sec(2t)^2-2)/2	-(sin(4t)^2-2sin(4t)+cos(4t)^2-1)(sin(4t)^2+2sin(4t)+cos(4t)^2-1)/(sin(4t)^2+cos(4t)^2+2cos(4*t)+1)^2			1	1
AlgEquiv	Pass	1+cosec(3*x)	1+csc(3*x)			1	1
AlgEquiv	Pass	1/(1+exp(-2*x))	tanh(x)/2+1/2			1	1
AlgEquiv	Pass	1+cosech(3*x)	1+csch(3*x)			1	1
AlgEquiv	Pass	-4sec(4z)^2sin(6z)-6tan(4z)cos(6z)	-4sec(4z)^2sin(6z)-6tan(4z)cos(6z)			1	1
AlgEquiv	Pass	-4sec(4z)^2sin(6z)-6tan(4z)cos(6z)	4sec(4z)^2sin(6z)+6tan(4z)cos(6z)			0	0
AlgEquiv	Pass	csc(6x)^2(7sin(6x)cos(7x)-6cos(6x)sin(7x))	-(6cos(6x)sin(7x)-7sin(6x)cos(7x))/sin(6*x)^2			1	1
AlgEquiv	Pass	csc(6x)^2(7sin(6x)cos(7x)-6cos(6x)sin(7x))	(6cos(6x)sin(7x)-7sin(6x)cos(7x))/sin(6*x)^2			0	0
AlgEquiv	Pass	-(7x^6+4x^3)/sin(7*y+x^7+x^4+1)^2	-(7x^6+4x^3)csc(7y+x^7+x^4+1)^2			1	1
AlgEquiv	Pass	sin((2%pin-%pi)/2)	-cos(n*%pi)			1	1
AlgEquiv	Pass	sin(x/2)/(1+tan(x)*tan(x/2))	sin(x/2)*cos(x)			1	1
AlgEquiv	Pass	(declare(n,integer),trigrat(sin((2%pin-%pi)/2)))	-(-1)^n			1	1
AlgEquiv	Pass	cot(%pi/20)+cot(%pi/24)-cot(%pi/10)	sqrt(1)+sqrt(2)+sqrt(3)+sqrt(4)+sqrt(5)+sqrt(6)			0	-3
AlgEquiv	Pass	trigeval(cot(%pi/20)+cot(%pi/24)-cot(%pi/10))	sqrt(1)+sqrt(2)+sqrt(3)+sqrt(4)+sqrt(5)+sqrt(6)			1	1
AlgEquiv	Pass	sin([1/8,1/6, 1/4, 1/3, 1/2, 1]*%pi)	[sqrt(2-sqrt(2))/2,1/2,1/sqrt(2),sqrt(3)/2,1,0]			0	-3	The entries underlined in red below are those that are incorrect. \\[\\left[ {\\color{red}{\\underline{\\sin \\left( \\frac{\\pi}{8} \\right)}}} , \\frac{1}{2} , \\frac{1}{\\sqrt{2}} , \\frac{\\sqrt{3}}{2} , 1 , 0 \\right] \\]	(ATList_wrongentries 1).
AlgEquiv	Pass	trigeval(sin([1/8,1/6, 1/4, 1/3, 1/2, 1]*%pi))	[sqrt(2-sqrt(2))/2,1/2,1/sqrt(2),sqrt(3)/2,1,0]			1	1
AlgEquiv	Pass	1+x	taylor(1/(1-x),x,0,1)			1	1
AlgEquiv	Pass	1	taylor(1/(1-x),x,0,1)			0	0
Logarithms
AlgEquiv	Pass	log(a^2*b)	2*log(a)+log(b)			1	1
AlgEquiv	Pass	(2log(2x)+x)/(2*x)	(log(2x)+2)/(2sqrt(x))			0	0
AlgEquiv	Pass	log(abs((x^2-9)))	log(abs(x-3))+log(abs(x+3))			0	0
AlgEquiv	Pass	lg(10^x)	x			1	1
AlgEquiv	Pass	lg(3^x,3)	x			1	1
AlgEquiv	Pass	lg(a^x,a)	x			1	1
AlgEquiv	Pass	1+lg(27,3)	4			1	1
AlgEquiv	Pass	1+lg(27,3)	3			0	0
AlgEquiv	Pass	lg(1/8,2)	-3			1	1
AlgEquiv	Pass	lg(root(x,n))	lg(x,10)/n			1	1
AlgEquiv	Pass	log(root(x,n))	lg(x,10)/n			0	0
AlgEquiv	Pass	x^log(y)	y^log(x)			1	1
Hyperbolic trig
AlgEquiv	Pass	e^1-e^(-1)	2*sinh(1)			1	1
Lists
AlgEquiv	Pass	x	[1,2,3]			0	0	Your answer should be a list, but is not. Note that the syntax to enter a list is to enclose the comma separated values with square brackets.	ATAlgEquiv_SA_not_list.
AlgEquiv	Pass	[1,2]	[1,2,3]			0	0	Your list should have \$3\$ elements, but it actually has \$2\$.	ATList_wronglen.
AlgEquiv	Pass	[1,2,4]	[1,2,3]			0	0	The entries underlined in red below are those that are incorrect. \\[\\left[ 1 , 2 , {\\color{red}{\\underline{4}}} \\right] \\]	(ATList_wrongentries 3).
AlgEquiv	Pass	[1,x>2]	[1,2<x]			1	1
AlgEquiv	Pass	[1,2,[2-x<0,{1,2,2,2, 1,3}]]	[1,2,[2-x<0,{1,2}]]			0	0	The entries underlined in red below are those that are incorrect. \\[\\left[ 1 , 2 , \\left[ 2-x < 0 , \\left \\{1 , 2 , 3 \\right \\} \\right] \\right] \\]	(ATList_wrongentries 3: (ATList_wrongentries 2: ATSet_wrongsz)).
AlgEquiv	Pass	[(k+8)/(k^2+4k-12),-(2k+6)/(k^2+4*k-12)]	[(k+8)/(k^2+4k-12),-(2k+6)/(k^2+4*k-12)]			1	1
Rounding of floats
AlgEquiv	Pass	round(0.5)	0.0			1	1
AlgEquiv	Pass	round(1.5)	2.0			1	1
AlgEquiv	Pass	round(2.5)	2.0			1	1
AlgEquiv	Pass	round(12.5)	12.0			1	1
AlgEquiv	Pass	significantfigures(0.5,1)	0.5			1	1
AlgEquiv	Pass	significantfigures(1.5,1)	2.0			1	1
AlgEquiv	Pass	significantfigures(2.5,1)	3.0			1	1
AlgEquiv	Pass	significantfigures(3.5,1)	4.0			1	1
AlgEquiv	Pass	significantfigures(11.5,2)	12.0			1	1
AlgEquiv	Pass	1500	scientific_notation(1500,3)			1	1
AlgEquiv	Pass	1500	displaysci(1.5,2,3)			1	1
AlgEquiv	Pass	[3,3.1,3.14,3.142,3.1416,3.14159,3.141593,3.1415927]	makelist(significantfigures(%pi,i),i,8)			1	1
Sets
AlgEquiv	Pass	x	{1,2,3}			0	0	Your answer should be a set, but is not. Note that the syntax to enter a set is to enclose the comma separated values with curly brackets.	ATAlgEquiv_SA_not_set.
AlgEquiv	Pass	co(1,2)	{1,2,3}			0	0	Your answer should be a set, but is not. Note that the syntax to enter a set is to enclose the comma separated values with curly brackets.	ATAlgEquiv_SA_not_set.
AlgEquiv	Pass	{1,2}	{1,2,3}			0	0	Your set should have \$3\$ different elements, but it actually has \$2\$.	ATSet_wrongsz.
AlgEquiv	Pass	{2/4, 1/3}	{1/2, 1/3}			1	1
AlgEquiv	Pass	{A[1],A[2],A[4]}	{A[1],A[2],A[3]}			0	0	The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \\[\\left \\{A_{4} \\right \\}\\]	ATSet_wrongentries.
AlgEquiv	Pass	{A[1],A[2],A[3]}	{A[1],A[2],A[3]}			1	1
AlgEquiv	Pass	{1,2,4}	{1,2,3}			0	0	The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \\[\\left \\{4 \\right \\}\\]	ATSet_wrongentries.
AlgEquiv	Pass	{1,x>4}	{4<x, 1}			1	1
AlgEquiv	Pass	{x-1=0,x>1 and 5>x}	{x>1 and x<5,x=1}			1	1
AlgEquiv	Pass	{x-1=0,x>1 and 5>x}	{x>1 and x<5,x=2}			0	0	The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \\[\\left \\{x-1=0 \\right \\}\\]	ATSet_wrongentries.
AlgEquiv	Pass	{x-1=0,x>1 and 5>x}	{x>1 and x<3,x=1}			0	0	The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \\[\\left \\{5-x > 0\\,{\\mbox{ and }}\\, x-1 > 0 \\right \\}\\]	ATSet_wrongentries.
Equivalence for elements of sets is different from expressions: see docs.
AlgEquiv	Pass	{-sqrt(2)/sqrt(3)}	{-2/sqrt(6)}			0	-3	The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \\[\\left \\{-\\frac{\\sqrt{2}}{\\sqrt{3}} \\right \\}\\]	ATSet_wrongentries.
AlgEquiv	Pass	{[-sqrt(2)/sqrt(3),0],[2/sqrt(6),0]}	{[2/sqrt(6),0],[-2/sqrt(6),0]}			0	-3	The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \\[\\left \\{\\left[ -\\frac{\\sqrt{2}}{\\sqrt{3}} , 0 \\right] \\right \\}\\]	ATSet_wrongentries.
AlgEquiv	Pass	ev(radcan({-sqrt(2)/sqrt(3)}),simp)	ev(radcan({-2/sqrt(6)}),simp)			1	1
AlgEquiv	Pass	ev(radcan(ratsimp({(-sqrt(10)/2)-2,sqrt(10)/2-2},algebraic:true)),simp)	ev(radcan(ratsimp({(-sqrt(5)/sqrt(2))-2,sqrt(5)/sqrt(2)-2},algebraic:true)),simp)			1	1
AlgEquiv	Pass	{(2-2^(5/2))/2,(2^(5/2)+2)/2}	{1-2^(3/2),2^(3/2)+1}			0	0	The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \\[\\left \\{\\frac{2-2^{\\frac{5}{2}}}{2} , \\frac{2^{\\frac{5}{2}}+2}{2} \\right \\}\\]	ATSet_wrongentries.
AlgEquiv	Pass	ev(radcan({(2-2^(5/2))/2,(2^(5/2)+2)/2}),simp)	{1-2^(3/2),2^(3/2)+1}			1	1
AlgEquiv	Pass	{(x-a)^6000}	{(a-x)^6000}			0	0	The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \\[\\left \\{{\\left(x-a\\right)}^{6000} \\right \\}\\]	ATSet_wrongentries.
AlgEquiv	Pass	{(k+8)/(k^2+4k-12),-(2k+6)/(k^2+4*k-12)}	{(k+8)/(k^2+4k-12),-(2k+6)/(k^2+4*k-12)}			1	1
Matrices
AlgEquiv	Pass	matrix([1,2],[2,3])	matrix([1,2],[2,3])			1	1
AlgEquiv	Pass	matrix([1,2],[2,3])	matrix([1,2,3],[2,3,3])			0	0	Your matrix should be \$2\$ by \$3\$, but it is actually \$2\$ by \$2\$.	ATMatrix_wrongsz_columns.
AlgEquiv	Pass	matrix([1,2],[2,3])	matrix([1,2],[2,5])			0	0	The entries underlined in red below are those that are incorrect. \\[ \\left[\\begin{array}{cc} 1 & 2 \\\\ 2 & {\\color{red}{\\underline{3}}} \\end{array}\\right]\\]	ATMatrix_wrongentries.
AlgEquiv	Pass	matrix([0.33,1],[1,1])	matrix([0.333,1],[1,1])			0	0	The entries underlined in red below are those that are incorrect. \\[ \\left[\\begin{array}{cc} {\\color{red}{\\underline{0.33}}} & 1 \\\\ 1 & 1 \\end{array}\\right]\\]	ATMatrix_wrongentries.
AlgEquiv	Pass	matrix([x+x,2],[2,x*x])	matrix([2*x,2],[2,x^2])			1	1
AlgEquiv	Pass	matrix([epsilon[0],2],[2,x^2])	matrix([epsilon[0],2],[2,x^2])			1	1
AlgEquiv	Pass	matrix([epsilon[2],2],[2,x^2])	matrix([epsilon[0],2],[2,x^3])			0	0	The entries underlined in red below are those that are incorrect. \\[ \\left[\\begin{array}{cc} {\\color{red}{\\underline{\\varepsilon_{2}}}} & 2 \\\\ 2 & {\\color{red}{\\underline{x^2}}} \\end{array}\\right]\\]	ATMatrix_wrongentries.
AlgEquiv	Pass	matrix([x>4,{1,x^2}],[[1,2],[1,3]])	matrix([4-x<0,{x^2, 1}],[[1,2],[1,3]])			1	1
AlgEquiv	Pass	matrix([x>4,{1,x^2}],[[1,2],[1,3]])	matrix([4-x<0,{x^2, 1}],[[1,2],[1,4]])			0	0	The entries underlined in red below are those that are incorrect. \\[ \\left[\\begin{array}{cc} x > 4 & \\left \\{1 , x^2 \\right \\} \\\\ \\left[ 1 , 2 \\right] & \\left[ 1 , {\\color{red}{\\underline{3}}} \\right] \\end{array}\\right]\\]	ATMatrix_wrongentries.
Vectors
AlgEquiv	Pass	a	stackvector(a)			0	0
Equations
AlgEquiv	Pass	1	x=1			0	0	Your answer should be an equation, but is not.	ATAlgEquiv_SA_not_equation.
AlgEquiv	Pass	x=1	x=1			1	1		ATEquation_sides
AlgEquiv	Pass	1=x	1=x			1	1		ATEquation_sides
AlgEquiv	Pass	1=x	x=1			1	1		ATEquation_sides_op
AlgEquiv	Pass	1=1	1=x			0	0		ATEquation_default
AlgEquiv	Pass	1=1	x=1			0	0		ATEquation_default
AlgEquiv	Pass	x=2	x=1			0	0		ATEquation_lhs_notrhs
AlgEquiv	Pass	2=x	x=1			0	0		ATEquation_default
AlgEquiv	Pass	x=x	y=y			1	1		ATEquation_zero
AlgEquiv	Pass	x+y=1	y=1-x			1	1
AlgEquiv	Pass	2x+2y=1	y=0.5-x			1	1		ATEquation_ratio
AlgEquiv	Pass	1/x+1/y=2	y = x/(2*x-1)			1	1		ATEquation_ratio
AlgEquiv	Pass	y=sin(2*x)	y/2=cos(x)*sin(x)			1	1		ATEquation_ratio
AlgEquiv	Pass	y=(x-a)^6000	y=(x-a)^6000			1	1		ATEquation_sides
AlgEquiv	Pass	y=(x-a)^5999	y=(x-a)^6000			0	0		ATEquation_lhs_notrhs
AlgEquiv	Pass	y=(a-x)^6000	y=(x-a)^6000			1	1		ATEquation_sides
AlgEquiv	Pass	y=(a-x)^5999	y=(x-a)^5999			0	0		ATEquation_lhs_notrhs
AlgEquiv	Pass	y=(a-x)^59999	y=(x-a)^5999			0	0		ATEquation_lhs_notrhs
AlgEquiv	Pass	x+y=i	y=i-x			1	1
AlgEquiv	Pass	(1+%i)*(x+y)=0	y=-x			1	1
AlgEquiv	Pass	s^2%e^(st)=0	s^2=0			0	0		ATEquation_default
AlgEquiv	Pass	0=-x+y/A+(y-z)/B	0=x-y/A-(y-z)/B			1	1
AlgEquiv	Pass	x^6000-x^6001=x^5999	x^5999*(1-x+x^2)=0			1	1		ATEquation_ratio
AlgEquiv	Pass	x^6000-x^6001=x^5999	x^5999*(1-x+x^3)=0			0	0		ATEquation_default
AlgEquiv	Pass	258552x^7(81*x^8+1)^398	x^3*(x^4+1)^399			0	0
AlgEquiv	Pass	Ia(R1+R2+R3)-IbR3=0	-Ia(R1+R2+R3)+IbR3=0			1	1
AlgEquiv	Pass	a=0 or b=0	a*b=0			1	1		ATEquation_sides
AlgEquiv	Pass	a*b=0	a=0 or b=0			1	1		ATEquation_sides
AlgEquiv	Pass	ax=ay	x=y			0	0		ATEquation_default
AlgEquiv	Pass	ax=ay	a=0 or x=y			1	1		ATEquation_ratio
Unary Equations
AlgEquiv	Pass	1	stackeq(1)			1	1
AlgEquiv	Pass	stackeq(1)	1			1	1
AlgEquiv	Pass	stackeq(1)	0			0	0
Equations: Loose/gain roots with nth powers of each side.
AlgEquiv	Pass	x=y	x^2=y^2			0	0		ATEquation_default
AlgEquiv	Pass	(x-2)^2=0	x=2			0	0		ATEquation_default
AlgEquiv	Pass	a^3*b^3=0	a=0 or b=0			0	0		ATEquation_default
AlgEquiv	Pass	a^3*b^3=0	a*b=0			0	0		ATEquation_default
AlgEquiv	Pass	(x-y)*(x+y)=0	x^2=y^2			1	1		ATEquation_ratio
AlgEquiv	Pass	x=1	(x-1)^3=0			0	0		ATEquation_default
AlgEquiv	Pass	sqrt(x)=sqrt(y)	x=y			0	0		ATEquation_default
AlgEquiv	Pass	x=sqrt(a)	x^2=a			0	0		ATEquation_default
AlgEquiv	Pass	(x-sqrt(a))*(x+sqrt(a))=0	x^2=a			1	1		ATEquation_ratio
AlgEquiv	Pass	(x-%isqrt(a))(x+%i*sqrt(a))=0	x^2=-a			1	1		ATEquation_ratio
AlgEquiv	Pass	(x-%isqrt(abs(a)))(x+%i*sqrt(abs(a)))=0	x^2=-abs(a)			1	1		ATEquation_ratio
AlgEquiv	Pass	y=sqrt(1-x^2)	x^2+y^2=1			0	0		ATEquation_default
AlgEquiv	Pass	(y-sqrt(1-x^2))*(y+sqrt(1-x^2))=0	x^2+y^2=1			1	1		ATEquation_ratio
AlgEquiv	Pass	(y-sqrt((1-x)(1+x)))(y+sqrt((1-x)*(1+x)))=0	x^2+y^2=1			1	1		ATEquation_ratio
AlgEquiv	Pass	(x-1)(x+1)(y-1)*(y+1)=0	y^2+x^2=1+x^2*y^2			1	1		ATEquation_ratio
Equations: edge cases. Teacher must enter an equation, all or none here.
AlgEquiv	Pass	all	x=x			1	1		ATEquation_zero
AlgEquiv	Pass	true	x=x			1	1		ATEquation_zero
AlgEquiv	Pass	x=x	all			1	1		ATEquation_zero
AlgEquiv	Pass	all	all			1	1		ATEquation_zero
AlgEquiv	Pass	true	all			1	1		ATEquation_zero
AlgEquiv	Pass	a=a	x=x			1	1		ATEquation_zero
AlgEquiv	Pass	false	x=x			0	0		ATEquation_zero_fail
AlgEquiv	Pass	false	all			0	0		ATEquation_zero_fail
AlgEquiv	Pass	none	all			0	0		ATEquation_zero_fail
AlgEquiv	Pass	all	none			0	0		ATEquation_empty_fail
AlgEquiv	Pass	2=3	1=4			1	1		ATEquation_empty
AlgEquiv	Pass	none	1=2			1	1		ATEquation_empty
AlgEquiv	Pass	false	1=2			1	1		ATEquation_empty
AlgEquiv	Pass	none	none			1	1		ATEquation_empty
AlgEquiv	Pass	false	none			1	1		ATEquation_empty
AlgEquiv	Pass	3=0	none			1	1		ATEquation_empty
AlgEquiv	Pass	0=3	none			1	1		ATEquation_empty
AlgEquiv	Pass	all	1=2			0	0		ATEquation_empty_fail
AlgEquiv	Pass	true	1=2			0	0		ATEquation_empty_fail
AlgEquiv	Pass	{}	1=2			0	0	Your answer should be an equation, but is not.	ATAlgEquiv_SA_not_equation.
AlgEquiv	Pass	[]	1=2			0	0	Your answer should be an equation, but is not.	ATAlgEquiv_SA_not_equation.
AlgEquiv	Pass	{}	none			0	0	Your answer should be an equation, inequality or a logical combination of many of these, but is not.	ATAlgEquiv_SA_not_logic.
Sets of real numbers
AlgEquiv	Pass	x^2	cc(1,3)			0	0	Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals.	ATAlgEquiv_SA_not_realset.
AlgEquiv	Pass	%union(oo(1,2),oo(3,4))	%union(oo(1,2),oo(3,4))			1	1		ATRealSet_true.
AlgEquiv	Pass	%union(oc(1,2),co(2,3))	oo(1,3)			1	1		ATRealSet_true.
AlgEquiv	Pass	%union(oc(1,2),co(2,3))	cc(1,3)			0	0		ATRealSet_false.
AlgEquiv	Pass	{-1,1}	%union({-1,1})			1	1		ATRealSet_true.
AlgEquiv	Pass	{1,3}	cc(1,3)			0	0		ATRealSet_false.
AlgEquiv	Pass	%intersection(oc(-1,1),co(1,2))	%union({1})			1	1		ATRealSet_true.
AlgEquiv	Pass	oo(-inf,1)	oo(-inf,1)			1	1		ATRealSet_true.
AlgEquiv	Pass	oo(-1,inf)	oo(0,inf)			0	0		ATRealSet_false.
AlgEquiv	Pass	%union(oc(-inf,0),oo(-1,4))	oo(-inf,4)			1	1		ATRealSet_true.
AlgEquiv	Pass	%union(oo(-inf,1),oo(-1,inf))	oo(-inf,inf)			1	1		ATRealSet_true.
AlgEquiv	Pass	all	oo(-inf,inf)			1	1		ATRealSet_true.
Complex numbers
AlgEquiv	Pass	a=b/%i	%i*a=b			1	1		ATEquation_num_i
AlgEquiv	Pass	b/%i=a	%i*a=b			1	1		ATEquation_num_i
AlgEquiv	Pass	b=a/%i	%i*a=b			0	0		ATEquation_lhs_notrhs_op
AlgEquiv	Pass	a*(2+%i)=b	a=b/(2+%i)			1	1		ATEquation_ratio
AlgEquiv	Pass	a*(2+%i)=b	a=b*(2-%i)/5			1	1		ATEquation_num_i
AlgEquiv	Pass	a*(2+%i)=b	a=b*(2-%i)/4			0	0		ATEquation_default
Absolute value in equations
AlgEquiv	Pass	abs(x)=abs(y)	x=y			0	0		ATEquation_default
AlgEquiv	Pass	abs(x)=abs(y)	x=y or x=-y			1	1
AlgEquiv	Pass	abs(x)=abs(y)	(x-y)*(x+y)=0			1	1
Functions
AlgEquiv	Expected failure	f(x):=1/0	f(x):=x^2		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	TEST_FAILED
AlgEquiv	Pass	1	f(x):=x^2			0	0	Your answer should be a function, defined using the operator `:=`, but is not.	ATAlgEquiv_SA_not_function.
AlgEquiv	Pass	f(x)=x^2	f(x):=x^2			0	0	Your answer should be a function, defined using the operator `:=`, but is not.	ATAlgEquiv_SA_not_function.
AlgEquiv	Pass	f(x):=x^2	f(x,y):=x^2+y^2			0	0		ATFunction_length_args. ATFunction_false.
AlgEquiv	Pass	f(x):=x^2	f(x)=x^2			0	0	Your answer should be an equation, but is not.	ATAlgEquiv_SA_not_equation.
AlgEquiv	Pass	f(x):=x^2	f(x):=x^2			1	1		ATFunction_true.
AlgEquiv	Pass	f(x):=x^2	f(x):=sin(x)			0	0		ATFunction_false.
AlgEquiv	Pass	g(x):=x^2	f(x):=x^2			0	0		ATFunction_wrongname. ATFunction_true.
AlgEquiv	Pass	f(y):=y^2	f(x):=x^2			1	1		ATFunction_arguments_different. ATFunction_true.
AlgEquiv	Pass	f(a,b):=a^2+b^2	f(x,y):=x^2+y^2			1	1		ATFunction_arguments_different. ATFunction_true.
Inequalities
AlgEquiv	Pass	1	x>1			0	0	Your answer should be an inequality, but is not.	ATAlgEquiv_SA_not_inequality.
AlgEquiv	Pass	x=1	x>1 and x<5			0	0	You have entered an equation, but an equation is not expected here. You may have typed something like "y=2x+1" when you only needed to type "2x+1".	ATAlgEquiv_TA_not_equation.
AlgEquiv	Pass	x<1	x>1			0	0	Your inequality appears to be backwards.	ATInequality_backwards.
AlgEquiv	Pass	1<x	x>1			1	1
AlgEquiv	Pass	a<b	b>a			1	1
AlgEquiv	Pass	2<2*x	x>1			1	1
AlgEquiv	Pass	-2>-2*x	x>1			1	1
AlgEquiv	Pass	x>1	x<=1			0	0	Your inequality should not be strict! Your inequality appears to be backwards.	ATInequality_strict. ATInequality_backwards.
AlgEquiv	Pass	x>=2	x<2			0	0	Your inequality should be strict, but is not! Your inequality appears to be backwards.	ATInequality_nonstrict. ATInequality_backwards.
AlgEquiv	Pass	x>=1	x>2			0	0	Your inequality should be strict, but is not!	ATInequality_nonstrict.
AlgEquiv	Pass	x>1	x>1			1	1
AlgEquiv	Pass	x>=1	x>=1			1	1
AlgEquiv	Pass	x>2	x>1			0	0
AlgEquiv	Pass	1<x	x>1			1	1
AlgEquiv	Pass	2*x>=x^2	x^2<=2*x			1	1
AlgEquiv	Pass	2*x>=x^2	x^2<=2*x			1	1
AlgEquiv	Pass	3x^2<9a	x^2-3*a<0			1	1
AlgEquiv	Pass	x^2>4	x>2 or x<-2			1	1		ATLogic_True.
AlgEquiv	Pass	1<x or x<-3	x<-3 or 1<x			1	1		ATLogic_True.
AlgEquiv	Pass	1<x or x<-3	x<-1 or 3<x			0	0
AlgEquiv	Pass	x>1 and x<5	x>1 and x<5			1	1		ATLogic_True.
AlgEquiv	Pass	x>1 and x<5	5>x and 1<x			1	1		ATLogic_True.
AlgEquiv	Pass	not (x<=2 and -2<=x)	x>2 or -2>x			1	1		ATLogic_True.
AlgEquiv	Pass	x>2 or -2>x	not (x<=2 and -2<=x)			1	1		ATLogic_True.
AlgEquiv	Pass	x>=1 or 1<=x	x>=1			1	1
AlgEquiv	Pass	x>=1 and x<=1	x=1			1	1		ATInequality_solver.
AlgEquiv	Pass	(x>4 and x<5) or (x<-4 and x>-5) or (x+5>0 and x<-4)	(x>-5 and x<-4) or (x>4 and x<5)			1	1		ATLogic_True.
AlgEquiv	Pass	(x>4 and x<5) or (x<-4 and x>-5) or (x+5>0 and x<-4)	(x>-5 and x<-4) or (x>8 and x<5)			0	0
AlgEquiv	Pass	(x < 0 nounor x >= 1) nounand x <= 3	x < 0 or (x >= 1 and x <= 3)			1	1		ATLogic_True.
AlgEquiv	Pass	(x < 0 nounor x >= 1) nounand x <= 3	x < 0 or x >= 1 and x <= 3			1	1		ATLogic_True.
AlgEquiv	Pass	(x < 0 nounor x >= 1) nounand x <= 3	x < 0 or (x >= 1 and x <= 3)			1	1		ATLogic_True.
AlgEquiv	Pass	(x < 0 nounor x >= 1) nounand x <= 3	(x < 0 or x >= 1) and x <= 3			1	1		ATLogic_True.
AlgEquiv	Pass	(x < 0 nounor x >= 1) nounand x <= 3	x < 0 or (x >= 1 and x <= 3)			1	1		ATLogic_True.
AlgEquiv	Pass	natural_domain(1/x^2)	natural_domain(1/x)			1	1		ATRealSet_true.
AlgEquiv	Pass	x^4>=0	x^2>=0			1	1
AlgEquiv	Pass	x^4>=16	x^2>=4			1	1
AlgEquiv	Pass	2*x^2+x>=6	x<=-2 or x>=3/2			1	1		ATLogic_True.
AlgEquiv	Pass	{2,-2}	x>2 nounor -2>x			0	0	Your answer should be an equation, inequality or a logical combination of many of these, but is not.	ATAlgEquiv_SA_not_logic.
AlgEquiv	Pass	x^2<4	x<2 nounand x>-2			1	1		ATLogic_Solver_True.
AlgEquiv	Pass	x^2<6	x<2 nounand x>-2			0	0
AlgEquiv	Pass	x>1 nounand x<-1	false			1	1		ATLogic_Solver_True.
AlgEquiv	Pass	x>1 nounand x<3	true			0	0
AlgEquiv	Pass	x>1 nounor x<3	true			1	1		ATLogic_Solver_True.
AlgEquiv	Pass	x>1 nounor x<3	all			1	1		ATLogic_Solver_True.
AlgEquiv	Pass	abs(x)<1	abs(x)<1			1	1
AlgEquiv	Pass	abs(x)<1	abs(x)<2			0	0
AlgEquiv	Pass	abs(x)<1	abs(x)>1			0	0	Your inequality appears to be backwards.	ATInequality_backwards.
AlgEquiv	Pass	abs(x)<2	-2<x and x<2			0	-3
AlgEquiv	Pass	-2<x and x<2	abs(x)<2			0	-3
AlgEquiv	Pass	abs(x)<2	-1<x and x<1			0	0
AlgEquiv	Pass	x^2<=9	abs(x)<3			0	0
AlgEquiv	Pass	x^2<=9	abs(x)<=3			0	-3
AlgEquiv	Pass	x^6<1	abs(x)<1			0	-3
AlgEquiv	Pass	abs(x)>1	x<-1 or x>1			0	-3
Surds
AlgEquiv	Pass	sqrt(12)	2*sqrt(3)			1	1
AlgEquiv	Pass	sqrt(11+6*sqrt(2))	3+sqrt(2)			1	1
AlgEquiv	Pass	(19601-13860*sqrt(2))^(7/4)	(5*sqrt(2)-7)^7			1	1
AlgEquiv	Pass	(19601-13861*sqrt(2))^(7/4)	(5*sqrt(2)-7)^7			0	0
AlgEquiv	Pass	(19601-13861*sqrt(2))^(7/4)	(5*sqrt(2)-7)^7			0	0
AlgEquiv	Pass	sqrt(2log(26)+4-2log(2))	sqrt(2*log(13)+4)			1	1
AlgEquiv	Pass	sqrt(2)sqrt(3)+2(sqrt(2/3))x-(2/3)(sqrt(2/3))x^2+(4/9)(sqrt(2/3))*x^3	4sqrt(6)x^3/27-(2sqrt(6)x^2)/9+(2sqrt(6)x)/3+sqrt(6)			1	1
Factorials and binomials
AlgEquiv	Pass	(n+1)*n!	(n+1)!			1	1
AlgEquiv	Pass	n/n!	1/(n-1)!			1	1
AlgEquiv	Pass	n/n!	1/(n+1)!			0	0
AlgEquiv	Pass	n!/(k!*(n-k)!)	binomial(n,k)			1	1
AlgEquiv	Pass	binomial(n,k)+binomial(n,k+1)	binomial(n+1,k+1)			0	-3
AlgEquiv	Pass	binomial(n,k)+binomial(n,k+1)	binomial(n+1,k)			0	0
AlgEquiv	Pass	binomial(n,k)	binomial(n,n-k)			1	1
AlgEquiv	Pass	175!56!/(55!176!)	17556/55176			1	1
Unevaluated derviatives
AlgEquiv	Pass	3sdiff(q(s),s)	3sdiff(q(s),s)			1	1
Sums and products
AlgEquiv	Pass	sum(k^n,n,0,3)	sum(k^n,n,0,3)			1	1
AlgEquiv	Pass	1+k+k^2+k^3	sum(k^n,n,0,3)			1	1
AlgEquiv	Pass	1+k+k^2	sum(k^n,n,0,3)			0	0
AlgEquiv	Pass	n(n+1)(2*n+1)/6	sum(k^2,k,1,n)			1	1
AlgEquiv	Pass	sum((k+1)^2,k,0,n-1)	sum(k^2,k,1,n)			1	1
AlgEquiv	Pass	product(cos(k*x),k,1,3)	product(cos(k*x),k,1,3)			1	1
AlgEquiv	Pass	cos(x)cos(2x)cos(3x)	product(cos(k*x),k,1,3)			1	1
AlgEquiv	Pass	cos(x)cos(2x)	product(cos(k*x),k,1,3)			0	0
Scientific units are ignored
AlgEquiv	Pass	9.81*m/s^2	stackunits(9.81,m/s^2)			1	1
AlgEquiv	Pass	6*stackunits(1,m)	stackunits(6,m)			1	1
AlgEquiv	Pass	stackunits(2,m)^2	stackunits(4,m^2)			1	1
AlgEquiv	Pass	stackunits(2,s)^2	stackunits(4,m^2)			0	0
Maxima does not simplify -inf (I agree!)
AlgEquiv	Pass	-inf	minf			0	0
These currently fail
AlgEquiv	Pass	2/%iln(sqrt((1+z)/2)+%isqrt((1-z)/2))	-%iln(z+%isqrt(1-z^2))			0	-3
AlgEquiv	Pass	abs(x^2-4)/(abs(x-2)*abs(x+2))	1			0	-3
AlgEquiv	Pass	abs(x^2-4)	abs(x-2)*abs(x+2)			0	-3
AlgEquiv	Pass	(-1)^n*cos(x)^n	(-cos(x))^n			0	-3
AlgEquiv	Pass	(sqrt(108)+10)^(1/3)-(sqrt(108)-10)^(1/3)	2			0	-3
AlgEquiv	Pass	(sqrt(2+sqrt(2))+sqrt(2-sqrt(2)))/(2*sqrt(2))	sqrt(sqrt(2)+2)/2			0	-3
AlgEquiv	Pass	sqrt(2xsqrt(x^2+1)+2*x^2+1)-sqrt(x^2+1)-x	0			0	-3
AlgEquiv	Pass	(77+20sqrt(13))^(1/6)-(77-20sqrt(13))^(1/6)	1			0	-3
AlgEquiv	Pass	(930249+416020sqrt(5))^(1/30)-(930249-416020sqrt(5))^(1/30)	1			0	-3
AlgEquiv	Pass	cos(2*%pi/17)	(-1+sqrt(17)+sqrt(34-2sqrt(17)))/16+(2sqrt(17+3sqrt(17)-sqrt(34-2sqrt(17))-2sqrt(34+2sqrt(17))))/16			0	-3
AlgEquiv	Pass	(41-sqrt(511))/2	(sqrt((4(cos((1/2(acos((61/1040sqrt(130)))-atan(11/3)))))^(2))+21)-(2cos((1/2(acos((61/1040sqrt(130)))-atan(11 / 3))))))^(2)			0	-3
AlgEquiv	Pass	a*(1+sqrt(2))=b	a=b*(sqrt(2)-1)/3			0	-3		ATEquation_default
This is only equivalent for x>=0...
AlgEquiv	Pass	atan(1/2)	%pi/2-atan(2)			0	-3
This is true for all x...
AlgEquiv	Pass	asinh(x)	ln(x+sqrt(x^2+1))			0	-3
Logical expressions
AlgEquiv	Pass	true and false	false			1	1		ATLogic_True.
AlgEquiv	Pass	true or false	false			0	0
AlgEquiv	Pass	A and B	B and A			1	1		ATLogic_True.
AlgEquiv	Pass	A and B	C and A			0	0
AlgEquiv	Pass	A and B=C	C=B and A			1	1		ATLogic_True.
AlgEquiv	Pass	A and (B and C)	A and B and C			1	1		ATLogic_True.
AlgEquiv	Pass	A and (B or C)	A and (B or C)			1	1		ATLogic_True.
AlgEquiv	Pass	(A and B) or (A and C)	A and (B or C)			1	1		ATLogic_True.
AlgEquiv	Pass	-(b#pm#sqrt(b^2-4ac))	-b#pm#sqrt(b^2-4ac)			1	1		ATLogic_True.
AlgEquiv	Pass	x=-b#pm#c^2	x=c^2-b or x=-c^2-b			1	1		ATLogic_True.
AlgEquiv	Pass	x#pm#a = y#pm#b	x#pm#a = y#pm#b			1	1		ATEquation_sides
AlgEquiv	Pass	x#pm#a = y#pm#b	x#pm#a = y#pm#c			0	0		ATEquation_lhs_notrhs
AlgEquiv	Pass	not(A) and not(B)	not(A or B)			1	1		ATLogic_True.
AlgEquiv	Pass	not(A) and not(B)	not(A and B)			0	0
AlgEquiv	Pass	not(A) or B	boolean_form(A implies B)			1	1
AlgEquiv	Pass	not(A) or B	A implies B			1	1		ATLogic_True.
AlgEquiv	Pass	not(A) and B	A implies B			0	0
AlgEquiv	Pass	(not A and B) or (not B and A)	A xor B			1	1		ATLogic_True.
AlgEquiv	Pass	(A and B) or (not A and not B)	A xnor B			1	1		ATLogic_True.
AlgEquiv	Pass	{not(A) or B,A and B}	{A implies B,A and B}			0	0	The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \\[\\left \\{{\\rm not}\\left( A \\right)\\,{\\mbox{ or }}\\, B \\right \\}\\]	ATSet_wrongentries.
AlgEquiv	Pass	{A implies B,A and B}	{not(A) and B,A and B}			0	0	The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \\[\\left \\{A\\,{\\mbox{ implies }}\\, B \\right \\}\\]	ATSet_wrongentries.
Differential equations
AlgEquiv	Pass	diff(x^2,x)	2*x			1	1
AlgEquiv	Pass	diff(x^2,x)	'diff(x^2,x)			1	1
AlgEquiv	Pass	noundiff(x^2,x)	2*x			1	1
AlgEquiv	Pass	diff(y,x)	0			1	1
AlgEquiv	Pass	noundiff(y,x)	0			1	1
AlgEquiv	Pass	diff(y(x),x)	0			0	0
AlgEquiv	Pass	diff(y(x),x)	diff(y,x)			0	0
AlgEquiv	Pass	diff(y,x)	diff(y,x,2)			1	1
Basic support for strings
AlgEquiv	Pass	"Hello"	"Hello"			1	1		ATAlgEquiv_String
AlgEquiv	Pass	"hello"	"Hello"			0	0		ATAlgEquiv_String
AlgEquiv	Pass	W	"Hello"			0	0	Your answer should be a string, but is not.	ATAlgEquiv_SA_not_string.
AlgEquiv	Pass	"Hello"	x^2			0	0	Your answer should be an expression, not an equation, inequality, list, set or matrix.	ATAlgEquiv_SA_not_expression.

AlgEquivNouns	Expected failure	1/0	1		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATAlgEquivNouns_STACKERROR_SAns.
AlgEquivNouns	Expected failure	1	1/0		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATAlgEquivNouns_STACKERROR_TAns.
AlgEquivNouns	Expected failure		(x-1)^2		The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question.	0	-1	The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question.	ATAlgEquivNounsTEST_FAILED-Empty SA.
AlgEquivNouns	Expected failure	x^2			The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty teacher answer, probably a CAS validation problem when authoring the question.	0	-1	The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty teacher answer, probably a CAS validation problem when authoring the question.	ATAlgEquivNounsTEST_FAILED-Empty TA.
AlgEquivNouns	Expected failure	x-1)^2	(x-1)^2		The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question.	0	-1	The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question.	ATAlgEquivNounsTEST_FAILED-Empty SA.
AlgEquivNouns	Pass	diff(x^2,x)	2*x			1	1
AlgEquivNouns	Pass	diff(x^2,x)	'diff(x^2,x)			0	0
AlgEquivNouns	Pass	diff(x^2,x)	'diff(x^2,x)			0	0
AlgEquivNouns	Pass	'diff(y,x)	noundiff(y,x)			1	1
AlgEquivNouns	Pass	diff(y,x)	0			1	1
AlgEquivNouns	Pass	'diff(y,x)	0			0	0
AlgEquivNouns	Pass	noundiff(y,x)	0			0	0
AlgEquivNouns	Pass	diff(y(x),x)	0			0	0
AlgEquivNouns	Pass	'diff(y,x,1)	'diff(y,x,2)			0	0
AlgEquivNouns	Pass	'diff(y(x),x)	'diff(y,x)			0	0
AlgEquivNouns	Pass	subst(y,y(x),'diff(y,x)+y=1)	'diff(y,x)+y=1			1	1		ATEquation_sides
AlgEquivNouns	Pass	subst(y,y(x),'diff(y(x),x)+y(x)=1)	'diff(y,x)+y=1			1	1		ATEquation_sides
AlgEquivNouns	Pass	subst(y(x),y,'diff(y,x)+y=1)	'diff(y(x),x)+y(x)=1			1	1		ATEquation_sides
AlgEquivNouns	Pass	subst(y(x),y,'diff(y,x)+y=1)	'diff(y,x)+y=1			0	0		ATEquation_default
AlgEquivNouns	Expected failure	subst(y(x),y,'diff(y(x),x)+y(x)=1)	'diff(y,x)+y=1		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. subst: cannot substitute y(x) for operator y in expression y(x)	ATAlgEquivNouns_STACKERROR_SAns.
AlgEquivNouns	Pass	y_x	'diff(y,x)			0	0
Partials
AlgEquivNouns	Pass	noundiff(f,x,1,y,1)	noundiff(noundiff(f,x),y)			1	1
AlgEquivNouns	Pass	noundiff(noundiff(f,y),x)	noundiff(noundiff(f,x),y)			1	1
AlgEquivNouns	Pass	noundiff(noundiff(f,x),x)	noundiff(f,x,2)			1	1
Differential equations
AlgEquivNouns	Pass	noundiff(H,x,2) = -R/T	noundiff(H,x,2) + R/T = 0			1	1		ATEquation_ratio
AlgEquivNouns	Pass	'diff(H,x,2) = -R/T	noundiff(H,x,2) + R/T = 0			1	1		ATEquation_ratio
AlgEquivNouns	Pass	y(t)=int(s^2,s,0,t)	y(t)=t^3/3			1	1		ATEquation_sides
AlgEquivNouns	Pass	y(t)='int(s^2,s,0,t)	y(t)=t^3/3			0	0		ATEquation_lhs_notrhs
AlgEquivNouns	Pass	y(t)='int(s^2,s,0,t)	y(t)=nounint(s^2,s,0,t)			1	1		ATEquation_sides
Logic nouns are still evaluated
AlgEquivNouns	Pass	true nounand false	false			1	1		ATLogic_True.

SubstEquiv	Expected failure	1/0	x^2-2*x+1		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSubstEquiv_STACKERROR_SAns.
SubstEquiv	Expected failure	x^2	x^2-2*x+1	[1/0]	TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSubstEquiv_STACKERROR_Opt.
SubstEquiv	Expected failure	x^2	x^2-2*x+1	x		0	-1	The option to this answer test must be a list. This is an error. Please contact your teacher.	ATSubstEquiv_Opt_List.
SubstEquiv	Pass	x^2+1	x^2+1			1	1
SubstEquiv	Pass	x^2+1	x^3+1			0	0
SubstEquiv	Pass	x^2+1	x^3+1			0	0
SubstEquiv	Pass	X^2+1	x^2+1			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ X=x \\right] \\]	ATSubstEquiv_Subst [X = x].
SubstEquiv	Pass	x^2+y	a^2+b			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ x=a , y=b \\right] \\]	ATSubstEquiv_Subst [x = a,y = b].
SubstEquiv	Pass	x^2+y/z	a^2+c/b			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ x=a , y=c , z=b \\right] \\]	ATSubstEquiv_Subst [x = a,y = c,z = b].
SubstEquiv	Pass	y=x^2	a^2=b			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ x=a , y=b \\right] \\]	ATSubstEquiv_Subst [x = a,y = b].
SubstEquiv	Pass	{x=1,y=2}	{x=2,y=1}			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ x=y , y=x \\right] \\]	ATSubstEquiv_Subst [x = y,y = x].
Where a variable is also a function name.
SubstEquiv	Pass	cos(ax)/(x(ln(x)))	cos(ay)/(y(ln(y)))			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ a=a , x=y \\right] \\]	ATSubstEquiv_Subst [a = a,x = y].
SubstEquiv	Pass	cos(ax)/(x(ln(x)))	cos(xa)/(a(ln(a)))			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ a=x , x=a \\right] \\]	ATSubstEquiv_Subst [a = x,x = a].
SubstEquiv	Pass	cos(ax)/(x(ln(x)))	cos(a*x)/(x(ln(x)))			0	0
SubstEquiv	Pass	cos(ax)/(x(ln(x)))	cos(a*y)/(y(ln(y)))			0	0
SubstEquiv	Pass	x+1>y	y+1>x			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ x=y , y=x \\right] \\]	ATSubstEquiv_Subst [x = y,y = x].
SubstEquiv	Pass	x+1>y	x<y+1			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ x=y , y=x \\right] \\]	ATSubstEquiv_Subst [x = y,y = x].
Matrices
SubstEquiv	Pass	matrix([1,A^2+A+1],[2,0])	matrix([1,x^2+x+1],[2,0])			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ A=x \\right] \\]	ATSubstEquiv_Subst [A = x].
SubstEquiv	Pass	matrix([B,A^2+A+1],[2,C])	matrix([y,x^2+x+1],[2,z])			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ A=x , B=y , C=z \\right] \\]	ATSubstEquiv_Subst [A = x,B = y,C = z].
SubstEquiv	Pass	matrix([B,A^2+A+1],[2,C])	matrix([y,x^2+x+1],[2,x])			0	0	The entries underlined in red below are those that are incorrect. \\[ \\left[\\begin{array}{cc} {\\color{red}{\\underline{B}}} & {\\color{red}{\\underline{A^2+A+1}}} \\\\ 2 & {\\color{red}{\\underline{C}}} \\end{array}\\right]\\]	ATMatrix_wrongentries.
Lists
SubstEquiv	Pass	[x^2+1,x^2]	[A^2+1,A^2]			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ x=A \\right] \\]	ATSubstEquiv_Subst [x = A].
SubstEquiv	Pass	[x^2-1,x^2]	[A^2+1,A^2]			0	0	The entries underlined in red below are those that are incorrect. \\[\\left[ {\\color{red}{\\underline{x^2-1}}} , {\\color{red}{\\underline{x ^2}}} \\right] \\]	(ATList_wrongentries 1, 2).
SubstEquiv	Pass	[A,B,C]	[B,C,A]			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ A=B , B=C , C=A \\right] \\]	ATSubstEquiv_Subst [A = B,B = C,C = A].
SubstEquiv	Pass	[A,B,C]	[B,B,A]			0	0	The entries underlined in red below are those that are incorrect. \\[\\left[ {\\color{red}{\\underline{A}}} , B , {\\color{red}{\\underline{C }}} \\right] \\]	(ATList_wrongentries 1, 3).
SubstEquiv	Pass	[1,[A,B],C]	[1,[a,b],C]			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ A=a , B=b , C=C \\right] \\]	ATSubstEquiv_Subst [A = a,B = b,C = C].
Sets
SubstEquiv	Pass	{x^2+1,x^2}	{A^2+1,A^2}			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ x=A \\right] \\]	ATSubstEquiv_Subst [x = A].
SubstEquiv	Pass	{x^2-1,x^2}	{A^2+1,A^2}			0	0	The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \\[\\left \\{x^2-1 , x^2 \\right \\}\\]	ATSet_wrongentries.
SubstEquiv	Pass	{A+1,B^2,C}	{B,C+1,A^2}			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ A=C , B=A , C=B \\right] \\]	ATSubstEquiv_Subst [A = C,B = A,C = B].
SubstEquiv	Pass	{1,{A,B},C}	{1,{a,b},C}			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ A=a , B=b , C=C \\right] \\]	ATSubstEquiv_Subst [A = a,B = b,C = C].
SubstEquiv	Pass	Acos(t)+Bsin(t)	Pcos(t)+Qsin(t)			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ A=P , B=Q , t=t \\right] \\]	ATSubstEquiv_Subst [A = P,B = Q,t = t].
SubstEquiv	Pass	Acos(t)+Bsin(t)	Pcos(x)+Qsin(x)			1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ A=P , B=Q , t=x \\right] \\]	ATSubstEquiv_Subst [A = P,B = Q,t = x].
Fix some variables.
SubstEquiv	Pass	Acos(t)+Bsin(t)	Pcos(x)+Qsin(x)	[x]		0	0
SubstEquiv	Pass	Acos(t)+Bsin(t)	Pcos(x)+Qsin(x)	[t]		1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ A=P , B=Q , t=x \\right] \\]	ATSubstEquiv_Subst [A = P,B = Q,t = x].
SubstEquiv	Pass	Acos(t)e^x+Bsin(t)e^x+Csin(2x)+Dcos(2x)	Pcos(t)e^x+Qsin(t)e^x+Rsin(2x)+Scos(2x)	[x,t]		1	1	Your answer would be correct if you used the following substitution of variables. \\[\\left[ A=P , B=Q , C=R , D=S \\right] \\]	ATSubstEquiv_Subst [A = P,B = Q,C = R,D = S].

EqualComAss	Expected failure	1/0	0			0	-1		ATEqualComAss_STACKERROR_SAns.
EqualComAss	Expected failure	0	1/0			0	-1		ATEqualComAss_STACKERROR_TAns.
Numbers
EqualComAss	Pass	2/4	1/2			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	3^2	8			0	0		ATEqualComAss (AlgEquiv-false).
EqualComAss	Pass	3^2	9			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	cos(0)	1			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	4^(1/2)	2			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	1/3^(1/2)	(1/3)^(1/2)			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	sqrt(3)/3	(1/3)^(1/2)			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	sqrt(3)	3^(1/2)			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	2*sqrt(2)	sqrt(8)			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	2*2^(1/2)	sqrt(8)			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	sqrt(2)/4	1/sqrt(8)			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	1/sqrt(2)	2^(1/2)/2			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	4.0	4			0	0		ATEqualComAss (AlgEquiv-true).
Case sensitivity
EqualComAss	Pass	X	x			0	0		ATEqualComAss (AlgEquiv-false)ATAlgEquiv_WrongCase.
EqualComAss	Pass	exdowncase(X)	x			1	1
EqualComAss	Pass	exdowncase((X-1)^2)	x^2-2*x+1			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	exdowncase(X^2-2*X+1)	x^2-2*x+1			1	1
Powers
EqualComAss	Pass	a^2/b^3	a^2*b^(-3)			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	lg(a^x,a)	x			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	x^(2/4)	x^(1/2)			0	0		ATEqualComAss (AlgEquiv-true).
Simple polynomials
EqualComAss	Pass	1+2*x	x*2+1			1	1
EqualComAss	Pass	1+x	2*x+1			0	0		ATEqualComAss (AlgEquiv-false).
EqualComAss	Pass	1+x+x	2*x+1			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	(x+y)+z	z+x+y			1	1
EqualComAss	Pass	x*x	x^2			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	(x+5)*x	x*(5+x)			1	1
EqualComAss	Pass	x*(x+5)	5*x+x^2			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	(1-x)^2	(x-1)^2			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	(a-x)^6000	(x-a)^6000			0	0		ATEqualComAss (AlgEquiv-true).
Expressions with subscripts
EqualComAss	Pass	rhozV/(4piepsilon[0]*(R^2+z^2)^(3/2))	rhozV/(4piepsilon[0]*(R^2+z^2)^(3/2))			1	1
EqualComAss	Pass	rhozV/(4piepsilon[1]*(R^2+z^2)^(3/2))	rhozV/(4piepsilon[0]*(R^2+z^2)^(3/2))			0	0		ATEqualComAss (AlgEquiv-false).
Unary minus
EqualComAss	Pass	-1+2	2-1			1	1
EqualComAss	Pass	-12+34	34-12			1	1
EqualComAss	Pass	(-12)+34	10			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	-12+34	34-12			1	1
EqualComAss	Pass	x*(-y)	-x*y			1	1
EqualComAss	Pass	x*(-y)	-(x*y)			1	1
EqualComAss	Pass	(-x)*(-x)	x*x			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	(-x)*(-x)	x^2			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	-1/4%pii	-(%i*%pi)/4			0	0		ATEqualComAss (AlgEquiv-true).
Rational expressions
EqualComAss	Pass	1/2	3/6			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	1/(1+2*x)	1/(2*x+1)			1	1
EqualComAss	Pass	2/(4+2*x)	1/(x+2)			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	(a*b)/c	a*(b/c)			1	1
EqualComAss	Pass	((x+1)/(x(x-1)))(x-1)	((x+1)(x-1))/(x(x-1))			1	1
EqualComAss	Pass	(-x)/y	-(x/y)			1	1
EqualComAss	Pass	x/(-y)	-(x/y)			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	-1/(1-x)	1/(x-1)			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	1/2*1/x	1/(2*x)			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	(k+8)/(k^2+4*k-12)	(k+8)/(k^2+4*k-12)			1	1
EqualComAss	Pass	(k+8)/(k^2+4*k-12)	(k+8)/((k-2)*(k+6))			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	(k+7)/(k^2+4*k-12)	(k+8)/(k^2+4*k-12)			0	0		ATEqualComAss (AlgEquiv-false).
EqualComAss	Pass	-(2k+6)/(k^2+4k-12)	-(2k+6)/(k^2+4k-12)			1	1
EqualComAss	Pass	(a+b)/1	(b+a)/1			1	1
No simplicifcation here
EqualComAss	Pass	1*x	x			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	23+0*x	23			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	x+0	x			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	x^1	x			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	(1/2)*(a+b)	(a+b)/2			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	1/3*logbase(27,6)	logbase(27,6)/3			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	1/3*lg(27,6)	lg(27,6)/3			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	lg(root(x, n))	lg(x, 10)/n			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	exp(x)	%e^x			1	1
EqualComAss	Pass	exp(x)^2	%e^(2*x)			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	exp(x)^2	(%e^(x))^2			1	1
EqualComAss	Pass	1/3*i	i/3			0	0		ATEqualComAss (AlgEquiv-true).
Complex numbers
EqualComAss	Pass	%i	e^(i*pi/2)			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	(4sqrt(3)%i+4)^(1/5)	rectform((4sqrt(3)%i+4)^(1/5))			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	(4sqrt(3)%i+4)^(1/5)	8^(1/5)(cos(%pi/15)+%isin(%pi/15))			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	(4sqrt(3)%i+4)^(1/5)	polarform((4sqrt(3)%i+4)^(1/5))			0	0		ATEqualComAss (AlgEquiv-true).
Equations
EqualComAss	Pass	y=x	x=y			1	1
EqualComAss	Pass	x+1	y=2*x+1			0	0	Your answer should be an equation, but is not.	ATEqualComAss ATAlgEquiv_SA_not_equation.
EqualComAss	Pass	y=1+2*x	y=2*x+1			1	1
EqualComAss	Pass	y=x+x+1	y=1+2*x			0	0		ATEqualComAss (AlgEquiv-true).
Logic
EqualComAss	Pass	A and B	B and A			1	1
EqualComAss	Pass	A or B	B or A			1	1
EqualComAss	Pass	A or B	B and A			0	0		ATEqualComAss (AlgEquiv-false).
EqualComAss	Pass	not(true)	false			0	0		ATEqualComAss (AlgEquiv-true).
Sets
EqualComAss	Pass	{2*x+1,2}	{2, 1+x*2}			1	1
EqualComAss	Pass	2	{2}			0	0	Your answer should be a set, but is not. Note that the syntax to enter a set is to enclose the comma separated values with curly brackets.	ATEqualComAss ATAlgEquiv_SA_not_set.
EqualComAss	Pass	{2*x+1, 1+1}	{2, 1+x*2}			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	{1,2}	{1,{2}}			0	0		ATEqualComAss (AlgEquiv-false)ATSet_wrongentries.
EqualComAss	Pass	{4,3}	{3,4}			1	1
EqualComAss	Pass	{4,4}	{4}			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	{-1,1,-1}	{-1,-1,1}			1	1
EqualComAss	Pass	{-1,1,-1}	{-1,1}			0	0		ATEqualComAss (AlgEquiv-true).
Lists
EqualComAss	Pass	[2*x+1,2]	[1+x*2,2]			1	1
EqualComAss	Pass	[x+x+1, 1+1]	[1+x*2,2]			0	0		ATEqualComAss (AlgEquiv-true).
Matrices
EqualComAss	Pass	matrix([1,2],[2,3])	matrix([1,2],[2,3])			1	1
EqualComAss	Pass	matrix([1,2],[2,3])	matrix([1,2,3],[2,3,3])			0	0		ATEqualComAss (AlgEquiv-false)ATMatrix_wrongsz_columns.
EqualComAss	Pass	matrix([1,2],[2,3])	matrix([1,2],[2,5])			0	0		ATEqualComAss (AlgEquiv-false)ATMatrix_wrongentries.
EqualComAss	Pass	matrix([1,2],[2,2+1])	matrix([1,2],[2,3])			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	matrix([x+x, 1],[1, 1])	matrix([2*x, 1],[1, 1])			0	0		ATEqualComAss (AlgEquiv-true).
Sums and products
EqualComAss	Pass	sum(k^n,n,0,3)	sum(k^n,n,0,3)			1	1
EqualComAss	Pass	1+k+k^2+k^3	sum(k^n,n,0,3)			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	sum(k,k,0,1+n)	sum(k,k,0,n+1)			1	1
EqualComAss	Pass	(n+1)*(n+2)/2	sum(k,k,0,n+1)			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	product(cos(k*x),k,1,3)	product(cos(k*x),k,1,3)			1	1
EqualComAss	Pass	cos(x)cos(2x)cos(3x)	product(cos(k*x),k,1,3)			0	0		ATEqualComAss (AlgEquiv-true).
Inequalities are not commutative under this test
EqualComAss	Pass	-6/5 > x	x < -6/5			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	x<1 and -3<x	-3<x and x<1			1	1
EqualComAss	Pass	1>x and -3<x	-3<x and x<1			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	make_less_ineq(-6/5 > x)	x < -6/5			1	1
EqualComAss	Pass	make_less_ineq(1>x and -3<x)	-3<x and x<1			1	1
EqualComAss	Pass	make_less_ineq(6/3 > x)	x < 2			0	0		ATEqualComAss (AlgEquiv-true).
Unary Equations
EqualComAss	Pass	1	stackeq(1)			1	1
EqualComAss	Pass	stackeq(1)	1			1	1
EqualComAss	Pass	stackeq(1+1)	2			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	stackeq(1)	0			0	0		ATEqualComAss (AlgEquiv-false).
EqualComAss	Pass	lowesttermsp(1/3)	true			1	1
EqualComAss	Pass	lowesttermsp(2/6)	true			0	0		ATEqualComAss (AlgEquiv-false).
EqualComAss	Pass	lowesttermsp(x^2/x)	true			0	0		ATEqualComAss (AlgEquiv-false).
EqualComAss	Pass	lowesttermsp(-y/-x)	true			0	0		ATEqualComAss (AlgEquiv-false).
EqualComAss	Pass	lowesttermsp((x^2-1)/(x-1))	true			0	0		ATEqualComAss (AlgEquiv-false).
EqualComAss	Pass	lowesttermsp((x^2-1)/(x+2))	true			1	1
Bad things in denominators
EqualComAss	Pass	rationalized(1+sqrt(3)/3)	true			1	1
EqualComAss	Pass	rationalized(1+1/sqrt(3))	[sqrt(3)]			1	1
EqualComAss	Pass	rationalized(1/sqrt(3))	[sqrt(3)]			1	1
EqualComAss	Pass	rationalized(1/sqrt(2)+i/sqrt(2))	[sqrt(2),sqrt(2)]			1	1
EqualComAss	Pass	rationalized(sqrt(2)/2+1/sqrt(3))	[sqrt(3)]			1	1
EqualComAss	Pass	rationalized(1/sqrt(2)+1/sqrt(3))	[sqrt(2),sqrt(3)]			1	1
EqualComAss	Pass	rationalized(1/(1+i))	[i]			1	1
EqualComAss	Pass	rationalized(1/(1+1/root(3,2)))	[root(3,2)]			1	1
Differential Equations
EqualComAss	Pass	diff(y,x)	0			1	1
EqualComAss	Pass	diff(x^2,x)	2*x			1	1
EqualComAss	Pass	noundiff(x^2,x)	2*x			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	diff(y,x)	'diff(y,x)			0	0		ATEqualComAss (AlgEquiv-true).
EqualComAss	Pass	noundiff(y,x)	'diff(y,x)			1	1
EqualComAss	Pass	'diff(y(x),x)	'diff(y(x),x,1)			1	1
EqualComAss	Pass	noundiff(y(x),x)=-x/4	4*noundiff(y(x),x)+x=0			0	0		ATEqualComAss (AlgEquiv-true).

EqualComAssRules	Expected failure	1/0	0	[]		0	-1		ATEqualComAssRules_STACKERROR_SAns.
EqualComAssRules	Expected failure	0	1/0	[]		0	-1		ATEqualComAssRules_STACKERROR_TAns.
EqualComAssRules	Expected failure	0+a	a		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test.	STACKERROR_OPTION.
EqualComAssRules	Expected failure	0+a	a	x		0	-1	The option to this answer test must be a non-empty list of supported rules. This is an error. Please contact your teacher.	ATEqualComAssRules_Opt_List.
EqualComAssRules	Expected failure	0+a	a	[x]		0	-1	The option to this answer test must be a non-empty list of supported rules. This is an error. Please contact your teacher.	ATEqualComAssRules_Opt_Wrong.
EqualComAssRules	Expected failure	0+a	a	[intMul,intFac]		0	-1	The option to this answer test contains incompatible rules. This is an error. Please contact your teacher.	ATEqualComAssRules_Opt_Incompatible.
Basic cases
EqualComAssRules	Pass	1+1	3	[zeroAdd]		0	0		ATEqualComAssRules (AlgEquiv-false).
EqualComAssRules	Pass	1+1	2	[zeroAdd]		0	0
EqualComAssRules	Pass	1+1	2	[testdebug,zeroAdd]		0	0		ATEqualComAssRules: [1 nounadd 1,2].
EqualComAssRules	Pass	0+a	a	[zeroAdd]		1	1
EqualComAssRules	Pass	a+0	a	[zeroAdd]		1	1
EqualComAssRules	Pass	1*a	a	[testdebug,zeroAdd]		0	0		ATEqualComAssRules: [1 nounmul a,a].
EqualComAssRules	Pass	1*a	a	[oneMul]		1	1
EqualComAssRules	Pass	1*a	a	ID_TRANS		1	1
EqualComAssRules	Pass	a/1	a	ID_TRANS		1	1
EqualComAssRules	Pass	0*a	0	ID_TRANS		1	1
EqualComAssRules	Pass	0-1*i	-i	ID_TRANS		1	1
EqualComAssRules	Pass	0-i	-i	ID_TRANS		1	1
EqualComAssRules	Pass	2+1*i	2+i	ID_TRANS		1	1
EqualComAssRules	Pass	x^0+x^1/1+x^2/2+x^3/3!+x^4/4!	1+x+x^2/2+x^3/3!+x^4/4!	ID_TRANS		1	1
EqualComAssRules	Pass	%e^x	exp(x)	[testdebug,ID_TRANS]		1	1		ATEqualComAssRules: [%e nounpow x,%e nounpow x].
EqualComAssRules	Pass	12%e^((2(%pi/2)*%i)/2)	12exp(%i(%pi/2))	ID_TRANS		0	0
EqualComAssRules	Pass	12%e^((2(%pi/2)*%i)/2)	12exp(%i(%pi/2))	[ID_TRANS,[negNeg,negDiv,negOrd],[recipMul,divDiv,divCancel],[intAdd,intMul,intPow]]		1	1
EqualComAssRules	Pass	0^(1-1)	0	ID_TRANS		0	0		ATEqualComAssRules_STACKERROR_SAns.
EqualComAssRules	Pass	0*a	0	delete(zeroMul, ID_TRANS)		0	0
EqualComAssRules	Pass	-(-a)	a	[negNeg]		1	1
EqualComAssRules	Pass	-(-(-a))	-a	[negNeg]		1	1
EqualComAssRules	Pass	-(-(-a))	a	[testdebug,negNeg]		0	0		ATEqualComAssRules (AlgEquiv-false).
EqualComAssRules	Pass	3/(-x)	-3/x	ID_TRANS		0	0
EqualComAssRules	Pass	3/(-x)	-3/x	[testdebug,ID_TRANS]		0	0		ATEqualComAssRules: [3 nounmul UNARY_RECIP UNARY_MINUS nounmul x,UNARY_MINUS nounmul 3 nounmul UNARY_RECIP x].
EqualComAssRules	Pass	-x*(x+1)	x*(-x-1)	[negDist]		1	1
EqualComAssRules	Pass	-x*(x-1)	x*(1-x)	NEG_TRANS		1	1
EqualComAssRules	Pass	-x*(x-1)	x*(1-x)	NEG_TRANS		1	1
EqualComAssRules	Pass	-5x(3-x)	5x(x-3)	NEG_TRANS		1	1
EqualComAssRules	Pass	-x(x-1)(x+1)	x(x-1)(-x-1)	NEG_TRANS		1	1
EqualComAssRules	Pass	-x(x-1)(x+1)	x(1-x)(x+1)	NEG_TRANS		1	1
EqualComAssRules	Pass	-x(y-1)(x-1)	x(1-x)(y-1)	NEG_TRANS		1	1
EqualComAssRules	Pass	-x(y-1)(x-1)	x(x-1)(1-y)	NEG_TRANS		1	1
EqualComAssRules	Pass	(x-y)*(y-x)	-(x-y)*(x-y)	NEG_TRANS		1	1
EqualComAssRules	Pass	(x-y)*(y-x)	-(x-y)^2	[testdebug,NEG_TRANS]		0	0		ATEqualComAssRules: [UNARY_MINUS nounmul (x nounadd UNARY_MINUS nounmul y) nounmul (x nounadd UNARY_MINUS nounmul y),UNARY_MINUS nounmul (x nounadd UNARY_MINUS nounmul y) nounpow 2].
EqualComAssRules	Pass	-x(x-1)(x+1)	x(1-x)(x+1)	[testdebug,negDist,negNeg]		0	0		ATEqualComAssRules: [x nounmul (UNARY_MINUS nounmul 1 nounadd UNARY_MINUS nounmul x) nounmul (x nounadd UNARY_MINUS nounmul 1),x nounmul (1 nounadd UNARY_MINUS nounmul x) nounmul (1 nounadd x)].
EqualComAssRules	Pass	-x(y-1)(x-1)	x(x-1)(1-y)	[testdebug,negDist,negNeg]		0	0		ATEqualComAssRules: [x nounmul (1 nounadd UNARY_MINUS nounmul x) nounmul (y nounadd UNARY_MINUS nounmul 1),x nounmul (1 nounadd UNARY_MINUS nounmul y) nounmul (x nounadd UNARY_MINUS nounmul 1)].
EqualComAssRules	Pass	3/(-x)	-3/x	[negDiv]		1	1
EqualComAssRules	Pass	3/(-x)	ev(-3,simp)/x	[negDiv]		1	1
EqualComAssRules	Pass	(-a)/(-x)	-(-a/x)	[testdebug,ID_TRANS]		0	0		ATEqualComAssRules: [UNARY_MINUS nounmul a nounmul UNARY_RECIP UNARY_MINUS nounmul x,UNARY_MINUS nounmul UNARY_MINUS nounmul a nounmul UNARY_RECIP x].
EqualComAssRules	Pass	(-a)/(-x)	-(-a/x)	[negDiv]		1	1
EqualComAssRules	Pass	(-a)/(-x)	a/x	[testdebug,negDiv]		0	0		ATEqualComAssRules: [UNARY_MINUS nounmul UNARY_MINUS nounmul a nounmul UNARY_RECIP x,a nounmul UNARY_RECIP x].
EqualComAssRules	Pass	(-a)/(-x)	a/x	[negDiv,negNeg]		1	1
EqualComAssRules	Pass	1/(-x)	(-1)/x	[negDiv]		1	1
EqualComAssRules	Pass	1/(-x)	ev(-1,simp)/x	[negDiv]		1	1
EqualComAssRules	Pass	(2/-3)*(x-y)	-(2/3)*(x-y)	[negDiv]		1	1
EqualComAssRules	Pass	(2/-3)*(x-y)	(2/3)*(y-x)	[negDiv]		0	0
EqualComAssRules	Pass	(2/-3)*(x-y)	(2/3)*(y-x)	[negDiv,negOrd]		1	1
EqualComAssRules	Pass	-2/(1-x)	2/(x-1)	[testdebug,negDiv]		0	0		ATEqualComAssRules: [UNARY_MINUS nounmul 2 nounmul UNARY_RECIP (1 nounadd UNARY_MINUS nounmul x),2 nounmul UNARY_RECIP (x nounadd UNARY_MINUS nounmul 1)].
EqualComAssRules	Pass	1/2*3/x	3/(2*x)	[testdebug,ID_TRANS]		0	0		ATEqualComAssRules: [3 nounmul (UNARY_RECIP 2) nounmul UNARY_RECIP x,3 nounmul UNARY_RECIP 2 nounmul x].
EqualComAssRules	Pass	1/2*3/x	3/(2*x)	[ID_TRANS,recipMul]		1	1
EqualComAssRules	Pass	5/2*3/x	15/(2*x)	[testdebug,ID_TRANS,recipMul]		0	0		ATEqualComAssRules: [3 nounmul 5 nounmul UNARY_RECIP 2 nounmul x,15 nounmul UNARY_RECIP 2 nounmul x].
EqualComAssRules	Pass	-(x-y)	y-x	[negOrd]		1	1
EqualComAssRules	Pass	5/2*3/x	15/(2*x)	[ID_TRANS,recipMul,intMul]		1	1
EqualComAssRules	Pass	(3+2)*x+x	5*x+x	[ID_TRANS,intAdd]		1	1
EqualComAssRules	Pass	(3-5)*x+x	-2*x+x	[ID_TRANS,intAdd]		1	1
EqualComAssRules	Pass	7x(-3*x)	-21xx	[ID_TRANS,intMul]		1	1
EqualComAssRules	Pass	(-7x)(-3*x)	21xx	[testdebug,ID_TRANS,intMul]		0	0		ATEqualComAssRules: [UNARY_MINUS nounmul UNARY_MINUS nounmul 21 nounmul x nounmul x,21 nounmul x nounmul x].
EqualComAssRules	Pass	(-7x)(-3*x)	21xx	[ID_TRANS,intMul,negNeg]		1	1
ev(a/b/c, simp)=a/(b*c)
EqualComAssRules	Pass	a/b/c	a/(b*c)	[testdebug,ID_TRANS]		0	0		ATEqualComAssRules: [a nounmul (UNARY_RECIP b) nounmul UNARY_RECIP c,a nounmul UNARY_RECIP b nounmul c].
EqualComAssRules	Pass	a/b/c	a/(b*c)	[ID_TRANS,recipMul]		1	1
EqualComAssRules	Pass	(a/b)/c	a/(b*c)	[ID_TRANS,recipMul]		1	1
ev(a/(b/c), simp)=(a*c)/b
EqualComAssRules	Pass	a/(b/c)	(a*c)/b	[testdebug,ID_TRANS]		0	0		ATEqualComAssRules: [a nounmul UNARY_RECIP b nounmul UNARY_RECIP c,a nounmul c nounmul UNARY_RECIP b].
EqualComAssRules	Pass	a/(b/c)	(a*c)/b	[testdebug,ID_TRANS,recipMul]		0	0		ATEqualComAssRules: [a nounmul UNARY_RECIP b nounmul UNARY_RECIP c,a nounmul c nounmul UNARY_RECIP b].
EqualComAssRules	Pass	a/(b/c)	(a*c)/b	[ID_TRANS,divDiv]		1	1
EqualComAssRules	Pass	Aa/(Bb/c)	A(ac)/(B*b)	[ID_TRANS,divDiv]		1	1
EqualComAssRules	Pass	Aa/(Bb/c)*1/d	A(ac)/(Bb)1/d	[ID_TRANS,divDiv]		1	1
EqualComAssRules	Pass	DAa/(Bb/c)1/d	A(ac)/(Bb)D/d	[ID_TRANS,divDiv]		1	1
EqualComAssRules	Pass	Aa/(Bb/c)*1/d	A(ac)/(Bbd)	[testdebug,ID_TRANS,divDiv]		0	0		ATEqualComAssRules: [A nounmul a nounmul c nounmul (UNARY_RECIP B nounmul b) nounmul UNARY_RECIP d,A nounmul a nounmul c nounmul UNARY_RECIP B nounmul b nounmul d].
EqualComAssRules	Pass	Aa/(Bb/c)*1/d	A(ac)/(Bbd)	[ID_TRANS,divDiv,recipMul]		1	1
EqualComAssRules	Pass	A/(B/(C/D))	AC/(BD)	[testdebug,ID_TRANS,divDiv]		0	0		ATEqualComAssRules: [A nounmul C nounmul (UNARY_RECIP B) nounmul UNARY_RECIP D,A nounmul C nounmul UNARY_RECIP B nounmul D].
EqualComAssRules	Pass	A/(B/(C/D))	AC/(BD)	[ID_TRANS,divDiv,recipMul]		1	1
EqualComAssRules	Pass	18	2*3^2	[intFac]		1	1
EqualComAssRules	Pass	0+%i*(-(1/27))	-(%i/27)	[[zeroAdd,zeroMul,oneMul,onePow,idPow,zeroPow,zPow,oneDiv],[negNeg,negDiv,negOrd],[recipMul,divDiv,divCancel],[intAdd,intMul,intPow]]		1	1

CasEqual	Expected failure	1/0	x^2-2*x+1			0	-1		ATCASEqual_STACKERROR_SAns.
CasEqual	Expected failure	x	1/0			0	-1		ATCASEqual_STACKERROR_TAns.
CasEqual	Pass	0.5	1/2	x		0	0		ATCASEqual (AlgEquiv-true).
CasEqual	Pass	x=1	1			0	0	You have entered an equation, but an equation is not expected here. You may have typed something like "y=2x+1" when you only needed to type "2x+1".	ATCASEqual ATAlgEquiv_TA_not_equation.
Case sensitivity
CasEqual	Pass	a	A			0	0		ATCASEqual_false.
CasEqual	Pass	exdowncase(X^2-2*X+1)	x^2-2*x+1			1	1		ATCASEqual_true.
Numbers
CasEqual	Pass	4^(-1/2)	1/2			0	0		ATCASEqual (AlgEquiv-true).
CasEqual	Pass	ev(4^(-1/2),simp)	ev(1/2,simp)			1	1		ATCASEqual_true.
CasEqual	Pass	2^2	4			0	0		ATCASEqual (AlgEquiv-true).
Powers
CasEqual	Pass	a^2/b^3	a^2*b^(-3)			0	0		ATCASEqual (AlgEquiv-true).
Expressions with subscripts
CasEqual	Pass	rhozV/(4piepsilon[0]*(R^2+z^2)^(3/2))	rhozV/(4piepsilon[0]*(R^2+z^2)^(3/2))			1	1		ATCASEqual_true.
CasEqual	Pass	rhozV/(4piepsilon[1]*(R^2+z^2)^(3/2))	rhozV/(4piepsilon[0]*(R^2+z^2)^(3/2))			0	0		ATCASEqual_false.
Mix of floats and rational numbers
CasEqual	Pass	0.5	1/2			0	0		ATCASEqual (AlgEquiv-true).
CasEqual	Pass	x^(1/2)	sqrt(x)			0	0		ATCASEqual (AlgEquiv-true).
CasEqual	Pass	ev(x^(1/2),simp)	ev(sqrt(x),simp)			1	1		ATCASEqual_true.
CasEqual	Pass	abs(x)	sqrt(x^2)			0	0		ATCASEqual (AlgEquiv-true).
CasEqual	Pass	ev(abs(x),simp)	ev(sqrt(x^2),simp)			1	1		ATCASEqual_true.
CasEqual	Pass	x-1	(x^2-1)/(x+1)			0	0		ATCASEqual (AlgEquiv-true).
Polynomials and rational function
CasEqual	Pass	x+x	2*x			0	0		ATCASEqual (AlgEquiv-true).
CasEqual	Pass	ev(x+x,simp)	ev(2*x,simp)			1	1		ATCASEqual_true.
CasEqual	Pass	x+x^2	x^2+x			0	0		ATCASEqual (AlgEquiv-true).
CasEqual	Pass	ev(x+x^2,simp)	ev(x^2+x,simp)			1	1		ATCASEqual_true.
CasEqual	Pass	(x-1)^2	x^2-2*x+1			0	0		ATCASEqual (AlgEquiv-true).
CasEqual	Pass	(x-1)^(-2)	1/(x^2-2*x+1)			0	0		ATCASEqual (AlgEquiv-true).
CasEqual	Pass	1/n-1/(n+1)	1/(n*(n+1))			0	0		ATCASEqual (AlgEquiv-true).
Trig functions
CasEqual	Pass	cos(x)	cos(-x)			0	0		ATCASEqual (AlgEquiv-true).
CasEqual	Pass	ev(cos(x),simp)	ev(cos(-x),simp)			1	1		ATCASEqual_true.
CasEqual	Pass	cos(x)^2+sin(x)^2	1			0	0		ATCASEqual (AlgEquiv-true).
CasEqual	Pass	2*cos(x)^2-1	cos(2*x)			0	0		ATCASEqual (AlgEquiv-true).
Predicate function wrapper
CasEqual	Pass	imag_numberp(2*%i)	true			1	1		ATCASEqual_true.
CasEqual	Pass	imag_numberp(%e^(%i*%pi/2))	true			1	1		ATCASEqual_true.
CasEqual	Pass	imag_numberp(2)	false			1	1		ATCASEqual_true.
CasEqual	Pass	imag_numberp(%e^(%pi/2))	false			1	1		ATCASEqual_true.
CasEqual	Pass	complex_exponentialp(3%e^(%i%pi/6))	true			1	1		ATCASEqual_true.
CasEqual	Pass	complex_exponentialp(3)	true			1	1		ATCASEqual_true.
CasEqual	Pass	complex_exponentialp(%e^(%i*%pi/6))	true			1	1		ATCASEqual_true.
CasEqual	Pass	complex_exponentialp(%e^%i)	true			1	1		ATCASEqual_true.
CasEqual	Pass	complex_exponentialp(%e^(%pi/6))	true			1	1		ATCASEqual_true.
CasEqual	Pass	complex_exponentialp(3+%i)	false			1	1		ATCASEqual_true.
CasEqual	Pass	complex_exponentialp(%e^(%i)/4)	true			1	1		ATCASEqual_true.
CasEqual	Pass	complex_exponentialp(3exp(%i%pi/6))	true			1	1		ATCASEqual_true.
CasEqual	Pass	integerp(-1)	true			0	0		ATCASEqual_false.
CasEqual	Pass	integerp(ev(-1,simp))	true			1	1		ATCASEqual_true.

SameType	Expected failure	1/0	1		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSameType_STACKERROR_SAns.
SameType	Expected failure	1	1/0		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSameType_STACKERROR_TAns.
Numbers
SameType	Pass	4^(-1/2)	1/2			1	1
Lists
SameType	Pass	x	[1,2,3]			0	0
SameType	Pass	[1,2]	[1,2,3]			1	1
SameType	Pass	[1,x>2]	[1,2<x]			1	1
SameType	Pass	[1,x,3]	[1,2<x,4]			0	0
Sets
SameType	Pass	x	{1,2,3}			0	0
SameType	Pass	{1,2}	{1,2,3}			1	1
Matrices
SameType	Pass	matrix([1,2],[2,3])	matrix([1,2],[2,3])			1	1
SameType	Pass	[[1,2],[2,3]]	matrix([1,2],[2,3])			0	0
SameType	Pass	matrix([1,2],[2,3])	matrix([1,2,3],[2,3,3])			1	1
SameType	Pass	matrix([x>4,{1,x^2}],[[1,2],[1,3]])	matrix([4-x<0,{x^2, 1}],[[1,2],[1,3]])			1	1
SameType	Pass	matrix([x>4,[1,x^2]],[[1,2],[1,3]])	matrix([4-x<0,{x^2, 1}],[[1,2],[1,4]])			0	0
Equations
SameType	Pass	1	x=1			0	0
SameType	Pass	x=1	x=1			1	1
Inequalities
SameType	Pass	1	x>1			0	0
SameType	Pass	x>2	x>1			1	1
SameType	Pass	x>1	x>=1			1	1
SameType	Pass	x>1 and x<3	x>=1			1	1
SameType	Pass	{x>1,x<3}	x>=1			0	0
SameType	Pass	sqrt(2)sqrt(3)+2(sqrt(2/3))x-(2/3)(sqrt(2/3))x^2+(4/9)(sqrt(2/3))*x^3	4sqrt(6)x^3/27-(2sqrt(6)x^2)/9+(2sqrt(6)x)/3+sqrt(6)			1	1

Basic tests
SysEquiv	Expected failure	1/0	[(x-1)*(x+1)=0]		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSysEquiv_STACKERROR_SAns.
SysEquiv	Expected failure	[(x-1)*(x+1)=0]	1/0		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSysEquiv_STACKERROR_TAns.
SysEquiv	Pass	1	[(x-1)*(x+1)=0]			0	0	Your answer should be a list, but it is not!	ATSysEquiv_SA_not_list.
SysEquiv	Pass	[(x-1)*(x+1)=0]	1			0	0	The teacher's answer is not a list. Please contact your teacher.	ATSysEquiv_SB_not_list.
SysEquiv	Pass	[1]	[90=vt,90=(v+5)(t-1/4)]			0	0	Your answer should be a list of equations, but it is not!	ATSysEquiv_SA_not_eq_list.
SysEquiv	Pass	[(x-1)*(x+1)=0]	[1]			0	0	The teacher's answer is not a list of equations, but should be.	ATSysEquiv_SB_not_eq_list.
SysEquiv	Pass	[x^2]	[(x-1)*(x+1)=0]			0	0	Your answer should be a list of equations, but it is not!	ATSysEquiv_SA_not_eq_list.
SysEquiv	Pass	[90=vt^t,90=(v+5)(t-1/4)]	[90=vt,90=(v+5)(t-1/4)]			0	0	One or more of your equations is not a polynomial!	ATSysEquiv_SA_not_poly_eq_list.
SysEquiv	Pass	[90=vt,90=(v+5)(t-1/4)]	[90=vt^t,90=(v+5)(t-1/4)]			0	0	The Teacher's answer should be a list of polynomial equations, but is not. Please contact your teacher.	ATSysEquiv_SB_not_poly_eq_list.
Tests of equivalence
SysEquiv	Pass	[x^2=1]	[(x-1)*(x+1)=0]			1	1
SysEquiv	Pass	[x^2+y^2=4,y=x]	[y=x,y^2=2]			1	1
SysEquiv	Pass	[x^2+y^2=2,y=x]	[y=x,y^2=2]			0	0	The entries underlined in red below are those that are incorrect. \\[\\left[ {\\color{red}{\\underline{y^2+x^2=2}}} , y=x \\right] \\]	ATSysEquiv_SA_system_overdetermined.
SysEquiv	Pass	[x=1]	[(x-1)(x+1)=0,(x-1)(x-3)=0]			1	1		ATSysEquiv_SA_Completely_solved.
SysEquiv	Pass	[3a+b-c=2, a-b+2c=5,b+c=5]	[a=1,b=2,c=3]			1	1
SysEquiv	Pass	[a=1,b=2,c=3]	[3a+b-c=2, a-b+2c=5,b+c=5]			1	1		ATSysEquiv_SA_Completely_solved.
SysEquiv	Pass	[x^2=1]	[(x-1)(x+1)(x-2)=0]			0	0	The entries underlined in red below are those that are incorrect. \\[\\left[ {\\color{red}{\\underline{x^2=1}}} \\right] \\]	ATSysEquiv_SA_system_overdetermined.
SysEquiv	Pass	[x=1,y=-1]	[(x-1)*(y+1)=0]			0	0		ATSysEquiv_SA_Not_completely_solved.
SysEquiv	Pass	[x=1]	[(x-1)*(x+1)=0]			0	0		ATSysEquiv_SA_Not_completely_solved.
SysEquiv	Pass	[x=1]	[(x-1)(x+1)y=0]			0	0		ATSysEquiv_SA_Not_completely_solved.
SysEquiv	Pass	[90=vt,90=(v+5)(t-1/4)]	[90=vt,90=(v+5)(t-1/4)]			1	1
SysEquiv	Pass	[90=vt,90=(v+5)(t*x-1/4)]	[90=vt,90=(v+5)(t-1/4)]			0	0	Your answer includes too many variables!	ATSysEquiv_SA_extra_variables.
SysEquiv	Pass	[90=vt,90=(v+5)(t-1/4)]	[90=vt,90=(v+5)(t*x-1/4)]			0	0	Your answer is missing one or more variables!	ATSysEquiv_SA_missing_variables.
SysEquiv	Pass	[90=v*t]	[90=vt,90=(v+5)(t-1/4)]			0	0	The equations in your system appear to be correct, but you need others besides.	ATSysEquiv_SA_system_underdetermined.
SysEquiv	Pass	[90=vt,90=(v+5)(t-1/4),90=(v+6)*(t-1/5)]	[90=vt,90=(v+5)(t-1/4)]			0	0	The entries underlined in red below are those that are incorrect. \\[\\left[ 90=t\\cdot v , 90=\\left(t-\\frac{1}{4}\\right)\\cdot \\left(v+5 \\right) , {\\color{red}{\\underline{90=\\left(t-\\frac{1}{5}\\right) \\cdot \\left(v+6\\right)}}} \\right] \\]	ATSysEquiv_SA_system_overdetermined.
SysEquiv	Pass	[90=vt,90=(v+5)(t-1/4),90=(v+6)(t-1/5),90=(v+7)(t-1/4),90=(v+8)*(t-1/3)]	[90=vt,90=(v+5)(t-1/4)]			0	0	The entries underlined in red below are those that are incorrect. \\[\\left[ 90=t\\cdot v , 90=\\left(t-\\frac{1}{4}\\right)\\cdot \\left(v+5 \\right) , {\\color{red}{\\underline{90=\\left(t-\\frac{1}{5}\\right) \\cdot \\left(v+6\\right)}}} , {\\color{red}{\\underline{90=\\left(t- \\frac{1}{4}\\right)\\cdot \\left(v+7\\right)}}} , {\\color{red} {\\underline{90=\\left(t-\\frac{1}{3}\\right)\\cdot \\left(v+8\\right)}}} \\right] \\]	ATSysEquiv_SA_system_overdetermined.
Wrong variables
SysEquiv	Pass	[b^2=a,a=9]	[x^2=y,y=9]			0	0	Your answer uses the wrong variables!	ATSysEquiv_SA_wrong_variables.
SysEquiv	Pass	[x^2=4]	[x^2=4,y=9]			0	0	Your answer is missing one or more variables!	ATSysEquiv_SA_missing_variables.
SysEquiv	Pass	[d=90,d=vt,d=(v+5)(t-1/4)]	[90=vt,90=(v+5)(t-1/4)]			0	0	Your answer includes too many variables!	ATSysEquiv_SA_extra_variables.
SysEquiv	Pass	stack_eval_assignments([d=90,d=vt,d=(v+5)(t-1/4)])	[90=vt,90=(v+5)(t-1/4)]			1	1

Sets	Expected failure	{1/0}	{0}		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSets_STACKERROR_SAns.
Sets	Expected failure	{0}	{1/0}		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSets_STACKERROR_TAns.
Sets	Pass	x	{1,2,3}			0	0	Your answer should be a set, but is not. Note that the syntax to enter a set is to enclose the comma separated values with curly brackets.	ATSets_SA_not_set.
Sets	Pass	{1,2}	x			0	0	The "Sets" answer test expects its second argument to be a set. This is an error. Please contact your teacher.	ATSets_SB_not_set.
Sets	Pass	{1,2}	{1,2,3}			0	0	The following are missing from your set. \\[\\left \\{3 \\right \\}\\]	ATSets_missingentries.
Sets	Pass	{1,2,4}	{1,2}			0	0	These entries should not be elements of your set. \\[\\left \\{4 \\right \\}\\]	ATSets_wrongentries.
Sets	Pass	{1,2,2+2}	{1,2}			0	0	These entries should not be elements of your set. \\[\\left \\{4 \\right \\}\\]	ATSets_wrongentries.
Sets	Pass	{5,1,2,4}	{1,2,3}			0	0	These entries should not be elements of your set. \\[\\left \\{4 , 5 \\right \\}\\] The following are missing from your set. \\[\\left \\{3 \\right \\}\\]	ATSets_wrongentries. ATSets_missingentries.
Sets	Pass	{2/4, 1/3}	{1/2, 1/3}			1	1
Duplicate entries
Sets	Pass	{1,2,1}	{1,2}			1	1	Your set appears to contain duplicate entries!	ATSets_duplicates.
Sets	Pass	{1,2,1+1}	{1,2}			1	1	Your set appears to contain duplicate entries!	ATSets_duplicates.
Sets	Pass	{1,2,1+1}	{1,2,3}			0	0	Your set appears to contain duplicate entries! The following are missing from your set. \\[\\left \\{3 \\right \\}\\]	ATSets_duplicates. ATSets_missingentries.
Sets	Pass	{(x-a)^6000}	{(a-x)^6000}			0	0	These entries should not be elements of your set. \\[\\left \\{{\\left(x-a\\right)}^{6000} \\right \\}\\] The following are missing from your set. \\[\\left \\{{\\left(a-x\\right)}^{6000} \\right \\}\\]	ATSets_wrongentries. ATSets_missingentries.

Expanded	Expected failure	1/0	0		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATExpanded_STACKERROR_SAns.
Expanded	Pass	x>2	x^2-2*x+1			0	0	Your answer should be an expression, not an equation, inequality, list, set or matrix.	ATExpanded_SA_not_expression.
Expanded	Pass	x^2-1	0			1	1		ATExpanded_TRUE.
Expanded	Pass	2*(x-1)	0			0	0		ATExpanded_FALSE.
Expanded	Pass	(x-1)*(x+1)	0			0	0		ATExpanded_FALSE.
Expanded	Pass	(x-a)*(x-b)	0			0	0		ATExpanded_FALSE.
Expanded	Pass	x^2-(a+b)x+ab	0			0	0		ATExpanded_FALSE.
Expanded	Pass	x^2-ax-bx+a*b	0			1	1		ATExpanded_TRUE.
Expanded	Pass	cos(2*x)	0			1	1		ATExpanded_TRUE.
Expanded	Pass	p+1	0			1	1		ATExpanded_TRUE.
Expanded	Pass	(p+1)*(p-1)	0			0	0		ATExpanded_FALSE.
Expanded	Pass	3+2*sqrt(3)	0			1	1		ATExpanded_TRUE.
Expanded	Pass	3+sqrt(12)	0			1	1		ATExpanded_TRUE.
Expanded	Pass	(1+sqrt(5))*(1-sqrt(3))	0			0	0		ATExpanded_FALSE.
This fails, but you are never going to ask students to do this anyway...
Expanded	Expected failure (maths)	(a-x)^6000	0			1	-2		ATExpanded_TRUE.

FacForm	Expected failure	1/0	0	x		0	-1		ATFacForm_STACKERROR_SAns.
FacForm	Expected failure	0	1/0	x		0	-1		ATFacForm_STACKERROR_TAns.
FacForm	Expected failure	0	0	1/0		0	-1		ATFacForm_STACKERROR_Opt.
Trivial cases
FacForm	Pass	2	2	x		1	1		ATFacForm_int_true.
FacForm	Pass	6	6	x		1	1		ATFacForm_int_true.
FacForm	Pass	1/3	1/3	x		1	1		ATFacForm_true.
FacForm	Pass	3*x^2	3*x^2	x		1	1		ATFacForm_true.
FacForm	Pass	4*x^2	4*x^2	x		1	1		ATFacForm_true.
Linear integer factors
FacForm	Pass	2*(x-1)	2*x-2	x		1	1		ATFacForm_true.
FacForm	Pass	2*x-2	2*x-2	x		0	0	Your answer is not factored. You need to take out a common factor.	ATFacForm_notfactored.
FacForm	Pass	2*(x+1)	2*x-2	x		0	0	Your answer is factored, well done. Note that your answer is not algebraically equivalent to the correct answer. You must have done something wrong.	ATFacForm_isfactored. ATFacForm_notalgequiv.
FacForm	Pass	2*x+2	2*x-2	x		0	0	Your answer is not factored. You need to take out a common factor. Note that your answer is not algebraically equivalent to the correct answer. You must have done something wrong.	ATFacForm_notfactored. ATFacForm_notalgequiv.
FacForm	Pass	2*(x+0.5)	2*x+1	x		1	1		ATFacForm_default_true.
Linear factors
FacForm	Pass	t(2x+1)	t(2x+1)	x		1	1		ATFacForm_true.
FacForm	Pass	t*x+t	t*(x+1)	x		0	0	Your answer is not factored.	ATFacForm_notfactored.
Quadratic, with no const
FacForm	Pass	2x(x-3)	2x^2-6x	x		1	1		ATFacForm_true.
FacForm	Pass	2(x^2-3x)	2x(x-3)	x		0	0	Your answer is not factored. You could still do some more work on the term \$x^2-3\\cdot x\$.	ATFacForm_notfactored.
FacForm	Pass	x(2x-6)	2x(x-3)	x		0	0	Your answer is not factored. You could still do some more work on the term \$2\\cdot x-6\$. You need to take out a common factor.	ATFacForm_notfactored.
Quadratic
FacForm	Pass	(x+2)*(x+3)	(x+2)*(x+3)	x		1	1		ATFacForm_true.
FacForm	Pass	(x+2)(2x+6)	2(x+2)(x+3)	x		0	0	Your answer is not factored. You could still do some more work on the term \$2\\cdot x+6\$. You need to take out a common factor.	ATFacForm_notfactored.
FacForm	Pass	(zx+z)(2*x+6)	2z(x+1)*(x+3)	x		0	0	Your answer is not factored. You could still do some more work on the term \$z\\cdot x+z\$. You could still do some more work on the term \$2\\cdot x+6\$. You need to take out a common factor.	ATFacForm_notfactored.
FacForm	Pass	(x+t)*(x-t)	x^2-t^2	x		1	1		ATFacForm_true.
FacForm	Pass	t^2-1	(t-1)*(t+1)	t		0	0	Your answer is not factored.	ATFacForm_notfactored.
FacForm	Pass	t^2+1	t^2+1	t		1	1		ATFacForm_true.
FacForm	Pass	v^2+1	v^2+1	v		1	1		ATFacForm_true.
FacForm	Pass	v^2-1	v^2-1	v		0	0	Your answer is not factored.	ATFacForm_notfactored.
FacForm	Pass	-(3w-4v+9u)(3w+4v-u)	-(3w-4v+9u)(3w+4v-u)	v		1	1		ATFacForm_true.
FacForm	Pass	-6k(4*b-k-1)	6k(1+k-4*b)	k		1	1		ATFacForm_default_true.
FacForm	Pass	-23k(4b-k-1)	6k(1+k-4*b)	k		1	1		ATFacForm_true.
FacForm	Pass	-(6k(4*b-k-1))	6k(1+k-4*b)	k		1	1		ATFacForm_default_true.
FacForm	Pass	-(6a(4*b-a-1))	6a(1+a-4*b)	a		1	1		ATFacForm_true.
FacForm	Pass	-(6a(4*b-a-1))	6a(-(4*b)+a+1)	a		1	1		ATFacForm_true.
FacForm	Pass	x*(x-4+4/x)	x^2-4*x+4	x		0	0	Your answer is not factored. You could still do some more work on the term \$x-4+\\frac{4}{x}\$. This term is expected to be a polynomial, but is not.	ATFacForm_notfactored.
These are delicate cases!
FacForm	Pass	(2-x)*(3-x)	(x-2)*(x-3)	x		1	1		ATFacForm_true.
FacForm	Pass	(1-x)^2	(x-1)^2	x		1	1		ATFacForm_true.
FacForm	Pass	(1-x)*(1-x)	(x-1)^2	x		1	1		ATFacForm_true.
FacForm	Pass	-(1-x)^2	-(x-1)^2	x		1	1		ATFacForm_true.
FacForm	Pass	(1-x)^2	(x-1)^2	x		1	1		ATFacForm_true.
FacForm	Pass	4*(1-x/2)^2	(x-2)^2	x		1	1		ATFacForm_default_true.
FacForm	Pass	-3(x-4)(x+1)	-3x^2+9x+12	x		1	1		ATFacForm_true.
FacForm	Pass	3(-x+4)(x+1)	-3x^2+9x+12	x		1	1		ATFacForm_true.
FacForm	Pass	3(4-x)(x+1)	-3x^2+9x+12	x		1	1		ATFacForm_true.
Cubics
FacForm	Pass	(x-1)*(x^2+x+1)	x^3-1	x		1	1		ATFacForm_true.
FacForm	Pass	x^3-x+1	x^3-x+1	x		1	1		ATFacForm_true.
FacForm	Pass	7x^3-7x+7	7*(x^3-x+1)	x		0	0	Your answer is not factored. You need to take out a common factor.	ATFacForm_notfactored.
FacForm	Pass	(1-x)(2-x)(3-x)	-x^3+6x^2-11x+6	x		1	1		ATFacForm_true.
FacForm	Pass	(2-x)(2-x)(3-x)	-x^3+7x^2-16x+12	x		1	1		ATFacForm_true.
FacForm	Pass	(2-x)^2*(3-x)	-x^3+7x^2-16x+12	x		1	1		ATFacForm_true.
FacForm	Pass	(x^2-4x+4)(3-x)	-x^3+7x^2-16x+12	x		0	0	Your answer is not factored. You could still do some more work on the term \$x^2-4\\cdot x+4\$.	ATFacForm_notfactored.
FacForm	Pass	(x^2-3x+2)(3-x)	-x^3+6x^2-11x+6	x		0	0	Your answer is not factored. You could still do some more work on the term \$x^2-3\\cdot x+2\$.	ATFacForm_notfactored.
FacForm	Pass	3y^3-6y^2-24*y	3(y-4)y*(y+2)	y		0	0	Your answer is not factored. You need to take out a common factor.	ATFacForm_notfactored.
FacForm	Pass	3(y^3-2y^2-8*y)	3(y-4)y*(y+2)	y		0	0	Your answer is not factored. You could still do some more work on the term \$y^3-2\\cdot y^2-8\\cdot y\$.	ATFacForm_notfactored.
FacForm	Pass	3y(y^2-2*y-8)	3(y-4)y*(y+2)	y		0	0	Your answer is not factored. You could still do some more work on the term \$y^2-2\\cdot y-8\$.	ATFacForm_notfactored.
FacForm	Pass	3(y^2-4y)*(y+2)	3(y-4)y*(y+2)	y		0	0	Your answer is not factored. You could still do some more work on the term \$y^2-4\\cdot y\$.	ATFacForm_notfactored.
FacForm	Pass	(y-4)y(3*y+6)	3(y-4)y*(y+2)	y		0	0	Your answer is not factored. You could still do some more work on the term \$3\\cdot y+6\$. You need to take out a common factor.	ATFacForm_notfactored.
FacForm	Pass	(a-x)^6000	(a-x)^6000	x		1	1		ATFacForm_true.
FacForm	Pass	(x-a)^6000	(a-x)^6000	x		1	1		ATFacForm_true.
Needs flattening
FacForm	Pass	2a(a*b-1)	2a(a*b-1)	a		1	1		ATFacForm_true.
FacForm	Pass	(2a)(a*b-1)	2a(a*b-1)	a		1	1		ATFacForm_true.
FacForm	Pass	3x(7y-3)(7*y+3)	3x(7y-3)(7*y+3)	x		1	1		ATFacForm_true.
FacForm	Pass	3x(7y-3)(7*y+3)	3x(7y-3)(7*y+3)	y		1	1		ATFacForm_true.
Not polynomials in a variable
FacForm	Pass	(sin(x)+1)*(sin(x)-1)	sin(x)^2-1	sin(x)		1	1		ATFacForm_true.
FacForm	Pass	(cos(t)-sqrt(2))^2	cos(t)^2-2sqrt(2)cos(t)+2	cos(t)		1	1		ATFacForm_true.
FacForm	Pass	7	7	x		1	1		ATFacForm_int_true.
Factors over other fields
FacForm	Pass	24*(x-1/4)	24*x-6	x		1	1		ATFacForm_default_true.
FacForm	Pass	(x-sqrt(2))*(x+sqrt(2))	x^2-2	x		1	1		ATFacForm_true.
FacForm	Pass	x^2-2	x^2-2	x		1	1		ATFacForm_true.
FacForm	Pass	(%ix-2%i)	%i*(x-2)	x		0	0	Your answer is not factored.	ATFacForm_notfactored.
FacForm	Pass	%i*(x-2)	(%ix-2%i)	x		1	1		ATFacForm_true.
FacForm	Pass	(x-%i)*(x+%i)	x^2+1	x		1	1		ATFacForm_true.
FacForm	Pass	(x-1)(x+(1+sqrt(3)%i)/2)(x+(1-sqrt(3)%i)/2)	x^3-1	x		1	1		ATFacForm_default_true.

CompSquare	Expected failure	1/0	0		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test.	STACKERROR_OPTION.
CompSquare	Expected failure	1/0	0	x	TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATCompSquare_STACKERROR_SAns.
CompSquare	Expected failure	0	1/0	x	TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATCompSquare_STACKERROR_TAns.
CompSquare	Expected failure	0	0	1/0	TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATCompSquare_STACKERROR_Opt.
Category errors.
CompSquare	Pass	1	(x-1)^2+1	x		0	0	Your answer should depend on the variable \$x\$ but it does not!	ATCompSquare_SA_not_depend_var.
CompSquare	Pass	(t-1)^2+1	(x-1)^2+1	x		0	0	Your answer should depend on the variable \$x\$ but it does not!	ATCompSquare_SA_not_depend_var.
CompSquare	Pass	(x-1)^2+1=0	(x-1)^2+1	x		0	0	Your answer should be an expression, not an equation, inequality, list, set or matrix.	ATCompSquare_STACKERROR_LIST.
CompSquare	Pass	sin(x-1)+a-1	(x-1)^2+1	x		0	0		ATCompSquare_false_not_AlgEquiv.
Trivial cases
CompSquare	Pass	1	1	x		1	1		ATCompSquare_true_trivial.
CompSquare	Pass	x-a	x-a	x		1	1		ATCompSquare_true_trivial.
CompSquare	Pass	x^2	x^2	x		1	1		ATCompSquare_true.
CompSquare	Pass	x^2-1	(x-1)*(x+1)	x		1	1		ATCompSquare_true.
CompSquare	Pass	(x-1)^2*k	(x-1)^2*k	x		1	1		ATCompSquare_true.
CompSquare	Pass	(x-1)^2/k	(x-1)^2/k	x		1	1		ATCompSquare_true.
Normal cases
CompSquare	Pass	(x-1)^2+1	(x-1)^2+1	x		1	1		ATCompSquare_true.
CompSquare	Pass	(1-x)^2+1	(x-1)^2+1	x		1	1		ATCompSquare_true.
CompSquare	Pass	(X-1)^2+1	(x-1)^2+1	x		0	0	Your answer should depend on the variable \$x\$ but it does not!	ATCompSquare_SA_not_depend_var.
CompSquare	Pass	9*(x-1)^2+1	(3*x-3)^2+1	x		1	1		ATCompSquare_true.
CompSquare	Pass	-(x-1)^2	-(x-1)^2	x		1	1		ATCompSquare_true.
CompSquare	Pass	-(1-x)^2	-(x-1)^2	x		1	1		ATCompSquare_true.
CompSquare	Pass	-(x-1)^2+3	-(x-1)^2+3	x		1	1		ATCompSquare_true.
CompSquare	Pass	-(1-x)^2+3	-(x-1)^2+3	x		1	1		ATCompSquare_true.
CompSquare	Pass	-4*(x-1)^2+3	-4*(x-1)^2+3	x		1	1		ATCompSquare_true.
CompSquare	Pass	-4*(x-1)^2+3	-(2*x-2)^2+3	x		1	1		ATCompSquare_true.
CompSquare	Pass	3-4*(x-1)^2	-(2*x-2)^2+3	x		1	1		ATCompSquare_true.
CompSquare	Pass	(x-1)^2+1	(x+1)^2+1	x		0	0	Your answer appears to be in the correct form, but is not equivalent to the correct answer.	ATCompSquare_true_not_AlgEquiv.
CompSquare	Pass	(x-a^2)^2+1+b	(x-a^2)^2+1+b	x		1	1		ATCompSquare_true.
CompSquare	Pass	x^2-2*x+2	(x-1)^2+1	x		0	0	The completed square is of the form \$ a(\\cdots\\cdots)^2 + b\$ where \$a\$ and \$b\$ do not depend on your variable. More than one of your summands appears to depend on the variable in your answer.	ATCompSquare_false_no_summands.
CompSquare	Pass	x+1	(x-1)^2+1	x		0	0		ATCompSquare_false_not_AlgEquiv.
CompSquare	Pass	a*(x-1)^2+1	a*(x-1)^2+1	x		1	1		ATCompSquare_true.
CompSquare	Pass	-a*(x-1)^2+1	1-a*(x-1)^2	x		1	1		ATCompSquare_true.
Not simple variable
CompSquare	Pass	(sin(x)-1)^2+1	(sin(x)-1)^2+1	sin(x)		1	1		ATCompSquare_true.
CompSquare	Pass	(x^2-1)^2+1	(x^2-1)^2+1	x^2		1	1		ATCompSquare_true.
CompSquare	Pass	(y-1)^2+1	(y-1)^2+1	y		1	1		ATCompSquare_true.
CompSquare	Pass	(y+1)^2+1	(y-1)^2+1	y		0	0	Your answer appears to be in the correct form, but is not equivalent to the correct answer.	ATCompSquare_true_not_AlgEquiv.
CompSquare	Pass	(x-1)^2+1	(sin(x)-1)^2+1	sin(x)		0	0	Your answer should depend on the variable \${\\it facdum}\$ but it does not!	ATCompSquare_SA_not_depend_var.

PropLogic	Expected failure	1/0	0		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATPropLogic_STACKERROR_SAns.
PropLogic	Expected failure	0	1/0		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATPropLogic_STACKERROR_TAns.
PropLogic	Pass	true	true			1	1
PropLogic	Pass	true	false			0	0
PropLogic	Pass	A implies B	not(A) or B			1	1
PropLogic	Pass	(a and b and c) xor (a and b) xor (a and c) xor a xor true	(a implies b) or c			1	1

Equiv	Expected failure	x	[x^2=4,x=2 or x=-2]			0	-1	The first argument to the Equiv answer test should be a list, but the test failed. Please contact your teacher.	ATEquiv_SA_not_list.
Equiv	Expected failure	[x^2=4,x=2 or x=-2]	x			0	-1	The second argument to the Equiv answer test should be a list, but the test failed. Please contact your teacher.	ATEquiv_SB_not_list.
Equiv	Expected failure	[1/0]	[x^2=4,x=2 or x=-2]			0	-1		ATEquiv_STACKERROR_SAns.
Equiv	Expected failure	[x^2=4,x=2 or x=-2]	[1/0]			0	-1		ATEquiv_STACKERROR_TAns.
Equiv	Pass	[x^2=4,x=2 or x=-2]	[x^2=4,x=2 or x=-2]			1	1	\\[\\begin{array}{lll} &x^2=4& \\cr \\color{green}{\\Leftrightarrow}&x=2\\,{\\mbox{ or }}\\, x=-2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[x^2=4,x=#pm#2,x=2 and x=-2]	[x^2=4,x=2 or x=-2]			0	0	\\[\\begin{array}{lll} &x^2=4& \\cr \\color{green}{\\Leftrightarrow}&x= \\pm 2& \\cr \\color{red}{\\mbox{and/or confusion!}}&\\left\\{\\begin{array}{l}x=2\\cr x=-2\\cr \\end{array}\\right.& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR,ANDOR]
Equiv	Pass	[x^2=4,x=2]	[x^2=4,x=2 or x=-2]			0	0	\\[\\begin{array}{lll} &x^2=4& \\cr \\color{red}{\\Leftarrow}&x=2& \\cr \\end{array}\\]	[EMPTYCHAR,IMPLIEDCHAR]
Equiv	Pass	[x^2=4,x=2]	[x^2=4,x=2]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&x^2=4& \\cr \\color{green}{\\Leftrightarrow}&x=2& \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR]
Equiv	Pass	[x^2=4,x^2-4=0,(x-2)*(x+2)=0,x=2 or x=-2]	[x^2=4,x=2 or x=-2]			1	1	\\[\\begin{array}{lll} &x^2=4& \\cr \\color{green}{\\Leftrightarrow}&x^2-4=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(x-2\\right)\\cdot \\left(x+2\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&x=2\\,{\\mbox{ or }}\\, x=-2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x^2=4,x= #pm#2, x=2 or x=-2]	[x^2=4,x=2 or x=-2]			1	1	\\[\\begin{array}{lll} &x^2=4& \\cr \\color{green}{\\Leftrightarrow}&x= \\pm 2& \\cr \\color{green}{\\Leftrightarrow}&x=2\\,{\\mbox{ or }}\\, x=-2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x^2-6*x+9=0,x=3]	[x^2-6*x+9=0,x=3]			1	1	\\[\\begin{array}{lll} &x^2-6\\cdot x+9=0& \\cr \\color{green}{\\mbox{(Same roots)}}&x=3& \\cr \\end{array}\\]	[EMPTYCHAR,SAMEROOTS]

EquivFirst	Expected failure	x	[x^2=4,x=2 or x=-2]			0	-1	The first argument to the Equiv answer test should be a list, but the test failed. Please contact your teacher.	ATEquivFirst_SA_not_list.
EquivFirst	Expected failure	[x^2=4,x=2 or x=-2]	x			0	-1	The second argument to the Equiv answer test should be a list, but the test failed. Please contact your teacher.	ATEquivFirst_SB_not_list.
EquivFirst	Expected failure	[1/0]	[x^2=4,x=2 or x=-2]			0	-1		ATEquivFirst_STACKERROR_SAns.
EquivFirst	Expected failure	[x^2=4,x=2 or x=-2]	[1/0]			0	-1		ATEquivFirst_STACKERROR_TAns.
EquivFirst	Pass	[x^2=4,x=2 or x=-2]	[x^2=4,x=2 or x=-2]			1	1	\\[\\begin{array}{lll} &x^2=4& \\cr \\color{green}{\\Leftrightarrow}&x=2\\,{\\mbox{ or }}\\, x=-2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
EquivFirst	Pass	[x^2=9,x=3 or x=-3]	[x^2=4,x=2 or x=-2]			0	0	The first line in your argument must be "\$x^2=4\$".	ATEquivFirst_SA_wrong_start
EquivFirst	Pass	[x^2=4,x=2]	[x^2=4,x=2 or x=-2]			0	0	\\[\\begin{array}{lll} &x^2=4& \\cr \\color{red}{\\Leftarrow}&x=2& \\cr \\end{array}\\]	[EMPTYCHAR,IMPLIEDCHAR]
EquivFirst	Pass	[x^2=4,x^2-4=0,(x-2)*(x+2)=0,x=2 or x=-2]	[x^2=4,x=2 or x=-2]			1	1	\\[\\begin{array}{lll} &x^2=4& \\cr \\color{green}{\\Leftrightarrow}&x^2-4=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(x-2\\right)\\cdot \\left(x+2\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&x=2\\,{\\mbox{ or }}\\, x=-2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
EquivFirst	Pass	[x^2=4,x= #pm#2, x=2 or x=-2]	[x^2=4,x=2 or x=-2]			1	1	\\[\\begin{array}{lll} &x^2=4& \\cr \\color{green}{\\Leftrightarrow}&x= \\pm 2& \\cr \\color{green}{\\Leftrightarrow}&x=2\\,{\\mbox{ or }}\\, x=-2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR]
EquivFirst	Pass	[x^2-6*x+9=0,x=3]	[x^2-6*x+9=0,x=3]			1	1	\\[\\begin{array}{lll} &x^2-6\\cdot x+9=0& \\cr \\color{green}{\\mbox{(Same roots)}}&x=3& \\cr \\end{array}\\]	[EMPTYCHAR,SAMEROOTS]

SingleFrac	Expected failure	1/0	1/n			0	-1		ATSingleFrac_STACKERROR_SAns.
SingleFrac	Expected failure	0	1/0			0	-1		ATSingleFrac_STACKERROR_TAns.
SingleFrac	Pass	x=3	2			0	0	Your answer should be an expression, not an equation, inequality, list, set or matrix.	ATSingleFrac_SA_not_expression.
SingleFrac	Pass	3	3			1	1
SingleFrac	Pass	3	2			0	0	Your answer is not algebraically equivalent to the correct answer. You must have done something wrong.	ATSingleFrac_ret_exp.
SingleFrac	Pass	1/m	1/n			0	0	Your answer is not algebraically equivalent to the correct answer. You must have done something wrong.	ATSingleFrac_true. ATSingleFrac_ret_exp.
SingleFrac	Pass	1/n	1/n			1	1		ATSingleFrac_true.
SingleFrac	Pass	a+1/2	(2*a+1)/2			0	0	Your answer needs to be a single fraction of the form \$ {a}\\over{b} \$.	ATSingleFrac_part.
SingleFrac	Pass	a+1/2	(2*a+1)/2			0	0	Your answer needs to be a single fraction of the form \$ {a}\\over{b} \$.	ATSingleFrac_part.
SingleFrac	Pass	4/(x^2+2x-24)+2/(x^2+4x-12)	(6x-16)/(x^3-28x+48)			0	0	Your answer needs to be a single fraction of the form \$ {a}\\over{b} \$.	ATSingleFrac_part.
2 subtly different answers for the same question
SingleFrac	Pass	2*(1/n)	2/n			0	0	Your answer needs to be a single fraction of the form \$ {a}\\over{b} \$.	ATSingleFrac_part.
SingleFrac	Pass	2/n	2/n			1	1		ATSingleFrac_true.
Simple Mistakes
SingleFrac	Pass	2/(n+1)	1/(n+1)			0	0	Your answer is not algebraically equivalent to the correct answer. You must have done something wrong.	ATSingleFrac_true. ATSingleFrac_ret_exp.
SingleFrac	Pass	(2*n+1)/(n+2)	1/n			0	0	Your answer is not algebraically equivalent to the correct answer. You must have done something wrong.	ATSingleFrac_true. ATSingleFrac_ret_exp.
SingleFrac	Pass	(2n)/(n(n+2))	(2n)/(n(n+3))			0	0	Your answer is not algebraically equivalent to the correct answer. You must have done something wrong.	ATSingleFrac_true. ATSingleFrac_ret_exp.
SingleFrac	Pass	(x-1)/(x^2-1)	1/(x+1)			1	1		ATSingleFrac_true.
Fractions within fractions
SingleFrac	Pass	(1/2)/(3/4)	2/3			0	0	Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction.	ATSingleFrac_div.
SingleFrac	Pass	(x-2)/4/(2/x^2)	(x-2)*x^2/8			0	0	Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction.	ATSingleFrac_div.
SingleFrac	Pass	1/(1-1/x)	x/(x-1)			0	0	Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction.	ATSingleFrac_div.
SingleFrac	Pass	(1+1/a)/a	(1+a)/a^2			0	0	Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction.	ATSingleFrac_div.
SingleFrac	Pass	a/(1+1/a)	a^2/(1+a)			0	0	Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction.	ATSingleFrac_div.
SingleFrac	Pass	(1+2*b/a)/c	(a+2b)/(ac)			0	0	Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction.	ATSingleFrac_div.
SingleFrac	Pass	c/(1+2*b/a)	ac/(a+2b)			0	0	Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction.	ATSingleFrac_div.
SingleFrac	Pass	ac/(a+2b)	ac/(a+2b)			1	1		ATSingleFrac_true.
Negative cases
SingleFrac	Pass	-1/2	-1/2			1	1		ATSingleFrac_true.
SingleFrac	Pass	-1/2	-1/3			0	0	Your answer is not algebraically equivalent to the correct answer. You must have done something wrong.	ATSingleFrac_true. ATSingleFrac_ret_exp.
SingleFrac	Pass	-(1/2)	-1/2			1	1		ATSingleFrac_true.
SingleFrac	Pass	-a/b	-a/b			1	1		ATSingleFrac_true.
SingleFrac	Pass	(-a)/b	-a/b			1	1		ATSingleFrac_true.
SingleFrac	Pass	a/(-b)	-a/b			1	1		ATSingleFrac_true.
SingleFrac	Pass	-(a/b)	-a/b			1	1		ATSingleFrac_true.
SingleFrac	Pass	-(1/(n-1))	1/(1-n)			1	1		ATSingleFrac_true.
SingleFrac	Pass	a/(-1-1/a)	-a^2/(1+a)			0	0	Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction.	ATSingleFrac_div.
Surds in answers
SingleFrac	Pass	((sqrt(5))^3 +6)/15	((sqrt(5))^3 +6)/15			1	1		ATSingleFrac_true.
SingleFrac	Pass	1/(1-sqrt(2))	1/(1-sqrt(2))			1	1		ATSingleFrac_true.
SingleFrac	Pass	((sqrt(5))^3+6)/15	((sqrt(5))^3+6)/15			1	1		ATSingleFrac_true.
SingleFrac	Pass	(5^(3/2)+6)/15	((sqrt(5))^3+6)/15			1	1		ATSingleFrac_true.

PartFrac	Expected failure	1/0	3*x^2		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test.	STACKERROR_OPTION.
PartFrac	Expected failure	1/0	3*x^2	x	TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATPartFrac_STACKERROR_SAns.
PartFrac	Expected failure	0	0	1/0	TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATPartFrac_STACKERROR_Opt.
PartFrac	Expected failure	0	1/0	x	TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATPartFrac_STACKERROR_TAns.
PartFrac	Pass	1/n=0	1/n	n		0	0	Your answer should be an expression, not an equation, inequality, list, set or matrix.	ATPartFrac_SA_not_expression.
PartFrac	Pass	1/n	{1/n}	n		0	0	The answer test failed. Please contact your systems administrator	ATPartFrac_TA_not_expression.
Basic tests
PartFrac	Pass	1/m	1/n	n		0	0	The variables in your answer are different to those of the question, please check them.	ATPartFrac_diff_variables.
PartFrac	Pass	2/(x+1)-1/(x+2)	s/((s+1)*(s+2))	s		0	0	The variables in your answer are different to those of the question, please check them.	ATPartFrac_diff_variables.
PartFrac	Pass	1/n	1/n	n		1	1		ATPartFrac_true.
PartFrac	Pass	1+n+n^2+1/(n-1)	n^3/(n-1)	n		1	1		ATPartFrac_true.
PartFrac	Pass	1+n+n^2-1/(1-n)	n^3/(n-1)	n		1	1		ATPartFrac_true.
Distinct linear factors in denominator
PartFrac	Pass	1/(n+1)-1/n	1/(n+1)-1/n	n		1	1		ATPartFrac_true.
PartFrac	Pass	1/(n+1)+1/(1-n)	1/(n+1)-1/(n-1)	n		1	1		ATPartFrac_true.
PartFrac	Pass	1/(2(n-1))-1/(2(n+1))	1/((n-1)*(n+1))	n		1	1		ATPartFrac_true.
PartFrac	Pass	1/(2(n+1))-1/(2(n-1))	1/((n-1)*(n+1))	n		0	0	Your answer as a single fraction is \$-\\frac{1}{\\left(n-1\\right)\\cdot \\left(n+1\\right)}\$	ATPartFrac_ret_expression.
PartFrac	Pass	-9/(x-2) + -9/(x+1)	-9/(x-2) + -9/(x+1)	x		1	1		ATPartFrac_true.
Addition and Subtraction errors
PartFrac	Pass	1/(x+1) + 1/(x+2)	2/(x+1) + 1/(x+2)	x		0	0	Your answer as a single fraction is \$\\frac{2\\cdot x+3}{\\left(x+1\\right)\\cdot \\left(x+2\\right)}\$	ATPartFrac_ret_expression.
PartFrac	Pass	1/(x+1) + 1/(x+2)	1/(x+1) + 2/(x+2)	x		0	0	Your answer as a single fraction is \$\\frac{2\\cdot x+3}{\\left(x+1\\right)\\cdot \\left(x+2\\right)}\$	ATPartFrac_ret_expression.
Denominator Error
PartFrac	Pass	1/(x+1) + 1/(x+2)	1/(x+3) + 1/(x+2)	x		0	0	Your answer as a single fraction is \$\\frac{2\\cdot x+3}{\\left(x+1\\right)\\cdot \\left(x+2\\right)}\$	ATPartFrac_ret_expression.
Repeated linear factors in denominator
PartFrac	Pass	(9*y-8)/(y-4)^2	(9*y-8)/(y-4)^2	y		0	0		ATPartFrac_false_factor.
PartFrac	Pass	9/(y-4)+28/(y-4)^2	(9*y-8)/(y-4)^2	y		1	1		ATPartFrac_true.
PartFrac	Pass	(-5/(x+3))+(16/(x+3)^2)-(2/(x+2))+4	(-5/(x+3))+(16/(x+3)^2)-(2/(x+2))+4	x		1	1		ATPartFrac_true.
PartFrac	Pass	(3x^2-5)/((x-4)^2x)	(3x^2-5)/((x-4)^2x)	x		0	0		ATPartFrac_false_factor.
PartFrac	Pass	-4/(16x)+53/(16(x-4))+43/(4*(x-4)^2)	(3x^2-5)/((x-4)^2x)	x		0	0	Your answer as a single fraction is \$\\frac{49\\cdot x^2-8\\cdot x-64}{16\\cdot {\\left(x-4\\right)}^2\\cdot x}\$	ATPartFrac_ret_expression.
PartFrac	Pass	-5/(16x)+53/(16(x-4))+43/(4*(x-4)^2)	(3x^2-5)/((x-4)^2x)	x		1	1		ATPartFrac_true.
PartFrac	Pass	(5x+6)/((x+1)(x+5)^2)	(5x+6)/((x+1)(x+5)^2)	x		0	0		ATPartFrac_false_factor.
PartFrac	Pass	-1/(16(x+5))+19/(4(x+5)^2)+1/(16*(x+1))	(5x+6)/((x+1)(x+5)^2)	x		1	1		ATPartFrac_true.
PartFrac	Pass	5/(x(x+3)(5*x-2))	5/(x(x+3)(5*x-2))	x		0	0		ATPartFrac_false_factor.
PartFrac	Pass	125/(34(5x-2))+5/(51(x+3))-5/(6x)	5/(x(x+3)(5*x-2))	x		1	1		ATPartFrac_true.
PartFrac	Pass	-4/(16x)+1/(2(x-1))-1/(8*(x-1)^2)	(3x^2-5)/((4x-4)^2*x)	x		0	0	Your answer as a single fraction is \$\\frac{2\\cdot x^2-x-2}{8\\cdot {\\left(x-1\\right)}^2\\cdot x}\$	ATPartFrac_ret_expression.
PartFrac	Pass	-5/(16x)+1/(2(x-1))-1/(8*(x-1)^2)	(3x^2-5)/((4x-4)^2*x)	x		1	1		ATPartFrac_true.
Irreducible quadratic in denominator
PartFrac	Pass	1/(x-1)-(x+1)/(x^2+1)	2/((x-1)*(x^2+1))	x		1	1		ATPartFrac_true.
PartFrac	Pass	1/(2x-2)-(x+1)/(2(x^2+1))	1/((x-1)*(x^2+1))	x		1	1		ATPartFrac_true.
PartFrac	Pass	1/(2(x-1))+x/(2(x^2+1))	1/((x-1)*(x^2+1))	x		0	0	Your answer as a single fraction is \$\\frac{2\\cdot x^2-x+1}{2\\cdot \\left(x-1\\right)\\cdot \\left(x^2+1 \\right)}\$	ATPartFrac_ret_expression.
PartFrac	Pass	(2*x+1)/(x^2+1)-2/(x-1)	(2*x+1)/(x^2+1)-2/(x-1)	x		1	1		ATPartFrac_true.
2 answers to the same question
PartFrac	Pass	3/(x+1) + 3/(x+2)	3(2x+3)/((x+1)*(x+2))	x		1	1		ATPartFrac_true.
PartFrac	Pass	3*(1/(x+1) + 1/(x+2))	3(2x+3)/((x+1)*(x+2))	x		1	1		ATPartFrac_true.
Algebraically equivalent, but numerators of same order than denominator, i.e. not in partial fraction form.
PartFrac	Pass	3x(1/(x+1) + 2/(x+2))	-12/(x+2)-3/(x+1)+9	x		0	0		ATPartFrac_false_factor.
PartFrac	Pass	(3x+3)(1/(x+1) + 2/(x+2))	9-6/(x+2)	x		0	0		ATPartFrac_false_factor.
PartFrac	Pass	n/(2n-1)-(n+1)/(2n+1)	1/(4n-2)-1/(4n+2)	n		0	0		ATPartFrac_false_factor.
Correct Answer, Numerator > Denominator
PartFrac	Pass	10/(x+3) - 2/(x+2) + x -2	(x^3 + 3x^2 + 4x +2)/((x+2)*(x+3))	x		1	1		ATPartFrac_true.
PartFrac	Pass	2*x+1/(x+1)+1/(x-1)	2*x^3/(x^2-1)	x		1	1		ATPartFrac_true.
Simple mistakes
PartFrac	Pass	1/(n*(n-1))	1/(n*(n-1))	n		0	0		ATPartFrac_false_factor.
PartFrac	Pass	1/(n-1)-1/n^2	1/((n+1)*n)	n		0	0	If your answer is written as a single fraction then the denominator would be \$\\left(n-1\\right)\\cdot n^2\$. In fact, it should be \$n\\cdot \\left(n+1\\right)\$.	ATPartFrac_denom_ret.
PartFrac	Pass	1/(n-1)-1/n	1/(n-1)+1/n	n		0	0	Your answer as a single fraction is \$\\frac{1}{\\left(n-1\\right)\\cdot n}\$	ATPartFrac_ret_expression.
PartFrac	Pass	1/(x+1)-1/x	1/(x-1)+1/x	x		0	0	Your answer as a single fraction is \$-\\frac{1}{x\\cdot \\left(x+1\\right)}\$	ATPartFrac_ret_expression.
PartFrac	Pass	1/(n*(n+1))+1/n	2/n-1/(n+1)	n		0	0		ATPartFrac_false_factor.
Too many parts in the partial fraction
PartFrac	Pass	s/((s+1)^2) + s/(s+2) - 1/(s+1)	s/((s+1)*(s+2))	s		0	0	If your answer is written as a single fraction then the denominator would be \${\\left(s+1\\right)}^2\\cdot \\left(s+2\\right)\$. In fact, it should be \$\\left(s+1\\right)\\cdot \\left(s+2\\right)\$.	ATPartFrac_denom_ret.
Too few parts in the partial fraction
PartFrac	Pass	s/(s+2) - 1/(s+1)	s/((s+1)(s+2)(s+3))	s		0	0	If your answer is written as a single fraction then the denominator would be \$\\left(s+1\\right)\\cdot \\left(s+2\\right)\$. In fact, it should be \$\\left(s+1\\right)\\cdot \\left(s+2\\right)\\cdot \\left(s+3\\right)\$.	ATPartFrac_denom_ret.
PartFrac	Pass	(3x^2-5)/((4x-4)^2*x)	(3x^2-5)/((4x-4)^2*x)	x		0	0		ATPartFrac_false_factor.

Diff	Expected failure	1/0	3*x^2		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test.	STACKERROR_OPTION.
Diff	Expected failure	0	1/0	(x	TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Option field is invalid. You have a missing right bracket ) in the expression: (x.	STACKERROR_OPTION.
Diff	Expected failure	1/0	3*x^2	x		0	-1		ATDiff_STACKERROR_SAns.
Diff	Expected failure	0	1/0	x		0	-1		ATDiff_STACKERROR_TAns.
Diff	Expected failure	0	0	1/0		0	-1		ATDiff_STACKERROR_Opt.
Basic tests
Diff	Pass	3*x^2	3*x^2	x		1	1		ATDiff_true.
Diff	Pass	3*X^2	3*x^2	x		0	0		ATDiff_var_SB_notSA.
Diff	Pass	x^4/4	3*x^2	x		0	0	It looks like you have integrated instead!	ATDiff_int.
Diff	Pass	x^4/4+1	3*x^2	x		0	0	It looks like you have integrated instead!	ATDiff_int.
Diff	Pass	x^4/4+c	3*x^2	x		0	0	It looks like you have integrated instead!	ATDiff_int.
Diff	Pass	y=x^4/4	x^4/4	x		0	0	Your answer should be an expression, not an equation, inequality, list, set or matrix.	ATDiff_SA_not_expression.
Diff	Pass	x^4/4	y=x^4/4	x		0	0
Diff	Pass	y=x^4/4	y=x^4/4	x		0	0	Your answer should be an expression, not an equation, inequality, list, set or matrix.	ATDiff_SA_not_expression.
Diff	Pass	6000*(x-a)^5999	6000*(x-a)^5999	x		1	1		ATDiff_true.
Diff	Pass	5999*(x-a)^5999	6000*(x-a)^5999	x		0	0
Variable mismatch tests
Diff	Pass	y^2-2*y+1	x^2-2*x+1	x		0	0		ATDiff_var_SB_notSA.
Diff	Pass	x^2-2*x+1	y^2-2*y+1	x		0	0		ATDiff_var_SA_notSB.
Diff	Pass	y^2+2*y+1	x^2-2*x+1	z		0	0		ATDiff_var_notSASB_SAnceSB.
Diff	Pass	x^4/4	3*x^2	y		0	0
Edge cases
Diff	Pass	e^x+c	e^x	x		0	0	It looks like you have integrated instead!	ATDiff_int.
Diff	Pass	e^x+2	e^x	x		0	0	It looks like you have integrated instead!	ATDiff_int.
Diff	Expected failure	n*x^n	n*x^(n-1)	x	TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. TIMEDOUT	ATDiff_STACKERROR_SAns.
Diff	Pass	n*x^n	(assume(n>0), n*x^(n-1))	x		0	0

Int	Expected failure	1/0	1		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test.	STACKERROR_OPTION.
Int	Expected failure	1/0	1	x		0	-1		ATInt_STACKERROR_SAns.
Int	Expected failure	1	1/0	x		0	-1		ATInt_STACKERROR_TAns.
Int	Expected failure	0	0	1/0		0	-1		ATInt_STACKERROR_Opt.
Int	Expected failure	0	0	[x,1/0]		0	-1		ATInt_STACKERROR_Opt.
Int	Expected failure	0	0	[x,NOCONST,1/0]		0	-1		ATInt_STACKERROR_Opt.
Basic tests
Int	Pass	x^3/3	x^3/3	x		0	0	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int	Pass	x^3/3+1	x^3/3	x		0	0	You need to add a constant of integration. This should be an arbitrary constant, not a number.	ATInt_const_int.
Int	Pass	x^3/3+c	x^3/3	x		1	1		ATInt_true.
Int	Pass	x^3/3+c+1	x^3/3	x		1	1		ATInt_true.
Int	Pass	x^3/3+3*c	x^3/3	x		1	1		ATInt_true.
Int	Pass	x^3/3-c	x^3/3	x		1	1		ATInt_true.
Int	Pass	x^3/3+c+k	x^3/3	x		0	0	The formal derivative of your answer does equal the expression that you were asked to integrate. However, you have a strange constant of integration. Please ask your teacher about this.	ATInt_weirdconst.
Int	Pass	x^3/3+c^2	x^3/3	x		0	0	The formal derivative of your answer does equal the expression that you were asked to integrate. However, you have a strange constant of integration. Please ask your teacher about this.	ATInt_weirdconst.
Int	Pass	x^3/3*c	x^3/3	x		0	0	The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[x^2\\] In fact, the derivative of your answer, with respect to \$x\$ is: \\[c\\cdot x^2\\] so you must have done something wrong!	ATInt_generic.
Int	Pass	X^3/3+c	x^3/3	x		0	0	The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[x^2\\] In fact, the derivative of your answer, with respect to \$x\$ is: \\[0\\] so you must have done something wrong!	ATInt_generic. ATInt_var_SB_notSA.
Int	Pass	sin(2*x)	x^3/3	x		0	0	The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[x^2\\] In fact, the derivative of your answer, with respect to \$x\$ is: \\[2\\cdot \\cos \\left( 2\\cdot x \\right)\\] so you must have done something wrong!	ATInt_generic.
Int	Pass	x^2/2-2*x+2+c	(x-2)^2/2	x		1	1		ATInt_true.
Int	Pass	(t-1)^5/5+c	(t-1)^5/5	t		1	1		ATInt_true.
Int	Pass	(v-1)^5/5+c	(v-1)^5/5	v		1	1		ATInt_true.
Int	Pass	cos(2*x)/2+1+c	cos(2*x)/2	x		1	1		ATInt_true.
Int	Pass	(x-a)^6001/6001+c	(x-a)^6001/6001	x		1	1		ATInt_true.
Int	Pass	(x-a)^6001/6001	(x-a)^6001/6001	x		0	0	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int	Pass	6000*(x-a)^5999	(x-a)^6001/6001	x		0	0	It looks like you have differentiated instead!	ATInt_diff.
Int	Pass	4%e^(4x)/(%e^(4*x)+1)	log(%e^(4*x)+1)+c	x		0	0	The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[\\frac{4\\cdot e^{4\\cdot x}}{e^{4\\cdot x}+1}\\] In fact, the derivative of your answer, with respect to \$x\$ is: \\[\\frac{16\\cdot e^{4\\cdot x}}{e^{4\\cdot x}+1}-\\frac{16\\cdot e^{8 \\cdot x}}{{\\left(e^{4\\cdot x}+1\\right)}^2}\\] so you must have done something wrong!	ATInt_generic.
The teacher adds a constant
Int	Pass	x^3/3+c	x^3/3+c	x		1	1		ATInt_true.
Int	Pass	x^2/2-2*x+2+c	(x-2)^2/2+k	x		1	1		ATInt_true.
The teacher condones lack of constant, or numerical constant
Int	Pass	x^3/3	x^3/3	[x,NOCONST]		1	1		ATInt_const_condone.
Int	Pass	x^3/3+c	x^3/3	[x,NOCONST]		1	1		ATInt_true.
Int	Pass	x^2/2-2*x+2	(x-2)^2/2+k	[x,NOCONST]		1	1		ATInt_const_condone.
Int	Pass	x^3/3+1	x^3/3	[x,NOCONST]		1	1		ATInt_const_int_condone.
Int	Pass	x^3/3+c^2	x^3/3	[x,NOCONST]		0	0	The formal derivative of your answer does equal the expression that you were asked to integrate. However, you have a strange constant of integration. Please ask your teacher about this.	ATInt_weirdconst.
Int	Pass	n*x^n	n*x^(n-1)	x		0	0	The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[\\left(n-1\\right)\\cdot n\\cdot x^{n-2}\\] In fact, the derivative of your answer, with respect to \$x\$ is: \\[n^2\\cdot x^{n-1}\\] so you must have done something wrong!	ATInt_generic.
Int	Pass	n*x^n	(assume(n>0), n*x^(n-1))	x		0	0	The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[\\left(n-1\\right)\\cdot n\\cdot x^{n-2}\\] In fact, the derivative of your answer, with respect to \$x\$ is: \\[n^2\\cdot x^{n-1}\\] so you must have done something wrong!	ATInt_generic.
Special case
Int	Pass	exp(x)+c	exp(x)	x		1	1		ATInt_true.
Int	Pass	exp(x)	exp(x)	x		0	0	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int	Pass	exp(x)	exp(x)	[x,NOCONST]		1	1		ATInt_const_condone.
Student differentiates by mistake
Int	Pass	2*x	x^3/3	x		0	0	It looks like you have differentiated instead!	ATInt_diff.
Int	Pass	2*x+c	x^3/3	x		0	0	It looks like you have differentiated instead!	ATInt_diff.
Sloppy logs (teacher ignores abs(x) )
Int	Pass	ln(x)	ln(x)	x		0	0	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int	Pass	ln(x)	ln(x)	[x,NOCONST]		1	1		ATInt_const_condone.
Int	Pass	ln(x)+c	ln(x)+c	x		1	1		ATInt_true_equiv.
Int	Pass	ln(k*x)	ln(x)+c	x		1	1		ATInt_true_equiv.
Fussy logs (teacher uses abs(x) )
Int	Pass	ln(x)	ln(abs(x))+c	x		0	0	The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \$\\int\\frac{1}{x} dx = \\log(\|x\|)+c\$, rather than \$\\int\\frac{1}{x} dx = \\log(x)+c\$. Please ask your teacher about this.	ATInt_EqFormalDiff. ATInt_logabs.
Int	Pass	ln(x)+c	ln(abs(x))+c	x		0	0	The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \$\\int\\frac{1}{x} dx = \\log(\|x\|)+c\$, rather than \$\\int\\frac{1}{x} dx = \\log(x)+c\$. Please ask your teacher about this.	ATInt_EqFormalDiff. ATInt_logabs.
Int	Pass	ln(x)	ln(abs(x))+c	[x, NOCONST]		0	0	The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \$\\int\\frac{1}{x} dx = \\log(\|x\|)+c\$, rather than \$\\int\\frac{1}{x} dx = \\log(x)+c\$. Please ask your teacher about this.	ATInt_EqFormalDiff. ATInt_logabs.
Int	Pass	ln(abs(x))	ln(abs(x))+c	x		0	0	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int	Pass	ln(abs(x))+c	ln(abs(x))+c	x		1	1		ATInt_true_equiv.
Int	Pass	ln(k*x)	ln(abs(x))+c	x		0	0	The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \$\\int\\frac{1}{x} dx = \\log(\|x\|)+c\$, rather than \$\\int\\frac{1}{x} dx = \\log(x)+c\$. Please ask your teacher about this.	ATInt_EqFormalDiff. ATInt_logabs.
Int	Pass	ln(k*abs(x))	ln(abs(x))+c	x		1	1		ATInt_true_equiv.
Int	Pass	ln(abs(k*x))	ln(abs(x))+c	x		1	1		ATInt_true_equiv.
Teacher uses ln(k*abs(x))
Int	Pass	ln(x)	ln(k*abs(x))	x		0	0	The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \$\\int\\frac{1}{x} dx = \\log(\|x\|)+c\$, rather than \$\\int\\frac{1}{x} dx = \\log(x)+c\$. Please ask your teacher about this.	ATInt_EqFormalDiff. ATInt_logabs.
Int	Pass	ln(x)+c	ln(k*abs(x))	x		0	0	The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \$\\int\\frac{1}{x} dx = \\log(\|x\|)+c\$, rather than \$\\int\\frac{1}{x} dx = \\log(x)+c\$. Please ask your teacher about this.	ATInt_EqFormalDiff. ATInt_logabs.
Int	Pass	ln(abs(x))	ln(k*abs(x))	x		0	0	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int	Pass	ln(abs(x))+c	ln(k*abs(x))	x		1	1		ATInt_true_equiv.
Int	Pass	ln(k*x)	ln(k*abs(x))	x		0	0	The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \$\\int\\frac{1}{x} dx = \\log(\|x\|)+c\$, rather than \$\\int\\frac{1}{x} dx = \\log(x)+c\$. Please ask your teacher about this.	ATInt_EqFormalDiff. ATInt_logabs.
Int	Pass	ln(k*abs(x))	ln(k*abs(x))	x		1	1		ATInt_true_equiv.
Other logs
Int	Pass	ln(x)+ln(a)	ln(k*abs(x+a))	x		0	0	The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \$\\int\\frac{1}{x} dx = \\log(\|x\|)+c\$, rather than \$\\int\\frac{1}{x} dx = \\log(x)+c\$. Please ask your teacher about this.	ATInt_generic. ATInt_logabs.
Int	Pass	log(x)^2-2log(c)log(x)+k	ln(c/x)^2	x		0	0	The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this.	ATInt_EqFormalDiff.
Int	Pass	log(x)^2-2log(c)log(x)+k	ln(abs(c/x))^2	x		0	0	The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[-\\frac{2\\cdot \\ln \\left( \\frac{\\left\| c\\right\| }{\\left\| x\\right\| } \\right)}{x}\\] In fact, the derivative of your answer, with respect to \$x\$ is: \\[\\frac{2\\cdot \\ln \\left( x \\right)}{x}-\\frac{2\\cdot \\ln \\left( c \\right)}{x}\\] so you must have done something wrong!	ATInt_generic.
Int	Pass	c-(log(2)-log(x))^2/2	-1/2*log(2/x)^2	x		1	1		ATInt_true_equiv.
Int	Pass	ln(abs(x+3))/2+c	ln(abs(2*x+6))/2+c	x		0	-3	The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this.	ATInt_EqFormalDiff.
Two logs
Int	Pass	log(abs(x-3))+log(abs(x+3))	log(abs(x-3))+log(abs(x+3))	x		0	0	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int	Pass	log(abs(x-3))+log(abs(x+3))+c	log(abs(x-3))+log(abs(x+3))	x		1	1		ATInt_true_equiv.
Int	Pass	log(abs(x-3))+log(abs(x+3))	log(x-3)+log(x+3)	x		0	0	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int	Pass	log(abs(x-3))+log(abs(x+3))+c	log(x-3)+log(x+3)	x		1	1		ATInt_true_equiv.
Int	Pass	log(x-3)+log(x+3)	log(x-3)+log(x+3)	x		0	0	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int	Pass	log(x-3)+log(x+3)+c	log(x-3)+log(x+3)	x		1	1		ATInt_true_equiv.
Int	Pass	log(x-3)+log(x+3)	log(abs(x-3))+log(abs(x+3))	x		0	0	The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \$\\int\\frac{1}{x} dx = \\log(\|x\|)+c\$, rather than \$\\int\\frac{1}{x} dx = \\log(x)+c\$. Please ask your teacher about this.	ATInt_EqFormalDiff. ATInt_logabs.
Int	Pass	log(x-3)+log(x+3)+c	log(abs(x-3))+log(abs(x+3))	x		0	0	The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \$\\int\\frac{1}{x} dx = \\log(\|x\|)+c\$, rather than \$\\int\\frac{1}{x} dx = \\log(x)+c\$. Please ask your teacher about this.	ATInt_EqFormalDiff. ATInt_logabs.
Int	Pass	log(abs((x-3)*(x+3)))+c	log(abs(x-3))+log(abs(x+3))	x		1	1		ATInt_true_equiv.
Int	Pass	log(abs((x^2-9)))+c	log(abs(x-3))+log(abs(x+3))	x		0	0	The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this.	ATInt_EqFormalDiff.
Int	Pass	2log(abs(x-2))-log(abs(x+2))+(x^2+4x)/2	-log(abs(x+2))+2log(abs(x-2))+(x^2+4x)/2+c	x		0	0	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int	Pass	-log(abs(x+2))+2log(abs(x-2))+(x^2+4x)/2+c	-log(abs(x+2))+2log(abs(x-2))+(x^2+4x)/2+c	x		1	1		ATInt_true_equiv.
Int	Pass	-log(abs(x+2))+2log(abs(x-2))+(x^2+4x)/2+c	-log((x+2))+2log((x-2))+(x^2+4x)/2	x		1	1		ATInt_true_equiv.
Inconsistent log(abs())
Int	Pass	log(abs(x-3))+log((x+3))+c	log(x-3)+log(x+3)	x		0	0	There appear to be strange inconsistencies between your use of \$\\log(...)\$ and \$\\log(\|...\|)\$. Please ask your teacher about this.	ATInt_true_equiv. ATInt_logabs_inconsistent.
Int	Pass	log((v-3))+log(abs(v+3))+c	log(v-3)+log(v+3)	v		0	0	There appear to be strange inconsistencies between your use of \$\\log(...)\$ and \$\\log(\|...\|)\$. Please ask your teacher about this.	ATInt_true_equiv. ATInt_logabs_inconsistent.
Int	Pass	log((x-3))+log(abs(x+3))	log(x-3)+log(x+3)	x		0	0	There appear to be strange inconsistencies between your use of \$\\log(...)\$ and \$\\log(\|...\|)\$. Please ask your teacher about this.	ATInt_const. ATInt_logabs_inconsistent.
Int	Pass	2log((x-2))-log(abs(x+2))+(x^2+4x)/2	-log(abs(x+2))+2log(abs(x-2))+(x^2+4x)/2	x		0	0	There appear to be strange inconsistencies between your use of \$\\log(...)\$ and \$\\log(\|...\|)\$. Please ask your teacher about this.	ATInt_EqFormalDiff. ATInt_logabs. ATInt_logabs_inconsistent.
Significant integration constant differences
Int	Pass	2(sqrt(t)-5)-10log((sqrt(t)-5))+c	2(sqrt(t)-5)-10log((sqrt(t)-5))+c	t		1	1		ATInt_true_equiv.
Int	Pass	2(sqrt(t))-10log((sqrt(t)-5))+c	2(sqrt(t)-5)-10log((sqrt(t)-5))+c	t		1	1		ATInt_true_differentconst.
Int	Pass	2(sqrt(t)-5)-10log((sqrt(t)-5))+c	2(sqrt(t)-5)-10log(abs(sqrt(t)-5))+c	t		0	0	The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \$\\int\\frac{1}{x} dx = \\log(\|x\|)+c\$, rather than \$\\int\\frac{1}{x} dx = \\log(x)+c\$. Please ask your teacher about this.	ATInt_EqFormalDiff. ATInt_logabs.
Int	Pass	2(sqrt(t))-10log(abs(sqrt(t)-5))+c	2(sqrt(t)-5)-10log(abs(sqrt(t)-5))+c	t		1	1		ATInt_true_differentconst.
Trig
Int	Pass	2sin(x)cos(x)	sin(2*x)+c	x		0	0	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int	Pass	2sin(x)cos(x)+k	sin(2*x)+c	x		1	1		ATInt_true.
Int	Pass	-2cos(3x)/3-3cos(2x)/2	-2cos(3x)/3-3cos(2x)/2+c	x		0	0	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int	Pass	-2cos(3x)/3-3cos(2x)/2+1	-2cos(3x)/3-3cos(2x)/2+c	x		0	0	You need to add a constant of integration. This should be an arbitrary constant, not a number.	ATInt_const_int.
Int	Pass	-2cos(3x)/3-3cos(2x)/2+c	-2cos(3x)/3-3cos(2x)/2+c	x		1	1		ATInt_true.
Int	Pass	(tan(2t)-2t)/2	-(tsin(4t)^2-sin(4t)+tcos(4t)^2+2tcos(4t)+t)/(sin(4t)^2+cos(4t)^2+2cos(4t)+1)	t		0	0	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int	Pass	(tan(2t)-2t)/2+1	-(tsin(4t)^2-sin(4t)+tcos(4t)^2+2tcos(4t)+t)/(sin(4t)^2+cos(4t)^2+2cos(4t)+1)	t		0	0	You need to add a constant of integration. This should be an arbitrary constant, not a number.	ATInt_const_int.
Int	Pass	(tan(2t)-2t)/2+c	-(tsin(4t)^2-sin(4t)+tcos(4t)^2+2tcos(4t)+t)/(sin(4t)^2+cos(4t)^2+2cos(4t)+1)	t		1	1		ATInt_true.
Int	Pass	tan(x)-x+c	tan(x)-x	x		1	1		ATInt_true.
Note the difference in feedback here, generated by the options.
Int	Pass	((5%e^7x-%e^7)%e^(5x))	((5%e^7x-%e^7)%e^(5x))/25+c	x		0	0	The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[\\frac{e^{5\\cdot x+7}}{5}+\\frac{\\left(5\\cdot e^7\\cdot x-e^7\\right) \\cdot e^{5\\cdot x}}{5}\\] In fact, the derivative of your answer, with respect to \$x\$ is: \\[5\\cdot e^{5\\cdot x+7}+5\\cdot \\left(5\\cdot e^7\\cdot x-e^7\\right) \\cdot e^{5\\cdot x}\\] so you must have done something wrong!	ATInt_generic.
Int	Pass	((5%e^7x-%e^7)%e^(5x))	((5%e^7x-%e^7)%e^(5x))/25+c	[x,x%e^(5x+7)]		0	0	The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[x\\cdot e^{5\\cdot x+7}\\] In fact, the derivative of your answer, with respect to \$x\$ is: \\[5\\cdot e^{5\\cdot x+7}+5\\cdot \\left(5\\cdot e^7\\cdot x-e^7\\right) \\cdot e^{5\\cdot x}\\] so you must have done something wrong!	ATInt_generic.
Inverse hyperbolic integrals
Int	Pass	log(x-3)/6-log(x+3)/6+c	log(x-3)/6-log(x+3)/6	x		1	1		ATInt_true_equiv.
Int	Pass	asinh(x)	ln(x+sqrt(x^2+1))	x		0	0	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int	Pass	asinh(x)+c	ln(x+sqrt(x^2+1))	x		1	1		ATInt_true.
Int	Pass	-acoth(x/3)/3	log(x-3)/6-log(x+3)/6	x		0	0	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int	Pass	-acoth(x/3)/3	log(x-3)/6-log(x+3)/6	[x, NOCONST]		1	1		ATInt_true.
Int	Pass	-acoth(x/3)/3+c	log(x-3)/6-log(x+3)/6	x		1	1		ATInt_true.
Int	Pass	-acoth(x/3)/3+c	log(abs(x-3))/6-log(abs(x+3))/6	x		1	1		ATInt_true.
Int	Pass	log(x-a)/(2a)-log(x+a)/(2a)+c	log(x-a)/(2a)-log(x+a)/(2a)	x		1	1		ATInt_true_equiv.
Int	Pass	-acoth(x/a)/a+c	log(x-a)/(2a)-log(x+a)/(2a)	x		1	1		ATInt_true.
Int	Pass	-acoth(x/a)/a+c	log(abs(x-a))/(2a)-log(abs(x+a))/(2a)	x		1	1		ATInt_true.
Int	Pass	log(x-a)/(2a)-log(x+a)/(2a)+c	log(abs(x-a))/(2a)-log(abs(x+a))/(2a)	x		0	0	The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Your teacher may expect you to use the result \$\\int\\frac{1}{x} dx = \\log(\|x\|)+c\$, rather than \$\\int\\frac{1}{x} dx = \\log(x)+c\$. Please ask your teacher about this.	ATInt_EqFormalDiff. ATInt_logabs.
Int	Pass	log(x-3)/6-log(x+3)/6+c	-acoth(x/3)/3	x		1	1		ATInt_true.
Int	Pass	log(abs(x-3))/6-log(abs(x+3))/6+c	-acoth(x/3)/3	x		1	1		ATInt_true.
Int	Pass	log(x-3)/6-log(x+3)/6	-acoth(x/3)/3	x		0	0	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int	Pass	atan(2*x-3)+c	atan(2*x-3)	x		1	1		ATInt_true.
Int	Pass	atan((x-2)/(x-1))+c	atan(2*x-3)	x		1	1		ATInt_true.
Int	Pass	atan((x-2)/(x-1))	atan(2*x-3)	x		0	0	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int	Pass	atan((x-1)/(x-2))	atan(2*x-3)	x		0	0	The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[\\frac{2}{{\\left(2\\cdot x-3\\right)}^2+1}\\] In fact, the derivative of your answer, with respect to \$x\$ is: \\[\\frac{\\frac{1}{x-2}-\\frac{x-1}{{\\left(x-2\\right)}^2}}{\\frac{{\\left( x-1\\right)}^2}{{\\left(x-2\\right)}^2}+1}\\] so you must have done something wrong!	ATInt_generic.
Stoutemyer (currently fails)
Int	Pass	2/3sqrt(3)(atan(sin(x)/(sqrt(3)*(cos(x)+1)))-(atan(sin(x)/(cos(x)+1))))+x/sqrt(3)	2atan(sin(x)/(sqrt(3)(cos(x)+1)))/sqrt(3)	x		0	-3	You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.

GT	Expected failure	1/0	1		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATGT_STACKERROR_SAns.
GT	Expected failure	1	1/0		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATGT_STACKERROR_TAns.
GT	Pass	1	1			0	0		ATGT_false.
GT	Pass	2	1			1	1		ATGT_true.
GT	Pass	1	2.1			0	0		ATGT_false.
GT	Pass	pi	3			1	1		ATGT_true.
GT	Pass	pi+2	5			1	1		ATGT_true.
Infinity
GT	Pass	-inf	0			0	0		Not number
GT	Pass	inf	0			0	0		Not number

GTE	Expected failure	1/0	1		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATGTE_STACKERROR_SAns.
GTE	Expected failure	1	1/0		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATGTE_STACKERROR_TAns.
GTE	Pass	1	1			1	1		ATGTE_true.
GTE	Pass	2	1			1	1		ATGTE_true.
GTE	Pass	1	2.1			0	0		ATGTE_false.
GTE	Pass	pi	3			1	1		ATGTE_true.
GTE	Pass	pi+2	5			1	1		ATGTE_true.

Basic tests
NumRelative	Expected failure	1/0	0		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATNumRelative_STACKERROR_SAns.
NumRelative	Expected failure	0	1/0		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATNumRelative_STACKERROR_TAns.
NumRelative	Expected failure	0	0	1/0	TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATNumRelative_STACKERROR_Opt.
NumRelative	Expected failure	0	(x		The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty teacher answer, probably a CAS validation problem when authoring the question.	0	-1	The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty teacher answer, probably a CAS validation problem when authoring the question.	ATNumRelativeTEST_FAILED-Empty TA.
NumRelative	Expected failure	1.5	1.5	x		0	-1	The numerical tolerance for ATNumerical should be a floating point number, but is not. This is an internal error with the test. Please ask your teacher about this.	ATNumerical_STACKERROR_tol.
NumRelative	Pass	1	0	(x		0	0
NumRelative	Pass	x=1.5	1.5			0	0	Your answer should be a floating point number, but is not.	ATNumerical_SA_not_number.
NumRelative	Pass	1.5	x=1.5			0	0	The value supplied for the teacher's answer should be a floating point number, but is not. This is an internal error with the test. Please ask your teacher about this.	ATNumerical_SB_not_number.
No option, so 5%
NumRelative	Pass	1.1	1			0	0
NumRelative	Pass	1.05	1			1	1
NumRelative	Pass	0.95	1			1	1
NumRelative	Pass	0.949	1			0	0
NumRelative	Pass	1.05e33	1e33			1	1
NumRelative	Pass	1.06e33	1e33			0	0
NumRelative	Pass	0.95e33	1e33			1	1
NumRelative	Pass	0.949e33	1e33			0	0
NumRelative	Pass	1.05e-33	1e-33			1	1
NumRelative	Pass	1.06e-33	1e-33			0	0
NumRelative	Pass	0.95e-33	1e-33			1	1
NumRelative	Pass	0.949e-33	1e-33			0	0
Remove display dp etc.
NumRelative	Pass	1	displaydp(1.05,2)	0.1		1	1
NumRelative	Pass	1000	displaysci(1.05,2,3)	0.1		1	1
Options passed
NumRelative	Pass	1.05	1	0.1		1	1
NumRelative	Pass	1.05	3	0.1		0	0
NumRelative	Pass	3.14	pi	0.001		1	1
Infinity
NumRelative	Pass	inf	0			0	0	Your answer should be a floating point number, but is not.	ATNumerical_SA_not_number.
Lists
NumRelative	Pass	1	[1,2]			0	0	Your answer should be a list, but is not. Note that the syntax to enter a list is to enclose the comma separated values with square brackets.	ATNumerical_SA_not_list.
NumRelative	Pass	[1,2]	[1,2,3]			0	0	Your list should have \$3\$ elements, but it actually has \$2\$.	ATNumerical_wronglen.
NumRelative	Pass	[1,2]	[1,2]			1	1
NumRelative	Pass	[3.141,1.414]	[pi,sqrt(2)]			1	1
NumRelative	Pass	[3,1.414]	[pi,sqrt(2)]	0.01		0	0	The entries underlined in red below are those that are incorrect. \\[\\left[ {\\color{red}{\\underline{3.0}}} , 1.414 \\right] \\]	ATNumerical_wrongentries SA/TA=[3.0].
NumRelative	Pass	[3,1.414]	{pi,sqrt(2)}	0.01		0	0	Your answer should be a set, but is not. Note that the syntax to enter a set is to enclose the comma separated values with curly brackets.	ATNumerical_SA_not_set.
NumRelative	Pass	{1.414,3.1}	{significantfigures(pi,6),sqrt(2)}	0.01		0	0	The entries underlined in red below are those that are incorrect. \\[\\left \\{{\\color{red}{\\underline{3.1}}} \\right \\}\\]	ATNumerical_wrongentries: TA/SA=[3.14159], SA/TA=[3.1].
NumRelative	Pass	{1.414,3.1}	{pi,sqrt(2)}	0.1		1	1

Basic tests
NumAbsolute	Expected failure	1/0	0		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATNumAbsolute_STACKERROR_SAns.
NumAbsolute	Expected failure	0	1/0		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATNumAbsolute_STACKERROR_TAns.
NumAbsolute	Expected failure	0	0	1/0	TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATNumAbsolute_STACKERROR_Opt.
NumAbsolute	Expected failure	0	(x		The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty teacher answer, probably a CAS validation problem when authoring the question.	0	-1	The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty teacher answer, probably a CAS validation problem when authoring the question.	ATNumAbsoluteTEST_FAILED-Empty TA.
NumAbsolute	Pass	1	0	(x		0	0
No option, so 5%
NumAbsolute	Pass	1.1	1			0	0
NumAbsolute	Pass	1.05	1			1	1
Options passed
NumAbsolute	Pass	1.05	1	0.1		1	1
NumAbsolute	Pass	1.05	3	0.1		0	0
NumAbsolute	Pass	3.14	pi	0.001		0	0
NumAbsolute	Pass	1.41e-2	1.41e-2	0.0001		1	1
NumAbsolute	Pass	0.0141	1.41e-2	0.0001		1	1
NumAbsolute	Pass	0.00141	0.00141	0.0001		1	1
NumAbsolute	Pass	0.00141	1.41*10^-3	0.0001		1	1
NumAbsolute	Pass	1.41*10^-3	1.41*10^-3	0.0001		1	1
NumAbsolute	Pass	[3.141,1.414]	[pi,sqrt(2)]	0.01		1	1
NumAbsolute	Pass	[3,1.414]	[pi,sqrt(2)]	0.01		0	0	The entries underlined in red below are those that are incorrect. \\[\\left[ {\\color{red}{\\underline{3.0}}} , 1.414 \\right] \\]	ATNumerical_wrongentries SA/TA=[3.0].
NumAbsolute	Pass	[3,1.414]	{pi,sqrt(2)}	0.01		0	0	Your answer should be a set, but is not. Note that the syntax to enter a set is to enclose the comma separated values with curly brackets.	ATNumerical_SA_not_set.
NumAbsolute	Pass	{1.414,3.1}	{significantfigures(pi,6),sqrt(2)}	0.01		0	0	The entries underlined in red below are those that are incorrect. \\[\\left \\{{\\color{red}{\\underline{3.1}}} \\right \\}\\]	ATNumerical_wrongentries: TA/SA=[3.14159], SA/TA=[3.1].
NumAbsolute	Pass	{1,1.414,3.1,2}	{1,2,pi,sqrt(2)}	0.1		1	1

Basic tests
NumSigFigs	Expected failure	3.141	3.1415927		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test.	STACKERROR_OPTION.
NumSigFigs	Expected failure	1/0	3	3		0	-1		ATNumSigFigs_STACKERROR_SAns.
NumSigFigs	Expected failure	0	1/0	3		0	-1		ATNumSigFigs_STACKERROR_TAns.
NumSigFigs	Expected failure	0	0	1/0		0	-1		ATNumSigFigs_STACKERROR_Opt.
NumSigFigs	Expected failure	0	1	(	TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Option field is invalid. You have a missing right bracket ) in the expression: (.	STACKERROR_OPTION.
NumSigFigs	Expected failure	(	1	1	The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question.	0	-1	The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question.	ATNumSigFigsTEST_FAILED-Empty SA.
NumSigFigs	Expected failure	1	3	pi		0	-1	The answer test failed to execute correctly: please alert your teacher.	ATNumSigFigs_STACKERROR_not_integer.
NumSigFigs	Expected failure	1	3	[3,x]		0	-1	The answer test failed to execute correctly: please alert your teacher.	ATNumSigFigs_STACKERROR_not_integer.
NumSigFigs	Expected failure	1	3	[1,2,3]		0	-1	The answer test failed to execute correctly: please alert your teacher.	ATNumSigFigs_STACKERROR_list_wrong_length.
NumSigFigs	Expected failure	1	3		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test.	STACKERROR_OPTION.
NumSigFigs	Pass	pi	pi	4		0	0	Your answer should be a decimal number, but is not!	ATNumSigFigs_NotDecimal.
Edge cases
NumSigFigs	Pass	0	0	2		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	0	0	1		1	1
NumSigFigs	Pass	0.0	0	1		1	1
NumSigFigs	Pass	0.0	0	2		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	0	0.0	2		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	0.0	0.0	2		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	0.00	0.00	2		1	1
Large numbers
NumSigFigs	Pass	5.4e21	5.3e21	2		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	5.3e21	5.3e21	2		1	1
NumSigFigs	Pass	5.3e22	5.3e22	2		1	1
NumSigFigs	Pass	5.3e20	5.3e22	2		0	0		ATNumSigFigs_VeryInaccurate.
NumSigFigs	Pass	6.02214086e23	6.02214086e23	9		1	1
NumSigFigs	Pass	6.0221409e23	6.02214086e23	9		0	0	Your answer contains the wrong number of significant digits. The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_WrongDigits. ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	6.02214087e23	6.02214086e23	9		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	6.02214085e23	6.02214086e23	9		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	5.3910632e-44	5.3910632e-44	8		1	1
NumSigFigs	Pass	5.391063e-44	5.3910632e-44	8		0	0	Your answer contains the wrong number of significant digits. The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_WrongDigits. ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	5.3910631e-44	5.3910632e-44	8		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	5.3910633e-44	5.3910632e-44	8		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	1.61622938e-35	1.61622938e-35	9		1	1
NumSigFigs	Pass	1.6162294e-35	1.61622938e-35	9		0	0	Your answer contains the wrong number of significant digits. The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_WrongDigits. ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	1.61622939e-35	1.61622938e-35	9		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	1.61622937e-35	1.61622938e-35	9		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	1.2345e82	1.2345e82	5		1	1
NumSigFigs	Pass	1.2346e82	1.2345e82	5		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	1.2344e82	1.2345e82	5		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
No trailing zeros.
NumSigFigs	Pass	1.234	4	1		0	0	Your answer contains the wrong number of significant digits. The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_WrongDigits. ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	3.141	3.1415927	3		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	3.141	3.1415927	4		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	3.146	3.1415927	4		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	3.147	3.1415927	4		0	0		ATNumSigFigs_VeryInaccurate.
NumSigFigs	Pass	3.142	3.1415927	4		1	1
NumSigFigs	Pass	3.142	pi	4		1	1
NumSigFigs	Pass	3141	3.1415927	4		0	0		ATNumSigFigs_VeryInaccurate.
NumSigFigs	Pass	0.00123	0.001234567	3		1	1
NumSigFigs	Pass	1.23e-3	0.001234567	3		1	1
NumSigFigs	Pass	138*10^-3	138*10^-3	3		1	1
NumSigFigs	Pass	-138*10^-3	-138*10^-3	3		1	1
NumSigFigs	Pass	138*10^-3	-138*10^-3	3		0	0	Your answer has the wrong algebraic sign.	ATNumSigFigs_WrongSign.
NumSigFigs	Pass	1.38*10^-1	138*10^-3	3		1	1
NumSigFigs	Pass	1.24e-3	0.001234567	3		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	1.235e-3	0.001234567	4		1	1
NumSigFigs	Pass	1000	999	2		1	1		ATNumSigFigs_WithinRange.
NumSigFigs	Pass	1E3	999	2		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	-100	-149	1		1	1
NumSigFigs	Pass	-0.05	-0.0499	1		1	1
NumSigFigs	Pass	-(0.05)	-0.0499	1		1	1
NumSigFigs	Pass	1170	1174.34	3		1	1
NumSigFigs	Pass	61300	61250	3		1	1
Previous tricky case
NumSigFigs	Pass	0.1667	0.1667	4		1	1
NumSigFigs	Pass	0.1666	0.1667	4		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	0.1663	0.1667	4		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	0.1662	0.1667	4		0	0		ATNumSigFigs_VeryInaccurate.
NumSigFigs	Pass	0.166	0.1667	4		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATNumSigFigs_VeryInaccurate.
NumSigFigs	Pass	0.16667	0.1667	4		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
Negative numbers
NumSigFigs	Pass	-3.141	-3.1415927	4		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	-3.141	-3.1415927	3		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	-3.141	-3.1415927	4		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	-3.142	-3.1415927	4		1	1
NumSigFigs	Pass	3.142	-3.1415927	4		0	0	Your answer has the wrong algebraic sign.	ATNumSigFigs_WrongSign.
NumSigFigs	Pass	-3.142	3.1415927	4		0	0	Your answer has the wrong algebraic sign.	ATNumSigFigs_WrongSign.
NumSigFigs	Pass	-3.149	3.1415927	4		0	0	Your answer has the wrong algebraic sign.	ATNumSigFigs_WrongSign. ATNumSigFigs_VeryInaccurate.
NumSigFigs	Pass	2.15	75701719/35227192	3		1	1
Round teacher answer
NumSigFigs	Pass	0.0499	0.04985	3		1	1
NumSigFigs	Pass	0.0498	0.04985	3		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	0.0498	0.04975	3		1	1
NumSigFigs	Pass	0.0497	0.04975	3		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	0.0499	0.0498	3		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
Final zeros after the decimal are significant.
NumSigFigs	Pass	1.5	1.500	3		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	1.50	1.500	3		1	1
NumSigFigs	Pass	1.500	1.500	3		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	245.0	245	3		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
Too few digits
NumSigFigs	Pass	180	178.35	3		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_WithinRange. ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	33	33.1558	3		0	0	Your answer contains the wrong number of significant digits. The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_WrongDigits. ATNumSigFigs_Inaccurate.
Mixed options
NumSigFigs	Pass	3.142	3.1415927	[4,3]		1	1
NumSigFigs	Pass	3.143	3.1415927	[4,3]		1	1
NumSigFigs	Pass	3.150	3.1415927	[4,3]		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	3.211	3.1415927	[4,3]		0	0		ATNumSigFigs_VeryInaccurate.
NumSigFigs	Pass	3.1416	3.1415927	[4,3]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	0.1666	0.1667	[4,3]		1	1
NumSigFigs	Pass	180	178.35	[3,1]		1	1		ATNumSigFigs_WithinRange.
NumSigFigs	Pass	33	33.1558	[3,1]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	1.500	1.5	[3,1]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	245.0	245	[3,1]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	12345.7	12345.654321	[6,6]		1	1
NumSigFigs	Pass	12345.7	12345.654321	[6,3]		1	1
NumSigFigs	Pass	12300.0	12345.654321	[6,3]		1	1
NumSigFigs	Pass	12400.0	12345.654321	[6,3]		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	13500.0	12345.654321	[6,3]		0	0		ATNumSigFigs_VeryInaccurate.
NumSigFigs	Pass	12000.0	12345.654321	[6,2]		1	1
NumSigFigs	Pass	13000.0	12345.654321	[6,2]		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	11000.0	12345.654321	[6,2]		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
Zero option and trailing zeros
NumSigFigs	Pass	0.0010	0	[1,0]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	0.0010	0	[2,0]		1	1
NumSigFigs	Pass	0.0010	0	[3,0]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	0.001	0	[1,0]		1	1
NumSigFigs	Pass	0.001	0	[2,0]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	0.00100	null	[2,0]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	0.00100	null	[3,0]		1	1
NumSigFigs	Pass	0.00100	null	[4,0]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	5.00	null	[2,0]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	5.00	null	[3,0]		1	1
NumSigFigs	Pass	5.00	null	[4,0]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	100	0	[1,0]		1	1
NumSigFigs	Pass	100	0	[2,0]		1	1		ATNumSigFigs_WithinRange.
NumSigFigs	Pass	100	0	[3,0]		1	1		ATNumSigFigs_WithinRange.
NumSigFigs	Pass	100	0	[4,0]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	10.0	0	[2,0]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	10.0	0	[3,0]		1	1
NumSigFigs	Pass	10.0	0	[4,0]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	0	0	[1,0]		1	1
NumSigFigs	Pass	0	0	[2,0]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	0.00	0	[1,0]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	0.00	0	[2,0]		1	1
NumSigFigs	Pass	0.00	0	[3,0]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	0.00	0	[4,0]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
Condone too many sfs.
NumSigFigs	Pass	8.250	8.250	[4,-1]		1	1
NumSigFigs	Pass	8.25	8.250	[4,-1]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs	Pass	8.250000	8.250	[4,-1]		1	1
NumSigFigs	Pass	8.250434	8.250	[4,-1]		1	1
NumSigFigs	Pass	82.4	82	[2,-1]		1	1
NumSigFigs	Pass	82.5	82	[2,-1]		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	83	82	[2,-1]		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
1/7 = 0.142857142857...
NumSigFigs	Pass	0.1430	1/7	[4,-1]		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	0.1429	1/7	[4,-1]		1	1
NumSigFigs	Pass	0.1428	1/7	[4,-1]		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	0.143	1/7	[4,-1]		0	0	Your answer contains the wrong number of significant digits. The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_WrongDigits. ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	0.14284	1/7	[4,-1]		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	0.14285	1/7	[4,-1]		1	1
NumSigFigs	Pass	0.14286	1/7	[4,-1]		1	1
NumSigFigs	Pass	0.14291	1/7	[4,-1]		1	1
NumSigFigs	Pass	0.14294	1/7	[4,-1]		1	1
NumSigFigs	Pass	0.14295	1/7	[4,-1]		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	0.142	1/7	[2,-1]		1	1
NumSigFigs	Pass	0.14290907676	1/7	[2,-1]		1	1
NumSigFigs	Pass	0.143	1/7	[2,-1]		1	1
NumSigFigs	Pass	0.1433333	1/7	[2,-1]		1	1
NumSigFigs	Pass	0.144	1/7	[2,-1]		1	1
NumSigFigs	Pass	0.145	1/7	[2,-1]		1	1
NumSigFigs	Pass	0.146	1/7	[2,-1]		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
Logarithms, numbers and surds
NumSigFigs	Pass	1.279	ev(lg(19),lg=logbasesimp)	4		1	1
NumSigFigs	Pass	3.14	pi	3		1	1
NumSigFigs	Pass	3.15	pi	3		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate.
NumSigFigs	Pass	1.73205	sqrt(3)	6		1	1
No support for matrices!
NumSigFigs	Expected failure	matrix([0.33,1],[1,1])	matrix([0.333,1],[1,1])	2		0	-1	Your answer should be a decimal number, but is not!	ATNumSigFigs_NotDecimal.
NumSigFigs	Expected failure	3.1415	matrix([0.333,1],[1,1])	2	TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. sigfigsfun(x,n,d) requires a real number, or a list of real numbers, as a first argument. Received: matrix([0.333,1],[1,1])	TEST_FAILED
Teacher uses dispsf
NumSigFigs	Pass	1.50	dispsf(1.500,3)	3		1	1
NumSigFigs	Pass	1.50	dispdp(1.500,3)	3		1	1

Basic tests
NumDecPlaces	Expected failure	1/0	3	2		0	-1		ATNumDecPlaces_STACKERROR_SAns.
NumDecPlaces	Expected failure	0.1	1/0	2		0	-1		ATNumDecPlaces_STACKERROR_TAns.
NumDecPlaces	Expected failure	0.1	0	1/0		0	-1		ATNumDecPlaces_STACKERROR_Opt.
NumDecPlaces	Expected failure	0.1	1	x		0	-1	For ATNumDecPlaces the test option must be a positive integer, in fact "\$x\$" was received.	ATNumDecPlaces_OptNotInt.
NumDecPlaces	Expected failure	0.1	1	-1		0	-1	For ATNumDecPlaces the test option must be a positive integer, in fact "\$-1\$" was received.	ATNumDecPlaces_OptNotInt.
NumDecPlaces	Expected failure	0.1	1	0		0	-1	For ATNumDecPlaces the test option must be a positive integer, in fact "\$0\$" was received.	ATNumDecPlaces_OptNotInt.
NumDecPlaces	Expected failure	0.1	1	(	TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Option field is invalid. You have a missing right bracket ) in the expression: (.	STACKERROR_OPTION.
NumDecPlaces	Expected failure	(	1	1	The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question.	0	-1	The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question.	ATNumDecPlacesTEST_FAILED-Empty SA.
Student's answer not a floating point number
NumDecPlaces	Pass	x	3.143	2		0	0	Your answer must be a floating point number, but is not.	ATNumDecPlaces_SA_Not_num.
NumDecPlaces	Pass	pi	3.000	3		0	0	Your answer must be a floating point number, but is not.	ATNumDecPlaces_SA_Not_num.
Right number of places
NumDecPlaces	Pass	3.14	3.143	2		1	1		ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.
NumDecPlaces	Pass	3.14	3.14	2		1	1		ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.
NumDecPlaces	Pass	3.140	3.140	3		1	1		ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.
NumDecPlaces	Pass	3141.5972	3141.5972	4		1	1		ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.
NumDecPlaces	Pass	4.14	3.14	2		0	0		ATNumDecPlaces_Correct. ATNumDecPlaces_Not_equiv.
NumDecPlaces	Pass	3.1416	pi	4		1	1		ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.
NumDecPlaces	Pass	-7.3	-7.3	1		1	1		ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.
Wrong number of places
NumDecPlaces	Pass	3.14	3.143	1		0	0	Your answer has been given to the wrong number of decimal places.	ATNumDecPlaces_Wrong_DPs. ATNumDecPlaces_Equiv.
NumDecPlaces	Pass	3.14	3.143	1		0	0	Your answer has been given to the wrong number of decimal places.	ATNumDecPlaces_Wrong_DPs. ATNumDecPlaces_Equiv.
NumDecPlaces	Pass	3.14	3.140	3		0	0	Your answer has been given to the wrong number of decimal places.	ATNumDecPlaces_Wrong_DPs. ATNumDecPlaces_Equiv.
NumDecPlaces	Pass	7.000	7	4		0	0	Your answer has been given to the wrong number of decimal places.	ATNumDecPlaces_Wrong_DPs. ATNumDecPlaces_Equiv.
NumDecPlaces	Pass	7.0000	7	4		1	1		ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.
Both wrong DPs and inaccurate.
NumDecPlaces	Pass	8.0000	7	3		0	0	Your answer has been given to the wrong number of decimal places.	ATNumDecPlaces_Wrong_DPs. ATNumDecPlaces_Not_equiv.
Teacher needs to round their answer.
NumDecPlaces	Pass	4.000	3.99999	3		1	1		ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.
Teacher uses displaydp
NumDecPlaces	Pass	0.10	displaydp(0.1,2)	2		1	1		ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.

Basic tests
NumDecPlacesWrong	Expected failure	1/0	3	2		0	-1		ATNumDecPlacesWrong_STACKERROR_SAns.
NumDecPlacesWrong	Expected failure	0.1	1/0	2		0	-1		ATNumDecPlacesWrong_STACKERROR_TAns.
NumDecPlacesWrong	Expected failure	0.1	0	1/0		0	-1		ATNumDecPlacesWrong_STACKERROR_Opt.
NumDecPlacesWrong	Expected failure	0.1	0	x		0	-1	For ATNumDecPlacesWrong the test option must be a positive integer, in fact "\$x\$" was received.	ATNumDecPlacesWrong_OptNotInt.
NumDecPlacesWrong	Pass	x^2	1234	4		0	0	Your answer must be a floating point number, but is not.	ATNumDecPlacesWrong_SA_Not_num.
NumDecPlacesWrong	Pass	1234.5	x^2	4		0	0		ATNumDecPlacesWrong_Tans_Not_Num.
NumDecPlacesWrong	Pass	3.141	31.41	4		1	1		ATNumDecPlacesWrong_Correct.
NumDecPlacesWrong	Pass	3.141	31.14	4		0	0		ATNumDecPlacesWrong_Wrong.
NumDecPlacesWrong	Pass	pi	31.14	4		0	0	Your answer must be a floating point number, but is not.	ATNumDecPlacesWrong_SA_Not_num.
NumDecPlacesWrong	Pass	0.1234	1234	4		1	1		ATNumDecPlacesWrong_Correct.
NumDecPlacesWrong	Pass	0.1235	1234	4		0	0		ATNumDecPlacesWrong_Wrong.
NumDecPlacesWrong	Pass	0.0001234	1234	4		1	1		ATNumDecPlacesWrong_Correct.
NumDecPlacesWrong	Pass	0.0001235	1234	4		0	0		ATNumDecPlacesWrong_Wrong.
NumDecPlacesWrong	Pass	0.1233	1234	3		1	1		ATNumDecPlacesWrong_Correct.
NumDecPlacesWrong	Pass	0.1243	1234	3		0	0		ATNumDecPlacesWrong_Wrong.
NumDecPlacesWrong	Pass	0.1230	1239	3		1	1		ATNumDecPlacesWrong_Correct.
NumDecPlacesWrong	Pass	0.1240	1239	3		0	0		ATNumDecPlacesWrong_Wrong.
NumDecPlacesWrong	Pass	1230	1239	3		1	1		ATNumDecPlacesWrong_Correct.
NumDecPlacesWrong	Pass	2230	1239	3		0	0		ATNumDecPlacesWrong_Wrong.
NumDecPlacesWrong	Pass	0.100	1.00	3		1	1		ATNumDecPlacesWrong_Correct.
NumDecPlacesWrong	Pass	0.1000	1.00	3		1	1		ATNumDecPlacesWrong_Correct.
NumDecPlacesWrong	Pass	0.1001	1.001	3		1	1		ATNumDecPlacesWrong_Correct.
Condone lack of trailing zeros
NumDecPlacesWrong	Pass	0.100	1.0	4		1	1		ATNumDecPlacesWrong_Correct.
NumDecPlacesWrong	Pass	1	1.00	4		1	1		ATNumDecPlacesWrong_Correct.
Teacher uses displaydp
NumDecPlacesWrong	Pass	0.101	displaydp(101,3)	3		1	1		ATNumDecPlacesWrong_Correct.

Basic tests
SigFigsStrict	Expected failure	3.141	null		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test.	STACKERROR_OPTION.
SigFigsStrict	Expected failure	3.141	null	x^2		0	-1		STACKERROR_OPTION.
SigFigsStrict	Expected failure	3.141	null	-2		0	-1		STACKERROR_OPTION.
SigFigsStrict	Expected failure	3.141	null	0		0	-1		STACKERROR_OPTION.
SigFigsStrict	Pass	0.0010	null	1		0	0
SigFigsStrict	Pass	0.0010	null	2		1	1
SigFigsStrict	Pass	0.0010	null	3		0	0
SigFigsStrict	Pass	0.00100	null	2		0	0
SigFigsStrict	Pass	0.00100	null	3		1	1
SigFigsStrict	Pass	0.00100	null	4		0	0
SigFigsStrict	Pass	0.001	null	1		1	1
SigFigsStrict	Pass	0.001	null	2		0	0
SigFigsStrict	Pass	100	null	1		1	1
SigFigsStrict	Pass	100	null	2		0	0		ATSigFigsStrict_WithinRange.
SigFigsStrict	Pass	100	null	3		0	0		ATSigFigsStrict_WithinRange.
SigFigsStrict	Pass	100	null	4		0	0
SigFigsStrict	Pass	100.	null	1		0	0
SigFigsStrict	Pass	100.	null	2		0	0
SigFigsStrict	Pass	100.	null	3		1	1
SigFigsStrict	Pass	100.	null	4		0	0
SigFigsStrict	Pass	123.	null	1		0	0
SigFigsStrict	Pass	123.	null	2		0	0
SigFigsStrict	Pass	123.	null	3		1	1
SigFigsStrict	Pass	123.	null	4		0	0
SigFigsStrict	Pass	1.00e2	null	1		0	0
SigFigsStrict	Pass	1.00e2	null	2		0	0
SigFigsStrict	Pass	1.00e2	null	3		1	1
SigFigsStrict	Pass	1.00e2	null	4		0	0
SigFigsStrict	Pass	10.0	null	2		0	0
SigFigsStrict	Pass	10.0	null	3		1	1
SigFigsStrict	Pass	10.0	null	4		0	0
SigFigsStrict	Pass	0	null	1		1	1
SigFigsStrict	Pass	0	null	2		0	0
SigFigsStrict	Pass	0.0	null	1		1	1
SigFigsStrict	Pass	0.0	null	2		0	0
SigFigsStrict	Pass	.0	null	1		1	1
SigFigsStrict	Pass	.0	null	2		0	0
SigFigsStrict	Pass	.001030	null	4		1	1
SigFigsStrict	Pass	0.00	null	1		0	0
SigFigsStrict	Pass	0.00	null	2		1	1
SigFigsStrict	Pass	0.00	null	3		0	0
SigFigsStrict	Pass	25.00e1	null	1		0	0
SigFigsStrict	Pass	25.00e1	null	3		0	0
SigFigsStrict	Pass	25.00e1	null	4		1	1
SigFigsStrict	Pass	25.00e1	null	5		0	0
SigFigsStrict	Pass	15.1	15.1	3		1	1
SigFigsStrict	Pass	15.10	15.1	3		0	0
SigFigsStrict	Pass	15.100	15.1	3		0	0
Units are ignored
SigFigsStrict	Pass	9.81*m/s^2	null	3		1	1

Units	Expected failure	1/0	1	2	TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATUnits_STACKERROR_SAns.
Units	Expected failure	1	1/0	2	TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATUnits_STACKERROR_TAns.
Units	Expected failure	1	1	1/0	TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATUnits_STACKERROR_Opt.
Units	Expected failure	x-1)^2	(x-1)^2	2	The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question.	0	-1	The answer test failed to execute correctly: please alert your teacher. Attempted to execute an answer test with an empty student answer, probably a CAS validation problem when authoring the question.	ATUnitsTEST_FAILED-Empty SA.
Units	Expected failure	12.3ms^(-1)	3*m	[3,x]		0	-1	The answer test failed to execute correctly: please alert your teacher.	ATNumSigFigs_STACKERROR_not_integer.
Units	Expected failure	3ms^(-1)	3*m	[1,2,3]		0	-1	The answer test failed to execute correctly: please alert your teacher.	ATNumSigFigs_STACKERROR_list_wrong_length.
Units	Expected failure	12.3ms^(-1)	{12.3ms^(-1)}	3		0	-1	The answer test failed to execute correctly: please alert your teacher.	ATUnits_TA_not_expression.
Units	Pass	x=12.3ms^(-1)	12.3ms^(-1)	3		0	0	Your answer needs to be a number together with units. Do not use sets, lists, equations or matrices.	ATUnits_SA_not_expression.
Missing units
Units	Pass	12.3	12.3*m	3		0	0	Your answer must have units.	ATUnits_SA_no_units.
Units	Pass	12	12.3*m	3		0	0	Your answer must have units.	ATUnits_SA_no_units.
Units	Pass	1/2	12.3*m	3		0	0	Your answer must have units.	ATUnits_SA_no_units.
Units	Pass	e^(1/2)	12.3*m	3		0	0	Your answer must have units.	ATUnits_SA_no_units.
Units	Expected failure	9.81*m	12.3	3		0	-1	The answer test failed to execute correctly: please alert your teacher.	ATUnits_SB_no_units.
Only units
Units	Pass	m/s	12.3*m/s	3		0	0	Your answer needs to be a number together with units. Your answer only has units.	ATUnits_SA_only_units.
Units	Pass	m	12.3*m/s	3		0	0	Your answer needs to be a number together with units. Your answer only has units.	ATUnits_SA_only_units.
Bad units
Units	Pass	9.81+m/s	9.81*m/s	3		0	0	Your answer must have units, and you must use multiplication to attach the units to a value, e.g. `3.2*m/s`.	ATUnits_SA_bad_units.
Basic tests
Units	Pass	12.3*m/s	12.3*m/s	3		1	1		ATUnits_units_match.
Units	Pass	12.4*m/s	12.3*m/s	3		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate. ATUnits_units_match.
Units	Pass	12.4*m/s	12.3*m/s	[3,2]		1	1		ATUnits_units_match.
Units	Pass	12.45*m/s	12.3*m/s	[3,2]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATUnits_units_match.
Units	Pass	13.45*m/s	12.3*m/s	[3,2]		0	0	Your answer contains the wrong number of significant digits. The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_WrongDigits. ATNumSigFigs_Inaccurate. ATUnits_units_match.
Units	Pass	7.54E-5(sM)^-1	5.625E-5*s^-1	[3,2]		0	0	Your units are incompatible with those used by the teacher.	ATNumSigFigs_VeryInaccurate. ATUnits_incompatible_units.
Units	Pass	7.54E-5(sM)^-1	stackunits(5.625E-5,1/s)	[3,2]		0	0	Your units are incompatible with those used by the teacher.	ATNumSigFigs_VeryInaccurate. ATUnits_incompatible_units.
Units	Pass	12*m/s	12.3*m/s	3		0	0	Your answer contains the wrong number of significant digits. The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_WrongDigits. ATNumSigFigs_Inaccurate. ATUnits_units_match.
Units	Pass	-9.81*m/s^2	-9.81*m/s^2	3		1	1		ATUnits_units_match.
Units	Pass	-9.82*m/s^2	-9.815*m/s^2	3		1	1		ATUnits_units_match.
Units	Pass	-9.81*m/s^2	-9.815*m/s^2	3		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate. ATUnits_units_match.
Units	Pass	-9.81ms^(-2)	-9.81*m/s^2	3		1	1		ATUnits_units_match.
Units	Pass	-9.82*m/s^2	-9.81*m/s^2	3		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate. ATUnits_units_match.
Units	Pass	-9.81ms^(-2)	-9.81*m/s^2	3		1	1		ATUnits_units_match.
Units	Pass	-9.81*m/s/s	-9.81*m/s^2	3		1	1		ATUnits_units_match.
Units	Pass	-9.81*m/s	-9.81*m/s^2	3		0	0	Your units are incompatible with those used by the teacher. Please check your units carefully.	ATUnits_incompatible_units. ATUnits_correct_numerical.
Units	Pass	-9.81*m/s	-9.81*m/s^2	3		0	0	Your units are incompatible with those used by the teacher. Please check your units carefully.	ATUnits_incompatible_units. ATUnits_correct_numerical.
Units	Pass	(-9.81)*m/s^2	-9.81*m/s^2	3		1	1		ATUnits_units_match.
Units	Pass	520*amu	520*amu	3		1	1		ATNumSigFigs_WithinRange. ATUnits_units_match.
Units	Pass	520*amu	521*amu	3		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_WithinRange. ATNumSigFigs_Inaccurate. ATUnits_units_match.
Missing units
Units	Pass	(-9.81)	-9.81*m/s^2	3		0	0	Your answer must have units.	ATUnits_SA_no_units.
Units	Pass	9.81*m/s	-9.81*m/s^2	3		0	0	Your answer has the wrong algebraic sign. Your units are incompatible with those used by the teacher.	ATNumSigFigs_WrongSign. ATUnits_incompatible_units.
Units	Pass	8.81*m/s	-9.81*m/s^2	3		0	0	Your answer has the wrong algebraic sign. Your units are incompatible with those used by the teacher.	ATNumSigFigs_WrongSign. ATNumSigFigs_VeryInaccurate. ATUnits_incompatible_units.
Units	Pass	8.1*m/s	-9.81*m/s^2	3		0	0	Your answer contains the wrong number of significant digits. Your answer has the wrong algebraic sign. Your units are incompatible with those used by the teacher.	ATNumSigFigs_WrongDigits. ATNumSigFigs_WrongSign. ATNumSigFigs_VeryInaccurate. ATUnits_incompatible_units.
Units	Pass	m/4	0.25*m	3		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATUnits_units_match.
Student is too exact
Units	Pass	pi*s	3.14*s	3		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATUnits_units_match.
Units	Pass	sqrt(2)*m	1.41*m	3		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATUnits_units_match.
Different units
Units	Pass	25*g	0.025*kg	2		1	1		ATUnits_compatible_units kg.
Units	Pass	26*g	0.025*kg	2		0	0	The accuracy of your answer is not correct. Either you have not rounded correctly, or you have rounded an intermediate answer which propagates an error.	ATNumSigFigs_Inaccurate. ATUnits_compatible_units kg.
Units	Pass	100*g	10*kg	2		0	0		ATNumSigFigs_WithinRange. ATNumSigFigs_VeryInaccurate. ATUnits_compatible_units kg.
Units	Pass	0.025*g	0.025*kg	2		0	0	Please check your units carefully.	ATUnits_compatible_units kg. ATUnits_correct_numerical.
Units	Pass	1000*m	1*km	2		1	1		ATNumSigFigs_WithinRange. ATUnits_compatible_units m.
Units	Pass	1*Mg/10^6	1Ns^2/(km)	1		1	1		ATUnits_compatible_units kg.
Units	Pass	1*Mg/10^6	1kNns/(mm*Hz)	1		1	1		ATUnits_compatible_units kg.
Units	Pass	3.14*Mg/10^6	%pikNns/(mm*Hz)	3		1	1		ATUnits_compatible_units kg.
Units	Pass	3.141*Mg/10^6	%pikNns/(mm*Hz)	3		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATUnits_compatible_units kg.
Units	Pass	4.141*Mg/10^6	%pikNns/(mm*Hz)	3		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATNumSigFigs_VeryInaccurate. ATUnits_compatible_units kg.
Units	Pass	400*cc	0.4*l	2		1	1		ATNumSigFigs_WithinRange. ATUnits_compatible_units m^3.
Units	Pass	400*cm^3	0.4*l	2		1	1		ATNumSigFigs_WithinRange. ATUnits_compatible_units m^3.
Units	Pass	400*ml	0.4*l	2		1	1		ATNumSigFigs_WithinRange. ATUnits_compatible_units m^3.
Units	Pass	18*kJ	18000.0*J	2		1	1		ATUnits_compatible_units (kg*m^2)/s^2.
Units	Pass	18.1*kJ	18000.0*J	2		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATUnits_compatible_units (kg*m^2)/s^2.
Units	Pass	120*kWh	0.12*MWh	2		1	1		ATUnits_compatible_units (kg*m^2)/s^2.
Units	Pass	2.0*hh	720000*s	2		1	1		ATUnits_compatible_units s.
Units	Pass	723*kVA	0.723*MVA	3		1	1		ATUnits_compatible_units (kg*m^2)/s^3.
Edge case
Units	Pass	0*m/s	0*m/s	1		1	1		ATUnits_units_match.
Units	Pass	0.0*m/s	0*m/s	1		1	1		ATUnits_units_match.
Units	Pass	0*m/s	0.0*m/s	1		1	1		ATUnits_units_match.
Units	Pass	0.00*m/s	0.0*m/s	2		1	1		ATUnits_units_match.
Units	Pass	0.0*km/s	0.0*m/s	1		1	1		ATUnits_compatible_units m/s.
Units	Pass	0.0*m	0.0*m/s	1		0	0	Your units are incompatible with those used by the teacher. Please check your units carefully.	ATUnits_incompatible_units. ATUnits_correct_numerical.
Units	Pass	0.0	0.0*m/s	1		0	0	Your answer must have units.	ATUnits_SA_no_units.
Imperial
Units	Pass	7*in	7*in	1		1	1		ATUnits_units_match.
Units	Pass	6*in	0.5*ft	1		1	1		ATUnits_compatible_units in.
Units	Pass	2640*ft	0.5*mi	4		1	1		ATNumSigFigs_WithinRange. ATUnits_compatible_units in.
Units	Pass	2650*ft	0.5*mi	4		0	0		ATNumSigFigs_WithinRange. ATNumSigFigs_VeryInaccurate. ATUnits_compatible_units in.
TODO
Units	Pass	142.8*C	415.9*K	4		0	-3	Your units are incompatible with those used by the teacher.	ATNumSigFigs_VeryInaccurate. ATUnits_incompatible_units.
Units	Pass	520*mamu	520*mamu	3		0	-3	The answer test failed to execute correctly: please alert your teacher.	ATUnits_SB_no_units.

Differences from the Units test only
UnitsStrict	Pass	25*g	0.025*kg	2		0	0		ATUnits_compatible_units kg.
UnitsStrict	Pass	1*Mg/10^6	1Ns^2/(km)	1		0	0		ATUnits_compatible_units kg.
UnitsStrict	Pass	1*Mg/10^6	1kNns/(mm*Hz)	1		0	0		ATUnits_compatible_units kg.
UnitsStrict	Pass	3.14*Mg/10^6	%pikNns/(mm*Hz)	3		0	0		ATUnits_compatible_units kg.
UnitsStrict	Pass	400*cc	0.4*l	2		0	0		ATNumSigFigs_WithinRange. ATUnits_compatible_units m^3.
UnitsStrict	Pass	400*cm^3	0.4*l	2		0	0		ATNumSigFigs_WithinRange. ATUnits_compatible_units m^3.
UnitsStrict	Pass	400*ml	0.4*l	2		0	0		ATNumSigFigs_WithinRange. ATUnits_compatible_units m^3.
UnitsStrict	Pass	400*mL	0.4*l	2		0	0		ATNumSigFigs_WithinRange. ATUnits_compatible_units m^3.
UnitsStrict	Pass	142.8*C	415.9*K	4		0	0		ATNumSigFigs_VeryInaccurate. ATUnits_incompatible_units.
We are not that strict!
UnitsStrict	Pass	-9.81*m/s/s	-9.81*m/s^2	3		1	1		ATUnits_units_match.
Edge case
UnitsStrict	Pass	0*m/s	0*m/s	1		1	1		ATUnits_units_match.
UnitsStrict	Pass	0.0*m/s	0*m/s	1		1	1		ATUnits_units_match.
UnitsStrict	Pass	0*m/s	0.0*m/s	1		1	1		ATUnits_units_match.
UnitsStrict	Pass	0.0*m/s	0.0*m/s	1		1	1		ATUnits_units_match.
UnitsStrict	Pass	0.0*km/s	0.0*m/s	1		0	0		ATUnits_compatible_units m/s.
UnitsStrict	Pass	0.0*m	0.0*m/s	1		0	0		ATUnits_incompatible_units. ATUnits_correct_numerical.
UnitsStrict	Pass	0.0	0.0*m/s	1		0	0	Your answer must have units.	ATUnits_SA_no_units.
UnitsStrict	Pass	2.33e-15*kg	2.33e-15*kg	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	7.03e-3*ng	7.03e-3*ng	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	2.35e-6*ug	2.35e-6*ug	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	9.83e-10*cg	9.83e-10*cg	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	9.73e-21*Gg	9.73e-21*Gg	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	7.19e-15*kg	7.19e-15*kg	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	8.12e-12*g	8.12e-12*g	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	9.34e-12*g	9.34e-12*g	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	1.07e-21*Gg	1.07e-21*Gg	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	1.91e-10*cg	1.91e-10*cg	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	5.67e-18*Mg	5.67e-18*Mg	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	2.04e-9*mg	2.04e-9*mg	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	6.75e-6*ug	6.75e-6*ug	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	6.58e-6*ug	6.58e-6*ug	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	3.58e-9*mg	3.58e-9*mg	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	9.99e-15*kg	9.99e-15*kg	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	9.8e-9*mg	9.8e-9*mg	[3,2]		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATUnits_units_match.
UnitsStrict	Pass	9.80e-9*mg	9.8e-9*mg	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	9.83e-9*mg	9.8e-9*mg	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	9.78e-9*mg	9.8e-9*mg	[3,2]		1	1		ATUnits_units_match.
UnitsStrict	Pass	36*Kj/mol	36*Kj/mol	2		1	1		ATUnits_units_match.
UnitsStrict	Pass	-36*Kj/mol	-36*Kj/mol	2		1	1		ATUnits_units_match.
UnitsStrict	Pass	(-36)*Kj/mol	-36*Kj/mol	2		1	1		ATUnits_units_match.
UnitsStrict	Pass	(-36*Kj)/mol	-36*Kj/mol	2		1	1		ATUnits_units_match.
UnitsStrict	Pass	-(36*Kj)/mol	-36*Kj/mol	2		1	1		ATUnits_units_match.
UnitsStrict	Pass	-(36.2*Kj)/mol	-36.3*Kj/mol	2		0	0	Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATUnits_units_match.

UnitsRelative	Pass	12.3*m/s	12.3*m/s	0.01		1	1		ATUnits_units_match.
UnitsRelative	Pass	12*m/s	12.3*m/s	0.01		0	0		ATUnits_units_match.
UnitsRelative	Pass	1.1*Mg/10^6	1.2kNns/(mm*Hz)	0.15		1	1		ATUnits_compatible_units kg.
UnitsRelative	Pass	1.1*Mg/10^6	1.2kNns/(mm*Hz)	0.05		0	0		ATUnits_compatible_units kg.
Edge case
UnitsRelative	Pass	0*m/s	0*m/s	0.01		1	1		ATUnits_units_match.
UnitsRelative	Pass	0.0*m/s	0*m/s	0.01		1	1		ATUnits_units_match.
UnitsRelative	Pass	0*m/s	0.0*m/s	0.01		1	1		ATUnits_units_match.
UnitsRelative	Pass	0.0*m/s	0.0*m/s	0.01		1	1		ATUnits_units_match.
UnitsRelative	Pass	0.0*km/s	0.0*m/s	0.01		1	1		ATUnits_compatible_units m/s.
UnitsRelative	Pass	0.0*m	0.0*m/s	0.01		0	0	Your units are incompatible with those used by the teacher. Please check your units carefully.	ATUnits_incompatible_units. ATUnits_correct_numerical.
UnitsRelative	Pass	0.0	0.0*m/s	0.01		0	0	Your answer must have units.	ATUnits_SA_no_units.
UnitsRelative	Pass	0.0*kVA	0.0*kVA	0.002		1	1		ATUnits_units_match.

UnitsStrictRelative	Pass	12.3*m/s	12.3*m/s	0.01		1	1		ATUnits_units_match.
UnitsStrictRelative	Pass	12*m/s	12.3*m/s	0.01		0	0		ATUnits_units_match.
UnitsStrictRelative	Pass	1.1*Mg/10^6	1.2kNns/(mm*Hz)	0.15		0	0		ATUnits_compatible_units kg.
UnitsStrictRelative	Pass	1.1*Mg/10^6	1.2kNns/(mm*Hz)	0.05		0	0		ATUnits_compatible_units kg.
Edge case
UnitsStrictRelative	Pass	0*m/s	0*m/s	0.01		1	1		ATUnits_units_match.
UnitsStrictRelative	Pass	0.0*m/s	0*m/s	0.01		1	1		ATUnits_units_match.
UnitsStrictRelative	Pass	0*m/s	0.0*m/s	0.01		1	1		ATUnits_units_match.
UnitsStrictRelative	Pass	0.0*m/s	0.0*m/s	0.01		1	1		ATUnits_units_match.
UnitsStrictRelative	Pass	0.0*km/s	0.0*m/s	0.01		0	0		ATUnits_compatible_units m/s.
UnitsStrictRelative	Pass	0.0*m	0.0*m/s	0.01		0	0		ATUnits_incompatible_units. ATUnits_correct_numerical.
UnitsStrictRelative	Pass	0.0	0.0*m/s	0.01		0	0	Your answer must have units.	ATUnits_SA_no_units.
UnitsStrictRelative	Pass	0*J	0.0*J	0.01		1	1		ATUnits_units_match.

UnitsAbsolute	Pass	-123000*J	-123*kJ	5*J		0	0	The units specified for the numerical tolerance must match the units used for the teacher's answer. This is an internal error with the test. Please ask your teacher about this.	ATUnits_SO_wrong_units.
UnitsAbsolute	Pass	12.3*m/s	12.3*m/s	0.01		1	1		ATUnits_units_match.
UnitsAbsolute	Pass	12*m/s	12.3*m/s	0.01		0	0		ATUnits_units_match.
UnitsAbsolute	Pass	1.1*Mg/10^6	1.2kNns/(mm*Hz)	0.15		1	1		ATUnits_compatible_units kg.
The following illustrates that we convert to base units to compare.
UnitsAbsolute	Pass	1.1*Mg/10^6	1.2kNns/(mm*Hz)	0.1		1	1		ATUnits_compatible_units kg.
UnitsAbsolute	Pass	1.1*Mg/10^6	1.2kNns/(mm*Hz)	0.09		0	0		ATUnits_compatible_units kg.
Units in the options
UnitsAbsolute	Pass	-123000*J	-123*kJ	5*kJ		1	1		ATUnits_compatible_units (kg*m^2)/s^2.
UnitsAbsolute	Pass	-123006*J	-123*kJ	5*kJ		1	1		ATUnits_compatible_units (kg*m^2)/s^2.
UnitsAbsolute	Pass	-129006*J	-123*kJ	5*kJ		0	0		ATUnits_compatible_units (kg*m^2)/s^2.
UnitsAbsolute	Pass	1.1*Mg/10^6	1.2kNns/(mm*Hz)	0.1kNns/(mm*Hz)		1	1		ATUnits_compatible_units kg.
UnitsAbsolute	Pass	1.1*Mg/10^6	1.2kNns/(mm*Hz)	0.09kNns/(mm*Hz)		0	0		ATUnits_compatible_units kg.
Edge case
UnitsAbsolute	Pass	0*m/s	0*m/s	0.01		1	1		ATUnits_units_match.
UnitsAbsolute	Pass	0.0*m/s	0*m/s	0.01		1	1		ATUnits_units_match.
UnitsAbsolute	Pass	0*m/s	0.0*m/s	0.01		1	1		ATUnits_units_match.
UnitsAbsolute	Pass	0.0*m/s	0.0*m/s	0.01		1	1		ATUnits_units_match.
UnitsAbsolute	Pass	0.0*km/s	0.0*m/s	0.01		1	1		ATUnits_compatible_units m/s.
UnitsAbsolute	Pass	0.0*m	0.0*m/s	0.01		0	0	Your units are incompatible with those used by the teacher. Please check your units carefully.	ATUnits_incompatible_units. ATUnits_correct_numerical.
UnitsAbsolute	Pass	0.0	0.0*m/s	0.01		0	0	Your answer must have units.	ATUnits_SA_no_units.
UnitsAbsolute	Pass	1.0*m/s	m/s	0.01		1	1		ATUnits_units_match.
UnitsAbsolute	Pass	15/pi*kN/mm^2	15/pi*kN/mm^2	0.01		1	1		ATUnits_units_match.
UnitsAbsolute	Pass	(15kN)/(pimm^2)	(15kN)/(pimm^2)	0.01		1	1		ATUnits_units_match.
UnitsAbsolute	Pass	(15/pi)*(kN/mm^2)	(15/pi)*(kN/mm^2)	0.01		1	1		ATUnits_units_match.
UnitsAbsolute	Pass	(600N)/(%pimm^2)	(600N)/(%pimm^2)	0.01		1	1		ATUnits_units_match.
UnitsAbsolute	Pass	(600/pi)*kN/m^2	(600/pi)*kN/m^2	0.01		1	1		ATUnits_units_match.
UnitsAbsolute	Pass	(600/pi)*kN/mm^2	(600/pi)*kN/mm^2	0.01		1	1		ATUnits_units_match.

String	Pass	Hello	hello			0	0
String	Pass	hello	hello			1	1
String	Pass	hello	heloo			0	0

StringSloppy	Pass	hello	Hello			1	1
StringSloppy	Pass	hel lo	Hello		TEST_FAILED	0	0	The answer test failed to execute correctly: please alert your teacher. Illegal spaces found in expression hel_lo.	ATStringSloppy_STACKERROR_SAns.
StringSloppy	Pass	hel lo	Hel*lo		TEST_FAILED	0	0	The answer test failed to execute correctly: please alert your teacher. Illegal spaces found in expression hel_lo.	ATStringSloppy_STACKERROR_SAns.
StringSloppy	Pass	hello	heloo			0	0

SRegExp	Expected failure	1/0	"hello"		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSRegExp_STACKERROR_SAns.
SRegExp	Expected failure	"1/0"	1/0		TEST_FAILED	0	-1	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSRegExp_STACKERROR_TAns.
SRegExp	Expected failure	Hello	hello			0	-1	The second argument to the SRegExp answer test must be a string. The test failed. Please contact your teacher.	ATSRegExp_SB_not_string.
SRegExp	Expected failure	Hello	"hello"			0	-1	The first argument to the SRegExp answer test must be a string. The test failed. Please contact your teacher.	ATSRegExp_SA_not_string.
SRegExp	Pass	"aaaaabbb"	"(aaa)*b"			1	1		ATSRegExp: ["aaab","aaa"].
SRegExp	Pass	"aab"	"(aaa)*b"			1	1		ATSRegExp: ["b",false].
SRegExp	Pass	"aaac"	"(aaa)*b"			0	0
Anchor pattern to the start and the end of the string
SRegExp	Pass	"aab"	"^[aA]*b$"			1	1		ATSRegExp: ["aab"].
SRegExp	Pass	"aab"	"^(aaa)*b$"			0	0
SRegExp	Pass	"aAb"	"^[aA]*b$"			1	1		ATSRegExp: ["aAb"].
SRegExp	Pass	" aAb"	"^[aA]*b$"			0	0
Case insensitive
SRegExp	Pass	"caAb"	"(?i:a*b)"			1	1		ATSRegExp: ["aAb"].
Options
SRegExp	Pass	"Alice went to the market"	"(Alice\|Bob) went to the (bank\|market)"			1	1		ATSRegExp: ["Alice went to the market","Alice","market"].
SRegExp	Pass	"Malice went to the shop"	"(Alice\|Bob) went to the (bank\|market)"			0	0
Whitespace, note test rendering issue, the test string has additional spaces and tabs as does the result
SRegExp	Pass	"Alice went to the market"	"(Alice\|Bob)\\\\s+went\\\\s+to\\\\s+the\\\\s+(bank\|market)"			1	1		ATSRegExp: ["Alice went to the market","Alice","market"].
SRegExp	Pass	"Alice went to themarket"	"(Alice\|Bob)\\\\s+went\\\\s+to\\\\s+the\\\\s+(bank\|market)"			0	0
Escaping patterns, note the function that does it
SRegExp	Pass	"x^2.2"	"x\\\\^2\\\\.2"			1	1		ATSRegExp: ["x^2.2"].
SRegExp	Pass	"x^2+sin(x)"	sconcat(string_to_regex("sin(x)"),"$")			1	1		ATSRegExp: ["sin(x)"].
SRegExp	Pass	"sin(x)+x^2"	sconcat(string_to_regex("sin(x)"),"$")			0	0

LowestTerms	Expected failure	1/0	0			0	-1		ATLowestTerms_STACKERROR_SAns.
Mix of floats and rational numbers
LowestTerms	Pass	0.5	0			1	1
LowestTerms	Pass	0.33	0			1	1
LowestTerms	Pass	2/4	0			0	0	The following terms in your answer are not in lowest terms. \\[\\left[ \\frac{2}{4} \\right] \\] Please try again.	ATLowestTerms_entries.
Negative numbers
LowestTerms	Pass	-1/3	0			1	1
LowestTerms	Pass	1/-3	0			1	1
LowestTerms	Pass	-2/4	0			0	0	The following terms in your answer are not in lowest terms. \\[\\left[ \\frac{-2}{4} \\right] \\] Please try again.	ATLowestTerms_entries.
LowestTerms	Pass	2/-4	0			0	0	The following terms in your answer are not in lowest terms. \\[\\left[ \\frac{2}{-4} \\right] \\] Please try again.	ATLowestTerms_entries.
LowestTerms	Pass	-1/-3	0			0	0	The following terms in your answer are not in lowest terms. \\[\\left[ \\frac{-1}{-3} \\right] \\] Please try again.	ATLowestTerms_entries.
LowestTerms	Pass	-2/-4	0			0	0	The following terms in your answer are not in lowest terms. \\[\\left[ \\frac{-2}{-4} \\right] \\] Please try again.	ATLowestTerms_entries.
Polynomials
LowestTerms	Pass	x+1/3	0			1	1
LowestTerms	Pass	x+2/6	0			0	0	The following terms in your answer are not in lowest terms. \\[\\left[ \\frac{2}{6} \\right] \\] Please try again.	ATLowestTerms_entries.
LowestTerms	Pass	2*x/4+2/6	0			0	0	The following terms in your answer are not in lowest terms. \\[\\left[ \\frac{2}{6} \\right] \\] Please try again.	ATLowestTerms_entries.
LowestTerms	Pass	2/4*x+2/6	0			0	0	The following terms in your answer are not in lowest terms. \\[\\left[ \\frac{2}{4} , \\frac{2}{6} \\right] \\] Please try again.	ATLowestTerms_entries.
LowestTerms	Pass	x-1/-4	0			0	0	The following terms in your answer are not in lowest terms. \\[\\left[ \\frac{-1}{-4} \\right] \\] Please try again.	ATLowestTerms_entries.
Trig functions
LowestTerms	Pass	cos(x)	0			1	1
LowestTerms	Pass	cos(3/6*x)	0			0	0	The following terms in your answer are not in lowest terms. \\[\\left[ \\frac{3}{6} \\right] \\] Please try again.	ATLowestTerms_entries.
Matrices
LowestTerms	Pass	matrix([1,2/4],[2,3])	0			0	0	The following terms in your answer are not in lowest terms. \\[\\left[ \\frac{2}{4} \\right] \\] Please try again.	ATLowestTerms_entries.
Equations
LowestTerms	Pass	x=1/2	0			1	1
LowestTerms	Pass	3/9=x	0			0	0	The following terms in your answer are not in lowest terms. \\[\\left[ \\frac{3}{9} \\right] \\] Please try again.	ATLowestTerms_entries.
Use predicate lowesttermsp
LowestTerms	Pass	x^2/x	0			1	1
LowestTerms	Pass	(2x)/(4t)	0			1	1
LowestTerms	Pass	(2/4)*(x^2/t)	0			0	0	The following terms in your answer are not in lowest terms. \\[\\left[ \\frac{2}{4} \\right] \\] Please try again.	ATLowestTerms_entries.
LowestTerms	Pass	x^(2/4)	0			0	0	The following terms in your answer are not in lowest terms. \\[\\left[ \\frac{2}{4} \\right] \\] Please try again.	ATLowestTerms_entries.
Need to rationalize demoninator
LowestTerms	Pass	sqrt(3)/3	sqrt(3)/3			1	1
LowestTerms	Pass	1/sqrt(3)	sqrt(3)/3			0	0	You must clear the following from the denominator of your fraction: \\[\\left[ \\sqrt{3} \\right] \\]	ATLowestTerms_not_rat.
LowestTerms	Pass	1/(1-sqrt(2))	1/(1-sqrt(2))			0	0	You must clear the following from the denominator of your fraction: \\[\\left[ \\sqrt{2} \\right] \\]	ATLowestTerms_not_rat.
LowestTerms	Pass	1/(1+i)	(1-i)/2			0	0	You must clear the following from the denominator of your fraction: \\[\\left[ \\mathrm{i} \\right] \\]	ATLowestTerms_not_rat.
LowestTerms	Pass	1+2/sqrt(3)	(2*sqrt(3)+3)/3			0	0	You must clear the following from the denominator of your fraction: \\[\\left[ \\sqrt{3} \\right] \\]	ATLowestTerms_not_rat.
LowestTerms	Pass	1/(1+1/root(3,2))	sqrt(3)/(sqrt(3)+1)			0	0	You must clear the following from the denominator of your fraction: \\[\\left[ 3^{\\frac{1}{2}} \\right] \\]	ATLowestTerms_not_rat.
LowestTerms	Pass	1/(1+1/root(2,3))	1/(1+1/root(2,3))			0	0	You must clear the following from the denominator of your fraction: \\[\\left[ 2^{\\frac{1}{3}} \\right] \\]	ATLowestTerms_not_rat.

Equiv	Pass	[]	[]			1	1	\\[\\begin{array}{lll} &\\left[ \\right] & \\cr \\end{array}\\]	[EMPTYCHAR]
Equiv	Pass	[x^2=-1]	[]			1	1	\\[\\begin{array}{lll} &x^2=-1& \\cr \\end{array}\\]	[EMPTYCHAR]
Equiv	Pass	[x=x,all]	[]			1	1	\\[\\begin{array}{lll} &x=x& \\cr \\color{green}{\\Leftrightarrow}&\\mathbb{R}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[x=x,true]	[]			1	1	\\[\\begin{array}{lll} &x=x& \\cr \\color{green}{\\Leftrightarrow}&\\mathbf{True}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[x=x,false]	[]			0	0	\\[\\begin{array}{lll} &x=x& \\cr \\color{red}{?}&\\mathbf{False}& \\cr \\end{array}\\]	[EMPTYCHAR,QMCHAR]
Equiv	Pass	[1=1,all]	[]			1	1	\\[\\begin{array}{lll} &1=1& \\cr \\color{green}{\\Leftrightarrow}&\\mathbb{R}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[1=1,true]	[]			1	1	\\[\\begin{array}{lll} &1=1& \\cr \\color{green}{\\Leftrightarrow}&\\mathbf{True}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[0=0,all]	[]			1	1	\\[\\begin{array}{lll} &0=0& \\cr \\color{green}{\\Leftrightarrow}&\\mathbb{R}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[0=0,true]	[]			1	1	\\[\\begin{array}{lll} &0=0& \\cr \\color{green}{\\Leftrightarrow}&\\mathbf{True}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[1=2,false]	[]			1	1	\\[\\begin{array}{lll} &1=2& \\cr \\color{green}{\\Leftrightarrow}&\\mathbf{False}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[1=2,none]	[]			1	1	\\[\\begin{array}{lll} &1=2& \\cr \\color{green}{\\Leftrightarrow}&\\emptyset& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[1=2,{}]	[]			1	1	\\[\\begin{array}{lll} &1=2& \\cr \\color{green}{\\Leftrightarrow}&\\left \\{ \\right \\}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[1=2,[]]	[]			1	1	\\[\\begin{array}{lll} &1=2& \\cr \\color{green}{\\Leftrightarrow}&\\left[ \\right] & \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[x=1,X=1]	[]			0	0	\\[\\begin{array}{lll} &x=1& \\cr \\color{red}{?}&X=1& \\cr \\end{array}\\]	[EMPTYCHAR,QMCHAR]
Equiv	Pass	[1/(x^2+1)=1/((x+%i)*(x-%i)),true]	[]			1	1	\\[\\begin{array}{lll} &\\frac{1}{x^2+1}=\\frac{1}{\\left(x+\\mathrm{i}\\right)\\cdot \\left(x-\\mathrm{i}\\right)}& \\cr \\color{green}{\\Leftrightarrow}&\\mathbf{True}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[2^2,stackeq(4)]	[]			1	1	\\[\\begin{array}{lll} &2^2& \\cr \\color{green}{\\checkmark}&=4& \\cr \\end{array}\\]	[EMPTYCHAR, CHECKMARK]
Equiv	Pass	[2^2,stackeq(3)]	[]			0	0	\\[\\begin{array}{lll} &2^2& \\cr \\color{red}{\\Rightarrow}&=3& \\cr \\end{array}\\]	[EMPTYCHAR,IMPLIESCHAR]
Equiv	Pass	[2^2,4]	[]			1	1	\\[\\begin{array}{lll} &2^2& \\cr \\color{green}{\\Leftrightarrow}&4& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[2^2,3]	[]			0	0	\\[\\begin{array}{lll} &2^2& \\cr \\color{red}{\\Rightarrow}&3& \\cr \\end{array}\\]	[EMPTYCHAR,IMPLIESCHAR]
Equiv	Pass	[lg(64,4),lg(4^3,4),3*lg(4,4),3]	[]			1	1	\\[\\begin{array}{lll} &\\log_{4}\\left(64\\right)& \\cr \\color{green}{\\Leftrightarrow}&\\log_{4}\\left(4^3\\right)& \\cr \\color{green}{\\Leftrightarrow}&3\\cdot \\log_{4}\\left(4\\right)& \\cr \\color{green}{\\Leftrightarrow}&3& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[lg(64,4),stackeq(lg(4^3,4)),stackeq(3*lg(4,4)),stackeq(3)]	[]			1	1	\\[\\begin{array}{lll} &\\log_{4}\\left(64\\right)& \\cr \\color{green}{\\checkmark}&=\\log_{4}\\left(4^3\\right)& \\cr \\color{green}{\\checkmark}&=3\\cdot \\log_{4}\\left(4\\right)& \\cr \\color{green}{\\checkmark}&=3& \\cr \\end{array}\\]	[EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK]
Equiv	Pass	[x=1 or x=2,x=1 or 2]	[]			0	0	\\[\\begin{array}{lll} &x=1\\,{\\mbox{ or }}\\, x=2& \\cr \\color{red}{\\mbox{Missing assignments}}&x=1\\,{\\mbox{ or }}\\, 2& \\cr \\end{array}\\]	[EMPTYCHAR,MISSINGVAR]
Equiv	Pass	[x=1 or x=2,x=1 and x=2]	[]			0	0	\\[\\begin{array}{lll} &x=1\\,{\\mbox{ or }}\\, x=2& \\cr \\color{red}{\\mbox{and/or confusion!}}&\\left\\{\\begin{array}{l}x=1\\cr x=2\\cr \\end{array}\\right.& \\cr \\end{array}\\]	[EMPTYCHAR,ANDOR]
Equiv	Pass	[x=1 and y=2,x=1 or y=2]	[]			0	0	\\[\\begin{array}{lll} &\\left\\{\\begin{array}{l}x=1\\cr y=2\\cr \\end{array}\\right.& \\cr \\color{red}{\\mbox{and/or confusion!}}&x=1\\,{\\mbox{ or }}\\, y=2& \\cr \\end{array}\\]	[EMPTYCHAR,ANDOR]
Equiv	Pass	[a=b,a^2=b^2]	[]			0	0	\\[\\begin{array}{lll} &a=b& \\cr \\color{red}{\\Rightarrow}&a^2=b^2& \\cr \\end{array}\\]	[EMPTYCHAR,IMPLIESCHAR]
Equiv	Pass	[a=b,sqrt(a)=sqrt(b)]	[]			0	0	\\[\\begin{array}{lll} &a=b& \\cr \\color{red}{\\Leftarrow}&\\sqrt{a}=\\sqrt{b}& \\cr \\end{array}\\]	[EMPTYCHAR,IMPLIEDCHAR]
Equiv	Pass	[a^2=b^2,a=b]	[]			0	0	\\[\\begin{array}{lll} &a^2=b^2& \\cr \\color{red}{\\Leftarrow}&a=b& \\cr \\end{array}\\]	[EMPTYCHAR,IMPLIEDCHAR]
Equiv	Pass	[a^2=b^2,a=b or a=-b]	[]			1	1	\\[\\begin{array}{lll} &a^2=b^2& \\cr \\color{green}{\\Leftrightarrow}&a=b\\,{\\mbox{ or }}\\, a=-b& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[a^2=b^2,a= #pm#b,a= b or a=-b]	[]			1	1	\\[\\begin{array}{lll} &a^2=b^2& \\cr \\color{green}{\\Leftrightarrow}&a= \\pm b& \\cr \\color{green}{\\Leftrightarrow}&a=b\\,{\\mbox{ or }}\\, a=-b& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[a=b,abs(a)=abs(b),a=b]	[]			0	0	\\[\\begin{array}{lll} &a=b& \\cr \\color{red}{\\Rightarrow}&\\left\| a\\right\| =\\left\| b\\right\| & \\cr \\color{red}{\\Leftarrow}&a=b& \\cr \\end{array}\\]	[EMPTYCHAR,IMPLIESCHAR,IMPLIEDCHAR]
Equiv	Pass	[abs(a)=abs(b),a=b or a=-b]	[]			1	1	\\[\\begin{array}{lll} &\\left\| a\\right\| =\\left\| b\\right\| & \\cr \\color{green}{\\Leftrightarrow}&a=b\\,{\\mbox{ or }}\\, a=-b& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[abs(a)=abs(b),a^2=b^2]	[]			1	1	\\[\\begin{array}{lll} &\\left\| a\\right\| =\\left\| b\\right\| & \\cr \\color{green}{\\Leftrightarrow}&a^2=b^2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[x^3=8,x=2]	[]			0	0	\\[\\begin{array}{lll} &x^3=8& \\cr \\color{red}{\\Leftarrow}&x=2& \\cr \\end{array}\\]	[EMPTYCHAR,IMPLIEDCHAR]
Equiv	Pass	[x^3=8,x=2]	[]	[assumereal]		1	1	\\[\\begin{array}{lll}\\color{blue}{(\\mathbb{R})}&x^3=8& \\cr \\color{green}{\\Leftrightarrow}\\, \\color{blue}{(\\mathbb{R})}&x=2& \\cr \\end{array}\\]	[ASSUMEREALVARS, EQUIVCHARREAL]
Equiv	Pass	[abs(x-1/2)+abs(x+1/2)=2,abs(x)=1]	[]			1	1	\\[\\begin{array}{lll} &\\left\| x-\\frac{1}{2}\\right\| +\\left\| x+\\frac{1}{2}\\right\| =2& \\cr \\color{green}{\\Leftrightarrow}&\\left\| x\\right\| =1& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[a^2=9 and a>0,a=3]	[]			1	1	\\[\\begin{array}{lll} &\\left\\{\\begin{array}{l}a^2=9\\cr a > 0\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&a=3& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[T=2pisqrt(L/g),T^2=4pi^2L/g,g=4pi^2L/T^2]	[]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&T=2\\cdot \\pi\\cdot \\sqrt{\\frac{L}{g}}& \\cr \\color{green}{\\Leftrightarrow}&T^2=\\frac{4\\cdot \\pi^2\\cdot L}{g}& \\cr \\color{green}{\\Leftrightarrow}&g=\\frac{4\\cdot \\pi^2\\cdot L}{T^2}& \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[a=b,a^2=b^2]	[]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&a=b& \\cr \\color{green}{\\Leftrightarrow}&a^2=b^2& \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR]
Equiv	Pass	[a=b,sqrt(a)=sqrt(b)]	[]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&a=b& \\cr \\color{green}{\\Leftrightarrow}&\\sqrt{a}=\\sqrt{b}& \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR]
Equiv	Pass	[a^2=b^2,a=b]	[]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&a^2=b^2& \\cr \\color{green}{\\Leftrightarrow}&a=b& \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR]
Equiv	Pass	[a^2=b^2,a=b or a=-b]	[]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&a^2=b^2& \\cr \\color{green}{\\Leftrightarrow}&a=b\\,{\\mbox{ or }}\\, a=-b& \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR]
Equiv	Pass	[a=b,abs(a)=abs(b)]	[]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&a=b& \\cr \\color{green}{\\Leftrightarrow}&\\left\| a\\right\| =\\left\| b\\right\| & \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR]
Equiv	Pass	[abs(a)=abs(b),a=b]	[]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&\\left\| a\\right\| =\\left\| b\\right\| & \\cr \\color{green}{\\Leftrightarrow}&a=b& \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR]
Equiv	Pass	[abs(a)=abs(b),a=-b]	[]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&\\left\| a\\right\| =\\left\| b\\right\| & \\cr \\color{green}{\\Leftrightarrow}&a=-b& \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR]
Equiv	Pass	[abs(a)=abs(b),a=b or a=-b]	[]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&\\left\| a\\right\| =\\left\| b\\right\| & \\cr \\color{green}{\\Leftrightarrow}&a=b\\,{\\mbox{ or }}\\, a=-b& \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR]
Equiv	Pass	[x=abs(-2),x=2]	[]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&x=\\left\| -2\\right\| & \\cr \\color{green}{\\Leftrightarrow}&x=2& \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR]
Equiv	Pass	[abs(a)=abs(b),a^2=b^2]	[]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&\\left\| a\\right\| =\\left\| b\\right\| & \\cr \\color{green}{\\Leftrightarrow}&a^2=b^2& \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR]
Equiv	Pass	[x^2=9,x=#pm#3,x=3 or x=-3,x=3]	[]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&x^2=9& \\cr \\color{green}{\\Leftrightarrow}&x= \\pm 3& \\cr \\color{green}{\\Leftrightarrow}&x=3\\,{\\mbox{ or }}\\, x=-3& \\cr \\color{green}{\\Leftrightarrow}&x=3& \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x^2=9,x=3]	[]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&x^2=9& \\cr \\color{green}{\\Leftrightarrow}&x=3& \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR]
Equiv	Pass	[x^2=2,x=#pm#sqrt(2),x=sqrt(2) or x=-sqrt(2)]	[]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&x^2=2& \\cr \\color{green}{\\Leftrightarrow}&x= \\pm \\sqrt{2}& \\cr \\color{green}{\\Leftrightarrow}&x=\\sqrt{2}\\,{\\mbox{ or }}\\, x=-\\sqrt{2}& \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x^2=2,x=sqrt(2)]	[]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&x^2=2& \\cr \\color{green}{\\Leftrightarrow}&x=\\sqrt{2}& \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR]
Equiv	Pass	[x^2 = a^2-b,x = sqrt(a^2-b)]	[]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&x^2=a^2-b& \\cr \\color{green}{\\Leftrightarrow}&x=\\sqrt{a^2-b}& \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR]
Equiv	Pass	[2(x-3) = 4x-3(x+2),2x-6=x-6,x=0]	[]			1	1	\\[\\begin{array}{lll} &2\\cdot \\left(x-3\\right)=4\\cdot x-3\\cdot \\left(x+2\\right)& \\cr \\color{green}{\\Leftrightarrow}&2\\cdot x-6=x-6& \\cr \\color{green}{\\Leftrightarrow}&x=0& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[2(x-3) = 5x-3(x+2),2x-6=2*x-6,0=0,all]	[]			1	1	\\[\\begin{array}{lll} &2\\cdot \\left(x-3\\right)=5\\cdot x-3\\cdot \\left(x+2\\right)& \\cr \\color{green}{\\Leftrightarrow}&2\\cdot x-6=2\\cdot x-6& \\cr \\color{green}{\\Leftrightarrow}&0=0& \\cr \\color{green}{\\Leftrightarrow}&\\mathbb{R}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[2(x-3) = 5x-3(x+1),2x-6=2*x-3,0=3,{}]	[]			1	1	\\[\\begin{array}{lll} &2\\cdot \\left(x-3\\right)=5\\cdot x-3\\cdot \\left(x+1\\right)& \\cr \\color{green}{\\Leftrightarrow}&2\\cdot x-6=2\\cdot x-3& \\cr \\color{green}{\\Leftrightarrow}&0=3& \\cr \\color{green}{\\Leftrightarrow}&\\left \\{ \\right \\}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[a^2=b^2,a^2-b^2=0,(a-b)*(a+b)=0,a=b or a=-b]	[]			1	1	\\[\\begin{array}{lll} &a^2=b^2& \\cr \\color{green}{\\Leftrightarrow}&a^2-b^2=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(a-b\\right)\\cdot \\left(a+b\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&a=b\\,{\\mbox{ or }}\\, a=-b& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[a^3=b^3,a^3-b^3=0,(a-b)(a^2+ab+b^2)=0,(a-b)=0,a=b]	[]			0	0	\\[\\begin{array}{lll} &a^3=b^3& \\cr \\color{green}{\\Leftrightarrow}&a^3-b^3=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(a-b\\right)\\cdot \\left(a^2+a\\cdot b+b^2\\right)=0& \\cr \\color{red}{\\Leftarrow}&a-b=0& \\cr \\color{green}{\\Leftrightarrow}&a=b& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR,IMPLIEDCHAR, EQUIVCHAR]
Equiv	Pass	[a^3=b^3,a^3-b^3=0,(a-b)(a^2+ab+b^2)=0,(a-b)=0 or (a^2+ab+b^2)=0, a=b or (a+(1+%isqrt(3))/2b)(a+(1-%isqrt(3))/2b)=0, a=b or a=-(1+%isqrt(3))/2b or a=-(1-%isqrt(3))/2b]	[]			1	1	\\[\\begin{array}{lll} &a^3=b^3& \\cr \\color{green}{\\Leftrightarrow}&a^3-b^3=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(a-b\\right)\\cdot \\left(a^2+a\\cdot b+b^2\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&a-b=0\\,{\\mbox{ or }}\\, a^2+a\\cdot b+b^2=0& \\cr \\color{green}{\\Leftrightarrow}&a=b\\,{\\mbox{ or }}\\, \\left(a+\\frac{1+\\mathrm{i}\\cdot \\sqrt{3}}{2}\\cdot b\\right)\\cdot \\left(a+\\frac{1-\\mathrm{i}\\cdot \\sqrt{3}}{2}\\cdot b\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&a=b\\,{\\mbox{ or }}\\, a=\\frac{-\\left(1+\\mathrm{i}\\cdot \\sqrt{3}\\right)}{2}\\cdot b\\,{\\mbox{ or }}\\, a=\\frac{-\\left(1-\\mathrm{i}\\cdot \\sqrt{3}\\right)}{2}\\cdot b& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x^2-x=30,x^2-x-30=0,(x-6)*(x+5)=0,x-6=0 or x+5=0,x=6 or x=-5]	[]			1	1	\\[\\begin{array}{lll} &x^2-x=30& \\cr \\color{green}{\\Leftrightarrow}&x^2-x-30=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(x-6\\right)\\cdot \\left(x+5\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&x-6=0\\,{\\mbox{ or }}\\, x+5=0& \\cr \\color{green}{\\Leftrightarrow}&x=6\\,{\\mbox{ or }}\\, x=-5& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x^2=2,x^2-2=0,(x-sqrt(2))*(x+sqrt(2))=0,x=sqrt(2) or x=-sqrt(2)]	[]			1	1	\\[\\begin{array}{lll} &x^2=2& \\cr \\color{green}{\\Leftrightarrow}&x^2-2=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(x-\\sqrt{2}\\right)\\cdot \\left(x+\\sqrt{2}\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&x=\\sqrt{2}\\,{\\mbox{ or }}\\, x=-\\sqrt{2}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x^2=2,x=#pm#sqrt(2),x=sqrt(2) or x=-sqrt(2)]	[]			1	1	\\[\\begin{array}{lll} &x^2=2& \\cr \\color{green}{\\Leftrightarrow}&x= \\pm \\sqrt{2}& \\cr \\color{green}{\\Leftrightarrow}&x=\\sqrt{2}\\,{\\mbox{ or }}\\, x=-\\sqrt{2}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[(2x-7)^2=(x+1)^2,(2x-7)^2 -(x+1)^2=0,(2x-7+x+1)(2x-7-x-1)=0,(3x-6)*(x-8)=0,x=2 or x=8]	[]			1	1	\\[\\begin{array}{lll} &{\\left(2\\cdot x-7\\right)}^2={\\left(x+1\\right)}^2& \\cr \\color{green}{\\Leftrightarrow}&{\\left(2\\cdot x-7\\right)}^2-{\\left(x+1\\right)}^2=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(2\\cdot x-7+x+1\\right)\\cdot \\left(2\\cdot x-7-x-1\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(3\\cdot x-6\\right)\\cdot \\left(x-8\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&x=2\\,{\\mbox{ or }}\\, x=8& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x^2-6*x=-9,(x-3)^2=0,x-3=0,x=3]	[]			1	1	\\[\\begin{array}{lll} &x^2-6\\cdot x=-9& \\cr \\color{green}{\\Leftrightarrow}&{\\left(x-3\\right)}^2=0& \\cr \\color{green}{\\mbox{(Same roots)}}&x-3=0& \\cr \\color{green}{\\Leftrightarrow}&x=3& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR,SAMEROOTS, EQUIVCHAR]
Equiv	Pass	[(2x-7)^2=(x+1)^2,sqrt((2x-7)^2)=sqrt((x+1)^2),2*x-7=x+1,x=8]	[]			0	0	\\[\\begin{array}{lll} &{\\left(2\\cdot x-7\\right)}^2={\\left(x+1\\right)}^2& \\cr \\color{green}{\\Leftrightarrow}&\\sqrt{{\\left(2\\cdot x-7\\right)}^2}=\\sqrt{{\\left(x+1\\right)}^2}& \\cr \\color{red}{\\Leftarrow}&2\\cdot x-7=x+1& \\cr \\color{green}{\\Leftrightarrow}&x=8& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR,IMPLIEDCHAR, EQUIVCHAR]
Equiv	Pass	[x^2-10*x+9 = 0, (x-5)^2-16 = 0, (x-5)^2 =16, x-5 =#pm#4, x-5 =4 or x-5=-4, x = 1 or x = 9]	[]			1	1	\\[\\begin{array}{lll} &x^2-10\\cdot x+9=0& \\cr \\color{green}{\\Leftrightarrow}&{\\left(x-5\\right)}^2-16=0& \\cr \\color{green}{\\Leftrightarrow}&{\\left(x-5\\right)}^2=16& \\cr \\color{green}{\\Leftrightarrow}&x-5= \\pm 4& \\cr \\color{green}{\\Leftrightarrow}&x-5=4\\,{\\mbox{ or }}\\, x-5=-4& \\cr \\color{green}{\\Leftrightarrow}&x=1\\,{\\mbox{ or }}\\, x=9& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x^2-2px-q=0,x^2-2px=q,x^2-2px+p^2=q+p^2,(x-p)^2=q+p^2,x-p=#pm#sqrt(q+p^2),x-p=sqrt(q+p^2) or x-p=-sqrt(q+p^2),x=p+sqrt(q+p^2) or x=p-sqrt(q+p^2)]	[]			1	1	\\[\\begin{array}{lll} &x^2-2\\cdot p\\cdot x-q=0& \\cr \\color{green}{\\Leftrightarrow}&x^2-2\\cdot p\\cdot x=q& \\cr \\color{green}{\\Leftrightarrow}&x^2-2\\cdot p\\cdot x+p^2=q+p^2& \\cr \\color{green}{\\Leftrightarrow}&{\\left(x-p\\right)}^2=q+p^2& \\cr \\color{green}{\\Leftrightarrow}&x-p= \\pm \\sqrt{q+p^2}& \\cr \\color{green}{\\Leftrightarrow}&x-p=\\sqrt{q+p^2}\\,{\\mbox{ or }}\\, x-p=-\\sqrt{q+p^2}& \\cr \\color{green}{\\Leftrightarrow}&x=p+\\sqrt{q+p^2}\\,{\\mbox{ or }}\\, x=p-\\sqrt{q+p^2}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x^2-10x+7=0,(x-5)^2-18=0,(x-5)^2=sqrt(18)^2,(x-5)^2-sqrt(18)^2=0,(x-5-sqrt(18))(x-5+sqrt(18))=0,x=5-sqrt(18) or x=5+sqrt(18)]	[]			1	1	\\[\\begin{array}{lll} &x^2-10\\cdot x+7=0& \\cr \\color{green}{\\Leftrightarrow}&{\\left(x-5\\right)}^2-18=0& \\cr \\color{green}{\\Leftrightarrow}&{\\left(x-5\\right)}^2={\\sqrt{18}}^2& \\cr \\color{green}{\\Leftrightarrow}&{\\left(x-5\\right)}^2-{\\sqrt{18}}^2=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(x-5-\\sqrt{18}\\right)\\cdot \\left(x-5+\\sqrt{18}\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&x=5-\\sqrt{18}\\,{\\mbox{ or }}\\, x=5+\\sqrt{18}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x^2+2ax = 0, x(x+2a)=0, (x+a-a)*(x+a+a)=0, (x+a)^2-a^2=0]	[]			1	1	\\[\\begin{array}{lll} &x^2+2\\cdot a\\cdot x=0& \\cr \\color{green}{\\Leftrightarrow}&x\\cdot \\left(x+2\\cdot a\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(x+a-a\\right)\\cdot \\left(x+a+a\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&{\\left(x+a\\right)}^2-a^2=0& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x^3-1=0,(x-1)*(x^2+x+1)=0,x=1]	[]			0	0	\\[\\begin{array}{lll} &x^3-1=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(x-1\\right)\\cdot \\left(x^2+x+1\\right)=0& \\cr \\color{red}{\\Leftarrow}&x=1& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR,IMPLIEDCHAR]
Equiv	Pass	[x^3-1=0,(x-1)(x^2+x+1)=0,x=1 or x^2+x+1=0,x=1 or x = -(sqrt(3)%i+1)/2 or x=(sqrt(3)*%i-1)/2]	[]			1	1	\\[\\begin{array}{lll} &x^3-1=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(x-1\\right)\\cdot \\left(x^2+x+1\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&x=1\\,{\\mbox{ or }}\\, x^2+x+1=0& \\cr \\color{green}{\\Leftrightarrow}&x=1\\,{\\mbox{ or }}\\, x=\\frac{-\\left(\\sqrt{3}\\cdot \\mathrm{i}+1\\right)}{2}\\,{\\mbox{ or }}\\, x=\\frac{\\sqrt{3}\\cdot \\mathrm{i}-1}{2}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[ax^2+bx+c=0 or a=0,a^2x^2+abx+ac=0,(ax)^2+b(ax)+ac=0, (ax)^2+b(ax)+b^2/4-b^2/4+ac=0,(ax+b/2)^2-b^2/4+ac=0,(ax+b/2)^2=b^2/4-ac, ax+b/2= #pm#sqrt(b^2/4-ac),ax=-b/2+sqrt(b^2/4-ac) or ax=-b/2-sqrt(b^2/4-ac), (a=0 or x=(-b+sqrt(b^2-4ac))/(2a)) or (a=0 or x=(-b-sqrt(b^2-4ac))/(2a)), a^2=0 or x=(-b+sqrt(b^2-4ac))/(2a) or x=(-b-sqrt(b^2-4ac))/(2a)]	[]			1	1	\\[\\begin{array}{lll} &a\\cdot x^2+b\\cdot x+c=0\\,{\\mbox{ or }}\\, a=0& \\cr \\color{green}{\\Leftrightarrow}&a^2\\cdot x^2+a\\cdot b\\cdot x+a\\cdot c=0& \\cr \\color{green}{\\Leftrightarrow}&{\\left(a\\cdot x\\right)}^2+b\\cdot \\left(a\\cdot x\\right)+a\\cdot c=0& \\cr \\color{green}{\\Leftrightarrow}&{\\left(a\\cdot x\\right)}^2+b\\cdot \\left(a\\cdot x\\right)+\\frac{b^2}{4}-\\frac{b^2}{4}+a\\cdot c=0& \\cr \\color{green}{\\Leftrightarrow}&{\\left(a\\cdot x+\\frac{b}{2}\\right)}^2-\\frac{b^2}{4}+a\\cdot c=0& \\cr \\color{green}{\\Leftrightarrow}&{\\left(a\\cdot x+\\frac{b}{2}\\right)}^2=\\frac{b^2}{4}-a\\cdot c& \\cr \\color{green}{\\Leftrightarrow}&a\\cdot x+\\frac{b}{2}= \\pm \\sqrt{\\frac{b^2}{4}-a\\cdot c}& \\cr \\color{green}{\\Leftrightarrow}&a\\cdot x=-\\frac{b}{2}+\\sqrt{\\frac{b^2}{4}-a\\cdot c}\\,{\\mbox{ or }}\\, a\\cdot x=-\\frac{b}{2}-\\sqrt{\\frac{b^2}{4}-a\\cdot c}& \\cr \\color{green}{\\Leftrightarrow}&a=0\\,{\\mbox{ or }}\\, x=\\frac{-b+\\sqrt{b^2-4\\cdot a\\cdot c}}{2\\cdot a}\\,{\\mbox{ or }}\\, \\left(a=0\\,{\\mbox{ or }}\\, x=\\frac{-b-\\sqrt{b^2-4\\cdot a\\cdot c}}{2\\cdot a}\\right)& \\cr \\color{green}{\\Leftrightarrow}&a^2=0\\,{\\mbox{ or }}\\, x=\\frac{-b+\\sqrt{b^2-4\\cdot a\\cdot c}}{2\\cdot a}\\,{\\mbox{ or }}\\, x=\\frac{-b-\\sqrt{b^2-4\\cdot a\\cdot c}}{2\\cdot a}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[ax^2+bx=-c,4a^2x^2+4abx+b^2=b^2-4ac,(2ax+b)^2=b^2-4ac,2ax+b=#pm#sqrt(b^2-4ac),2ax=-b#pm#sqrt(b^2-4ac),x=(-b#pm#sqrt(b^2-4ac))/(2a)]	[]			0	0	\\[\\begin{array}{lll} &a\\cdot x^2+b\\cdot x=-c& \\cr \\color{red}{\\Rightarrow}&4\\cdot a^2\\cdot x^2+4\\cdot a\\cdot b\\cdot x+b^2=b^2-4\\cdot a\\cdot c& \\cr \\color{green}{\\Leftrightarrow}&{\\left(2\\cdot a\\cdot x+b\\right)}^2=b^2-4\\cdot a\\cdot c& \\cr \\color{green}{\\Leftrightarrow}&2\\cdot a\\cdot x+b= \\pm \\sqrt{b^2-4\\cdot a\\cdot c}& \\cr \\color{green}{\\Leftrightarrow}&2\\cdot a\\cdot x={-b \\pm \\sqrt{b^2-4\\cdot a\\cdot c}}& \\cr \\color{red}{?}&x=\\frac{{-b \\pm \\sqrt{b^2-4\\cdot a\\cdot c}}}{2\\cdot a}& \\cr \\end{array}\\]	[EMPTYCHAR,IMPLIESCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR,QMCHAR]
Equiv	Pass	[ax^2+bx=-c or a=0,4a^2x^2+4abx+b^2=b^2-4ac,(2ax+b)^2=b^2-4ac,2ax+b=#pm#sqrt(b^2-4ac),2ax=-b#pm#sqrt(b^2-4ac),x=(-b#pm#sqrt(b^2-4ac))/(2a) or a=0]	[]			1	1	\\[\\begin{array}{lll} &a\\cdot x^2+b\\cdot x=-c\\,{\\mbox{ or }}\\, a=0& \\cr \\color{green}{\\Leftrightarrow}&4\\cdot a^2\\cdot x^2+4\\cdot a\\cdot b\\cdot x+b^2=b^2-4\\cdot a\\cdot c& \\cr \\color{green}{\\Leftrightarrow}&{\\left(2\\cdot a\\cdot x+b\\right)}^2=b^2-4\\cdot a\\cdot c& \\cr \\color{green}{\\Leftrightarrow}&2\\cdot a\\cdot x+b= \\pm \\sqrt{b^2-4\\cdot a\\cdot c}& \\cr \\color{green}{\\Leftrightarrow}&2\\cdot a\\cdot x={-b \\pm \\sqrt{b^2-4\\cdot a\\cdot c}}& \\cr \\color{green}{\\Leftrightarrow}&x=\\frac{{-b \\pm \\sqrt{b^2-4\\cdot a\\cdot c}}}{2\\cdot a}\\,{\\mbox{ or }}\\, a=0& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[sqrt(3x+4) = 2+sqrt(x+2), 3x+4=4+4sqrt(x+2)+(x+2),x-1=2sqrt(x+2),x^2-2x+1 = 4x+8,x^2-6x-7 = 0,(x-7)(x+1) = 0,x=7 or x=-1]	[]			0	0	\\[\\begin{array}{lll} &\\sqrt{3\\cdot x+4}=2+\\sqrt{x+2}&{\\color{blue}{{x \\in {\\left[ -\\frac{4}{3},\\, \\infty \\right)}}}}\\cr \\color{red}{\\Rightarrow}&3\\cdot x+4=4+4\\cdot \\sqrt{x+2}+\\left(x+2\\right)&{\\color{blue}{{x \\in {\\left[ -2,\\, \\infty \\right)}}}}\\cr \\color{green}{\\Leftrightarrow}&x-1=2\\cdot \\sqrt{x+2}&{\\color{blue}{{x \\in {\\left[ -2,\\, \\infty \\right)}}}}\\cr \\color{red}{\\Rightarrow}&x^2-2\\cdot x+1=4\\cdot x+8& \\cr \\color{green}{\\Leftrightarrow}&x^2-6\\cdot x-7=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(x-7\\right)\\cdot \\left(x+1\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&x=7\\,{\\mbox{ or }}\\, x=-1& \\cr \\end{array}\\]	[EMPTYCHAR,IMPLIESCHAR, EQUIVCHAR,IMPLIESCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[sqrt(3x+4) = 2+sqrt(x+2), 3x+4=4+4sqrt(x+2)+(x+2),x-1=2sqrt(x+2),x^2-2x+1 = 4x+8,x^2-6x-7 = 0,(x-7)(x+1) = 0,x=7 or x=-1,x=7]	[]	[assumepos]		1	1	\\[\\begin{array}{lll}\\color{blue}{\\mbox{Assume +ve vars}}&\\sqrt{3\\cdot x+4}=2+\\sqrt{x+2}&{\\color{blue}{{x \\in {\\left[ 0,\\, \\infty \\right)}}}}\\cr \\color{green}{\\Leftrightarrow}&3\\cdot x+4=4+4\\cdot \\sqrt{x+2}+\\left(x+2\\right)&{\\color{blue}{{x \\in {\\left[ 0,\\, \\infty \\right)}}}}\\cr \\color{green}{\\Leftrightarrow}&x-1=2\\cdot \\sqrt{x+2}&{\\color{blue}{{x \\in {\\left[ 0,\\, \\infty \\right)}}}}\\cr \\color{green}{\\Leftrightarrow}&x^2-2\\cdot x+1=4\\cdot x+8& \\cr \\color{green}{\\Leftrightarrow}&x^2-6\\cdot x-7=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(x-7\\right)\\cdot \\left(x+1\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&x=7\\,{\\mbox{ or }}\\, x=-1& \\cr \\color{green}{\\Leftrightarrow}&x=7& \\cr \\end{array}\\]	[ASSUMEPOSVARS, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x(x-1)(x-2)=0,x(x-1)=0,x(x-1)(x-2)=0,x(x^2-2)=0]	[]			0	0	\\[\\begin{array}{lll} &x\\cdot \\left(x-1\\right)\\cdot \\left(x-2\\right)=0& \\cr \\color{red}{\\Leftarrow}&x\\cdot \\left(x-1\\right)=0& \\cr \\color{red}{\\Rightarrow}&x\\cdot \\left(x-1\\right)\\cdot \\left(x-2\\right)=0& \\cr \\color{red}{?}&x\\cdot \\left(x^2-2\\right)=0& \\cr \\end{array}\\]	[EMPTYCHAR,IMPLIEDCHAR,IMPLIESCHAR,QMCHAR]
Equiv	Pass	[x^2-6*x=-9,x=3]	[]			1	1	\\[\\begin{array}{lll} &x^2-6\\cdot x=-9& \\cr \\color{green}{\\mbox{(Same roots)}}&x=3& \\cr \\end{array}\\]	[EMPTYCHAR,SAMEROOTS]
Equiv	Pass	[x=1 nounor x=-2 nounor x=1,x^3-3*x=-2,x=1 nounor x=-2]	[]			1	1	\\[\\begin{array}{lll} &x=1\\,{\\mbox{ or }}\\, x=-2\\,{\\mbox{ or }}\\, x=1& \\cr \\color{green}{\\Leftrightarrow}&x^3-3\\cdot x=-2& \\cr \\color{green}{\\mbox{(Same roots)}}&x=1\\,{\\mbox{ or }}\\, x=-2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR,SAMEROOTS]
Equiv	Pass	[9x^3-24x^2+13*x=2,x=1/3 nounor x=2]	[]			1	1	\\[\\begin{array}{lll} &9\\cdot x^3-24\\cdot x^2+13\\cdot x=2& \\cr \\color{green}{\\mbox{(Same roots)}}&x=\\frac{1}{3}\\,{\\mbox{ or }}\\, x=2& \\cr \\end{array}\\]	[EMPTYCHAR,SAMEROOTS]
Equiv	Pass	[(x-2)^43(x+1/3)^60=0,(3x+1)^4*(x-2)^2=0,x=-1/3 nounor x=2]	[]			1	1	\\[\\begin{array}{lll} &{\\left(x-2\\right)}^{43}\\cdot {\\left(x+\\frac{1}{3}\\right)}^{60}=0& \\cr \\color{green}{\\mbox{(Same roots)}}&{\\left(3\\cdot x+1\\right)}^4\\cdot {\\left(x-2\\right)}^2=0& \\cr \\color{green}{\\mbox{(Same roots)}}&x=\\frac{-1}{3}\\,{\\mbox{ or }}\\, x=2& \\cr \\end{array}\\]	[EMPTYCHAR,SAMEROOTS,SAMEROOTS]
Equiv	Pass	[2^x=4,xlog(2)=log(4),x=log(2^2)/log(2),x=2log(2)/log(2),x=2]	[]			1	1	\\[\\begin{array}{lll} &2^{x}=4& \\cr \\color{green}{\\Leftrightarrow}&x\\cdot \\ln \\left( 2 \\right)=\\ln \\left( 4 \\right)& \\cr \\color{green}{\\Leftrightarrow}&x=\\frac{\\ln \\left( 2^2 \\right)}{\\ln \\left( 2 \\right)}& \\cr \\color{green}{\\Leftrightarrow}&x=\\frac{2\\cdot \\ln \\left( 2 \\right)}{\\ln \\left( 2 \\right)}& \\cr \\color{green}{\\Leftrightarrow}&x=2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x^log(y),stackeq(e^(log(x)log(y))),stackeq(e^(log(y)log(x))),stackeq(y^log(x))]	[]			1	1	\\[\\begin{array}{lll} &x^{\\ln \\left( y \\right)}& \\cr \\color{green}{\\checkmark}&=e^{\\ln \\left( x \\right)\\cdot \\ln \\left( y \\right)}& \\cr \\color{green}{\\checkmark}&=e^{\\ln \\left( y \\right)\\cdot \\ln \\left( x \\right)}& \\cr \\color{green}{\\checkmark}&=y^{\\ln \\left( x \\right)}& \\cr \\end{array}\\]	[EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK]
Equiv	Pass	[lg(x+17,3)-2=lg(2x,3),lg(x+17,3)-lg(2x,3)=2,lg((x+17)/(2x),3)=2,(x+17)/(2x)=3^2,(x+17)=18x,17x=17,x=1]	[]			1	1	\\[\\begin{array}{lll} &\\log_{3}\\left(x+17\\right)-2=\\log_{3}\\left(2\\cdot x\\right)&{\\color{blue}{{x \\in {\\left( 0,\\, \\infty \\right)}}}}\\cr \\color{green}{\\Leftrightarrow}&\\log_{3}\\left(x+17\\right)-\\log_{3}\\left(2\\cdot x\\right)=2&{\\color{blue}{{x \\in {\\left( 0,\\, \\infty \\right)}}}}\\cr \\color{green}{\\Leftrightarrow}&\\log_{3}\\left(\\frac{x+17}{2\\cdot x}\\right)=2& \\cr \\color{green}{\\log(?)}&\\frac{x+17}{2\\cdot x}=3^2&{\\color{blue}{{x \\not\\in {\\left \\{0 \\right \\}}}}}\\cr \\color{green}{\\Leftrightarrow}&x+17=18\\cdot x& \\cr \\color{green}{\\Leftrightarrow}&17\\cdot x=17& \\cr \\color{green}{\\Leftrightarrow}&x=1& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR,EQUIVLOG, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x=(1+y/n)^n,x^(1/n)=(1+y/n),y/n=x^(1/n)-1,y=n*(x^(1/n)-1)]	[]			0	0	\\[\\begin{array}{lll} &x={\\left(1+\\frac{y}{n}\\right)}^{n}& \\cr \\color{red}{?}&x^{\\frac{1}{n}}=1+\\frac{y}{n}& \\cr \\color{green}{\\Leftrightarrow}&\\frac{y}{n}=x^{\\frac{1}{n}}-1& \\cr \\color{green}{\\Leftrightarrow}&y=n\\cdot \\left(x^{\\frac{1}{n}}-1\\right)& \\cr \\end{array}\\]	[EMPTYCHAR,QMCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[a^3=b^3,a^3-b^3=0,(a-b)(a^2+ab+b^2)=0,(a-b)=0,a=b]	[]	[assumereal]		0	0	\\[\\begin{array}{lll}\\color{blue}{(\\mathbb{R})}&a^3=b^3& \\cr \\color{green}{\\Leftrightarrow}&a^3-b^3=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(a-b\\right)\\cdot \\left(a^2+a\\cdot b+b^2\\right)=0& \\cr \\color{red}{\\Leftarrow}&a-b=0& \\cr \\color{green}{\\Leftrightarrow}&a=b& \\cr \\end{array}\\]	[ASSUMEREALVARS, EQUIVCHAR, EQUIVCHAR,IMPLIEDCHAR, EQUIVCHAR]
Equiv	Pass	[x^3-1=0,(x-1)*(x^2+x+1)=0,x=1]	[]	[assumereal]		1	1	\\[\\begin{array}{lll}\\color{blue}{(\\mathbb{R})}&x^3-1=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(x-1\\right)\\cdot \\left(x^2+x+1\\right)=0& \\cr \\color{green}{\\Leftrightarrow}\\, \\color{blue}{(\\mathbb{R})}&x=1& \\cr \\end{array}\\]	[ASSUMEREALVARS, EQUIVCHAR, EQUIVCHARREAL]
Equiv	Pass	[x^4=2,x^4-2=0,(x^2-sqrt(2))*(x^2+sqrt(2))=0,x^2=sqrt(2),x=#pm# 2^(1/4)]	[]	[assumereal]		1	1	\\[\\begin{array}{lll}\\color{blue}{(\\mathbb{R})}&x^4=2& \\cr \\color{green}{\\Leftrightarrow}&x^4-2=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(x^2-\\sqrt{2}\\right)\\cdot \\left(x^2+\\sqrt{2}\\right)=0& \\cr \\color{green}{\\Leftrightarrow}\\, \\color{blue}{(\\mathbb{R})}&x^2=\\sqrt{2}& \\cr \\color{green}{\\Leftrightarrow}&x= \\pm 2^{\\frac{1}{4}}& \\cr \\end{array}\\]	[ASSUMEREALVARS, EQUIVCHAR, EQUIVCHAR, EQUIVCHARREAL, EQUIVCHAR]
Equiv	Pass	[6x-12=3(x-2),6x-12+3(x-2)=0,9*x-18=0,x=2]	[]			1	1	\\[\\begin{array}{lll} &6\\cdot x-12=3\\cdot \\left(x-2\\right)& \\cr \\color{green}{\\Leftrightarrow}&6\\cdot x-12+3\\cdot \\left(x-2\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&9\\cdot x-18=0& \\cr \\color{green}{\\Leftrightarrow}&x=2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x^2-6x+9=0,x^2-6x=-9,x(x-6)=3-3,x=3 or x-6=-3,x=3]	[]			1	1	\\[\\begin{array}{lll} &x^2-6\\cdot x+9=0& \\cr \\color{green}{\\Leftrightarrow}&x^2-6\\cdot x=-9& \\cr \\color{green}{\\Leftrightarrow}&x\\cdot \\left(x-6\\right)=3\\cdot \\left(-3\\right)& \\cr \\color{green}{\\Leftrightarrow}&x=3\\,{\\mbox{ or }}\\, x-6=-3& \\cr \\color{green}{\\mbox{(Same roots)}}&x=3& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR,SAMEROOTS]
Equiv	Pass	[(x+3)*(2-x)=4,x+3=4 or (2-x)=4,x=1 or x=-2]	[]			1	1	\\[\\begin{array}{lll} &\\left(x+3\\right)\\cdot \\left(2-x\\right)=4& \\cr \\color{green}{\\Leftrightarrow}&x+3=4\\,{\\mbox{ or }}\\, 2-x=4& \\cr \\color{green}{\\Leftrightarrow}&x=1\\,{\\mbox{ or }}\\, x=-2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[(x-p)(x-q)=0,x^2-px-qx+pq=0,1+q-x-p-pq+px+x+qx-x^2=1-p+q,(1+q-x)(1-p+x)=1-p+q,(1+q-x)=1-p+q or (1-p+x)=1-p+q,x=p or x=q]	[]			1	1	\\[\\begin{array}{lll} &\\left(x-p\\right)\\cdot \\left(x-q\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&x^2-p\\cdot x+\\left(-q\\right)\\cdot x+p\\cdot q=0& \\cr \\color{green}{\\Leftrightarrow}&1+q-x-p+\\left(-p\\right)\\cdot q+p\\cdot x+x+q\\cdot x-x^2=1-p+q& \\cr \\color{green}{\\Leftrightarrow}&\\left(1+q-x\\right)\\cdot \\left(1-p+x\\right)=1-p+q& \\cr \\color{green}{\\Leftrightarrow}&1+q-x=1-p+q\\,{\\mbox{ or }}\\, 1-p+x=1-p+q& \\cr \\color{green}{\\Leftrightarrow}&x=p\\,{\\mbox{ or }}\\, x=q& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[a=b, a^2=ab, a^2-b^2=ab-b^2, (a-b)(a+b)=b(a-b), a+b=b, 2*a=a, 1=2]	[]			0	0	\\[\\begin{array}{lll} &a=b& \\cr \\color{red}{\\Rightarrow}&a^2=a\\cdot b& \\cr \\color{green}{\\Leftrightarrow}&a^2-b^2=a\\cdot b-b^2& \\cr \\color{green}{\\Leftrightarrow}&\\left(a-b\\right)\\cdot \\left(a+b\\right)=b\\cdot \\left(a-b\\right)& \\cr \\color{red}{\\Leftarrow}&a+b=b& \\cr \\color{green}{\\Leftrightarrow}&2\\cdot a=a& \\cr \\color{red}{\\Leftarrow}&1=2& \\cr \\end{array}\\]	[EMPTYCHAR,IMPLIESCHAR, EQUIVCHAR, EQUIVCHAR,IMPLIEDCHAR, EQUIVCHAR,IMPLIEDCHAR]
Equiv	Pass	[a=b or a=0, a^2=ab, a^2-b^2=ab-b^2, (a-b)(a+b)=b(a-b), a+b=b or a-b=0, 2*a=a or a=b, 2=1 or a=0 or a=b, a=0 or a=b]	[]			1	1	\\[\\begin{array}{lll} &a=b\\,{\\mbox{ or }}\\, a=0& \\cr \\color{green}{\\Leftrightarrow}&a^2=a\\cdot b& \\cr \\color{green}{\\Leftrightarrow}&a^2-b^2=a\\cdot b-b^2& \\cr \\color{green}{\\Leftrightarrow}&\\left(a-b\\right)\\cdot \\left(a+b\\right)=b\\cdot \\left(a-b\\right)& \\cr \\color{green}{\\Leftrightarrow}&a+b=b\\,{\\mbox{ or }}\\, a-b=0& \\cr \\color{green}{\\Leftrightarrow}&2\\cdot a=a\\,{\\mbox{ or }}\\, a=b& \\cr \\color{green}{\\Leftrightarrow}&2=1\\,{\\mbox{ or }}\\, a=0\\,{\\mbox{ or }}\\, a=b& \\cr \\color{green}{\\Leftrightarrow}&a=0\\,{\\mbox{ or }}\\, a=b& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[(x^2-4)/(x-2)=0,(x-2)*(x+2)/(x-2)=0,x+2=0,x=-2]	[]			1	1	\\[\\begin{array}{lll} &\\frac{x^2-4}{x-2}=0&{\\color{blue}{{x \\not\\in {\\left \\{2 \\right \\}}}}}\\cr \\color{green}{\\Leftrightarrow}&\\frac{\\left(x-2\\right)\\cdot \\left(x+2\\right)}{x-2}=0& \\cr \\color{green}{\\Leftrightarrow}&x+2=0& \\cr \\color{green}{\\Leftrightarrow}&x=-2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[(x^2-4)/(x-2)=0,(x^2-4)=0,(x-2)*(x+2)=0,x=-2 or x=2]	[]			0	0	\\[\\begin{array}{lll} &\\frac{x^2-4}{x-2}=0&{\\color{blue}{{x \\not\\in {\\left \\{2 \\right \\}}}}}\\cr \\color{red}{\\Rightarrow}&x^2-4=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(x-2\\right)\\cdot \\left(x+2\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&x=-2\\,{\\mbox{ or }}\\, x=2& \\cr \\end{array}\\]	[EMPTYCHAR,IMPLIESCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[5x/(2x+1)-3/(x+1) = 1,5x(x+1)-3(2x+1)=(x+1)(2x+1),5x^2+5x-6x-3=2x^2+3x+1,3x^2-4x-4=0,(x-2)(3*x+2)=0,x=2 or x=-2/3]	[]			1	1	\\[\\begin{array}{lll} &\\frac{5\\cdot x}{2\\cdot x+1}-\\frac{3}{x+1}=1&{\\color{blue}{{x \\not\\in {\\left \\{-1 , -\\frac{1}{2} \\right \\}}}}}\\cr \\color{green}{\\Leftrightarrow}&5\\cdot x\\cdot \\left(x+1\\right)-3\\cdot \\left(2\\cdot x+1\\right)=\\left(x+1\\right)\\cdot \\left(2\\cdot x+1\\right)& \\cr \\color{green}{\\Leftrightarrow}&5\\cdot x^2+5\\cdot x-6\\cdot x-3=2\\cdot x^2+3\\cdot x+1& \\cr \\color{green}{\\Leftrightarrow}&3\\cdot x^2-4\\cdot x-4=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(x-2\\right)\\cdot \\left(3\\cdot x+2\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&x=2\\,{\\mbox{ or }}\\, x=\\frac{-2}{3}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[(x+10)/(x-6)-5= (4x-40)/(13-x),(x+10-5(x-6))/(x-6)= (4x-40)/(13-x), (4x-40)/(6-x)= (4*x-40)/(13-x),6-x= 13-x,6= 13]	[]			0	0	\\[\\begin{array}{lll} &\\frac{x+10}{x-6}-5=\\frac{4\\cdot x-40}{13-x}&{\\color{blue}{{x \\not\\in {\\left \\{6 , 13 \\right \\}}}}}\\cr \\color{green}{\\Leftrightarrow}&\\frac{x+10-5\\cdot \\left(x-6\\right)}{x-6}=\\frac{4\\cdot x-40}{13-x}&{\\color{blue}{{x \\not\\in {\\left \\{6 , 13 \\right \\}}}}}\\cr \\color{green}{\\Leftrightarrow}&\\frac{4\\cdot x-40}{6-x}=\\frac{4\\cdot x-40}{13-x}&{\\color{blue}{{x \\not\\in {\\left \\{6 , 13 \\right \\}}}}}\\cr \\color{red}{?}&6-x=13-x& \\cr \\color{green}{\\Leftrightarrow}&6=13& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR,QMCHAR, EQUIVCHAR]
Equiv	Pass	[(x+5)/(x-7)-5= (4x-40)/(13-x),(x+5-5(x-7))/(x-7)= (4x-40)/(13-x), (4x-40)/(7-x)= (4*x-40)/(13-x),7-x= 13-x,7= 13]	[]			0	0	\\[\\begin{array}{lll} &\\frac{x+5}{x-7}-5=\\frac{4\\cdot x-40}{13-x}&{\\color{blue}{{x \\not\\in {\\left \\{7 , 13 \\right \\}}}}}\\cr \\color{green}{\\Leftrightarrow}&\\frac{x+5-5\\cdot \\left(x-7\\right)}{x-7}=\\frac{4\\cdot x-40}{13-x}&{\\color{blue}{{x \\not\\in {\\left \\{7 , 13 \\right \\}}}}}\\cr \\color{green}{\\Leftrightarrow}&\\frac{4\\cdot x-40}{7-x}=\\frac{4\\cdot x-40}{13-x}&{\\color{blue}{{x \\not\\in {\\left \\{7 , 13 \\right \\}}}}}\\cr \\color{red}{\\Leftarrow}&7-x=13-x& \\cr \\color{green}{\\Leftrightarrow}&7=13& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR,IMPLIEDCHAR, EQUIVCHAR]
Equiv	Pass	[(x+5)/(x-7)-5= (4x-40)/(13-x),(x+5-5(x-7))/(x-7)= (4x-40)/(13-x), (4x-40)/(7-x)= (4x-40)/(13-x),7-x= 13-x or 4x-40=0,7= 13 or 4*x=40,x=10]	[]			1	1	\\[\\begin{array}{lll} &\\frac{x+5}{x-7}-5=\\frac{4\\cdot x-40}{13-x}&{\\color{blue}{{x \\not\\in {\\left \\{7 , 13 \\right \\}}}}}\\cr \\color{green}{\\Leftrightarrow}&\\frac{x+5-5\\cdot \\left(x-7\\right)}{x-7}=\\frac{4\\cdot x-40}{13-x}&{\\color{blue}{{x \\not\\in {\\left \\{7 , 13 \\right \\}}}}}\\cr \\color{green}{\\Leftrightarrow}&\\frac{4\\cdot x-40}{7-x}=\\frac{4\\cdot x-40}{13-x}&{\\color{blue}{{x \\not\\in {\\left \\{7 , 13 \\right \\}}}}}\\cr \\color{green}{\\Leftrightarrow}&7-x=13-x\\,{\\mbox{ or }}\\, 4\\cdot x-40=0& \\cr \\color{green}{\\Leftrightarrow}&7=13\\,{\\mbox{ or }}\\, 4\\cdot x=40& \\cr \\color{green}{\\Leftrightarrow}&x=10& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[ax^2+bx+c=0,a=0 nounand b=0 nounand c=0,ax^2+bx+c=0]	[]			1	1	\\[\\begin{array}{lll} &a\\cdot x^2+b\\cdot x+c=0& \\cr \\color{green}{\\equiv (\\cdots ? x)}&\\left\\{\\begin{array}{l}a=0\\cr b=0\\cr c=0\\cr \\end{array}\\right.& \\cr \\color{green}{(\\cdots ? x)\\equiv}&a\\cdot x^2+b\\cdot x+c=0& \\cr \\end{array}\\]	[EMPTYCHAR,EQUATECOEFFLOSS(x),EQUATECOEFFGAIN(x)]
Equiv	Pass	[ax^2+bx+c=Ax^2+Bx+C,a=A nounand b=B nounand c=C,ax^2+bx+c=Ax^2+Bx+C]	[]			1	1	\\[\\begin{array}{lll} &a\\cdot x^2+b\\cdot x+c=A\\cdot x^2+B\\cdot x+C& \\cr \\color{green}{\\equiv (\\cdots ? x)}&\\left\\{\\begin{array}{l}a=A\\cr b=B\\cr c=C\\cr \\end{array}\\right.& \\cr \\color{green}{(\\cdots ? x)\\equiv}&a\\cdot x^2+b\\cdot x+c=A\\cdot x^2+B\\cdot x+C& \\cr \\end{array}\\]	[EMPTYCHAR,EQUATECOEFFLOSS(x),EQUATECOEFFGAIN(x)]
Equiv	Pass	[(x-1)(x+4), stackeq(x^2-x+4x-4),stackeq(x^2+3*x-4)]	[]			1	1	\\[\\begin{array}{lll} &\\left(x-1\\right)\\cdot \\left(x+4\\right)& \\cr \\color{green}{\\checkmark}&=x^2-x+4\\cdot x-4& \\cr \\color{green}{\\checkmark}&=x^2+3\\cdot x-4& \\cr \\end{array}\\]	[EMPTYCHAR, CHECKMARK, CHECKMARK]
Equiv	Pass	[(x-1)(x+4), stackeq(x^2-x+4x-4),stackeq(x^2+3*x-4)]	[]			1	1	\\[\\begin{array}{lll} &\\left(x-1\\right)\\cdot \\left(x+4\\right)& \\cr \\color{green}{\\checkmark}&=x^2-x+4\\cdot x-4& \\cr \\color{green}{\\checkmark}&=x^2+3\\cdot x-4& \\cr \\end{array}\\]	[EMPTYCHAR, CHECKMARK, CHECKMARK]
Equiv	Pass	[x^2-2,stackeq((x-sqrt(2))*(x+sqrt(2)))]	[]			1	1	\\[\\begin{array}{lll} &x^2-2& \\cr \\color{green}{\\checkmark}&=\\left(x-\\sqrt{2}\\right)\\cdot \\left(x+\\sqrt{2}\\right)& \\cr \\end{array}\\]	[EMPTYCHAR, CHECKMARK]
Equiv	Pass	[x^2+4,stackeq((x-2i)(x+2*i))]	[]			1	1	\\[\\begin{array}{lll} &x^2+4& \\cr \\color{green}{\\checkmark}&=\\left(x-2\\cdot \\mathrm{i}\\right)\\cdot \\left(x+2\\cdot \\mathrm{i}\\right)& \\cr \\end{array}\\]	[EMPTYCHAR, CHECKMARK]
Equiv	Pass	[x^2+2ax,x^2+2ax+a^2-a^2,(x+a)^2-a^2]	[]			1	1	\\[\\begin{array}{lll} &x^2+2\\cdot a\\cdot x& \\cr \\color{green}{\\Leftrightarrow}&x^2+2\\cdot a\\cdot x+a^2-a^2& \\cr \\color{green}{\\Leftrightarrow}&{\\left(x+a\\right)}^2-a^2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x^2+2ax,stackeq(x^2+2ax+a^2-a^2),stackeq((x+a)^2-a^2)]	[]			1	1	\\[\\begin{array}{lll} &x^2+2\\cdot a\\cdot x& \\cr \\color{green}{\\checkmark}&=x^2+2\\cdot a\\cdot x+a^2-a^2& \\cr \\color{green}{\\checkmark}&={\\left(x+a\\right)}^2-a^2& \\cr \\end{array}\\]	[EMPTYCHAR, CHECKMARK, CHECKMARK]
Equiv	Pass	[(y-z)/(yz)+(z-x)/(zx)+(x-y)/(xy),(x(y-z)+y(z-x)+z(x-y))/(xyz),0]	[]			1	1	\\[\\begin{array}{lll} &\\frac{y-z}{y\\cdot z}+\\frac{z-x}{z\\cdot x}+\\frac{x-y}{x\\cdot y}& \\cr \\color{green}{\\Leftrightarrow}&\\frac{x\\cdot \\left(y-z\\right)+y\\cdot \\left(z-x\\right)+z\\cdot \\left(x-y\\right)}{x\\cdot y\\cdot z}& \\cr \\color{green}{\\Leftrightarrow}&0& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[(y-z)/(yz)+(z-x)/(zx)+(x-y)/(xy),stackeq((x(y-z)+y(z-x)+z(x-y))/(xyz)),stackeq(0)]	[]			1	1	\\[\\begin{array}{lll} &\\frac{y-z}{y\\cdot z}+\\frac{z-x}{z\\cdot x}+\\frac{x-y}{x\\cdot y}& \\cr \\color{green}{\\checkmark}&=\\frac{x\\cdot \\left(y-z\\right)+y\\cdot \\left(z-x\\right)+z\\cdot \\left(x-y\\right)}{x\\cdot y\\cdot z}& \\cr \\color{green}{\\checkmark}&=0& \\cr \\end{array}\\]	[EMPTYCHAR, CHECKMARK, CHECKMARK]
Equiv	Pass	[2(a^2b^2+b^2c^2+c^2a^2)-(a^4+b^4+c^4),stackeq(4a^2b^2-(a^4+b^4+c^4+2a^2b^2-2b^2c^2-2c^2a^2)),stackeq((2ab)^2-(b^2+a^2-c^2)^2,(2ab+b^2+a^2-c^2)(2ab-b^2-a^2+c^2)),stackeq(((a+b)^2-c^2)(c^2-(a-b)^2)),stackeq((a+b+c)(a+b-c)(c+a-b)*(c-a+b))]	[]			1	1	\\[\\begin{array}{lll} &2\\cdot \\left(a^2\\cdot b^2+b^2\\cdot c^2+c^2\\cdot a^2\\right)-\\left(a^4+b^4+c^4\\right)& \\cr \\color{green}{\\checkmark}&=4\\cdot a^2\\cdot b^2-\\left(a^4+b^4+c^4+2\\cdot a^2\\cdot b^2-2\\cdot b^2\\cdot c^2-2\\cdot c^2\\cdot a^2\\right)& \\cr \\color{green}{\\checkmark}&={\\left(2\\cdot a\\cdot b\\right)}^2-{\\left(b^2+a^2-c^2\\right)}^2& \\cr \\color{green}{\\checkmark}&=\\left({\\left(a+b\\right)}^2-c^2\\right)\\cdot \\left(c^2-{\\left(a-b\\right)}^2\\right)& \\cr \\color{green}{\\checkmark}&=\\left(a+b+c\\right)\\cdot \\left(a+b-c\\right)\\cdot \\left(c+a-b\\right)\\cdot \\left(c-a+b\\right)& \\cr \\end{array}\\]	[EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK]
Equiv	Pass	[abs(x-1/2)+abs(x+1/2)-2,stackeq(abs(x)-1)]	[]			0	0	\\[\\begin{array}{lll} &\\left\| x-\\frac{1}{2}\\right\| +\\left\| x+\\frac{1}{2}\\right\| -2& \\cr \\color{red}{?}&=\\left\| x\\right\| -1& \\cr \\end{array}\\]	[EMPTYCHAR,QMCHAR]
Equiv	Pass	[11sqrt(abs(x)+1)=25-x,11^2(abs(x)+1)=(25-x)^2,11^2abs(x)=(25-x)^2-11^2,11^4x^2=((25-x)^2-11^2)^2, ((25-x)^2-11^2)^2-11^4x^2=0,((25-x)^2-11^2-11^2x)((25-x)^2-11^2+11^2x)=0,(x^2-50x+504-121x)(x^2-50x+504+121x)=0, (x-168)(x-3)(x+8)(x+63)=0]	[]			0	0	\\[\\begin{array}{lll} &11\\cdot \\sqrt{\\left\| x\\right\| +1}=25-x& \\cr \\color{red}{?}&11^2\\cdot \\left(\\left\| x\\right\| +1\\right)={\\left(25-x\\right)}^2& \\cr \\color{green}{\\Leftrightarrow}&11^2\\cdot \\left\| x\\right\| ={\\left(25-x\\right)}^2-11^2& \\cr \\color{green}{\\Leftrightarrow}&11^4\\cdot x^2={\\left({\\left(25-x\\right)}^2-11^2\\right)}^2& \\cr \\color{green}{\\Leftrightarrow}&{\\left({\\left(25-x\\right)}^2-11^2\\right)}^2-11^4\\cdot x^2=0& \\cr \\color{green}{\\Leftrightarrow}&\\left({\\left(25-x\\right)}^2-11^2+\\left(-11^2\\right)\\cdot x\\right)\\cdot \\left({\\left(25-x\\right)}^2-11^2+11^2\\cdot x\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(x^2-50\\cdot x+504-121\\cdot x\\right)\\cdot \\left(x^2-50\\cdot x+504+121\\cdot x\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&\\left(x-168\\right)\\cdot \\left(x-3\\right)\\cdot \\left(x+8\\right)\\cdot \\left(x+63\\right)=0& \\cr \\end{array}\\]	[EMPTYCHAR,QMCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[1/(x^2+1)=1/((x+%i)(x-%i)), stackeq(1/(2%i)*(1/(x-%i)-1/(x+%i)))]	[]			1	1	\\[\\begin{array}{lll}\\color{green}{\\checkmark}&\\frac{1}{x^2+1}=\\frac{1}{\\left(x+\\mathrm{i}\\right)\\cdot \\left(x-\\mathrm{i}\\right)}& \\cr \\color{green}{\\checkmark}&=\\frac{1}{2\\cdot \\mathrm{i}}\\cdot \\left(\\frac{1}{x-\\mathrm{i}}-\\frac{1}{x+\\mathrm{i}}\\right)& \\cr \\end{array}\\]	[CHECKMARK, CHECKMARK]
Equiv	Pass	[((a-b)/(a^2+ab))/((a^2-2ab+b^2)/(a^4-b^4)),stackeq(((a-b)(a-b)(a+b)(a^2+b^2))/(a(a+b)(a-b)^2)),stackeq((a^2+b^2)/a),stackeq(a+b^2/a)]	[]			1	1	\\[\\begin{array}{lll} &\\frac{\\frac{a-b}{a^2+a\\cdot b}}{\\frac{a^2-2\\cdot a\\cdot b+b^2}{a^4-b^4}}& \\cr \\color{green}{\\checkmark}&=\\frac{\\left(a-b\\right)\\cdot \\left(a-b\\right)\\cdot \\left(a+b\\right)\\cdot \\left(a^2+b^2\\right)}{a\\cdot \\left(a+b\\right)\\cdot {\\left(a-b\\right)}^2}& \\cr \\color{green}{\\checkmark}&=\\frac{a^2+b^2}{a}& \\cr \\color{green}{\\checkmark}&=a+\\frac{b^2}{a}& \\cr \\end{array}\\]	[EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK]
Equiv	Pass	[sum(k,k,1,n+1),stackeq(sum(k,k,1,n)+(n+1)),stackeq(n(n+1)/2 +n+1),stackeq((n+1)(n+1+1)/2),stackeq((n+1)*(n+2)/2)]	[]			1	1	\\[\\begin{array}{lll} &\\sum_{k=1}^{n+1}{k}& \\cr \\color{green}{\\checkmark}&=\\sum_{k=1}^{n}{k}+\\left(n+1\\right)& \\cr \\color{green}{\\checkmark}&=\\frac{n\\cdot \\left(n+1\\right)}{2}+n+1& \\cr \\color{green}{\\checkmark}&=\\frac{\\left(n+1\\right)\\cdot \\left(n+1+1\\right)}{2}& \\cr \\color{green}{\\checkmark}&=\\frac{\\left(n+1\\right)\\cdot \\left(n+2\\right)}{2}& \\cr \\end{array}\\]	[EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK]
Equiv	Pass	[log((a-1)^nproduct(x_i^(-a),i,1,n)),stackeq(nlog(a-1)-a*sum(log(x_i),i,1,n))]	[]			1	1	\\[\\begin{array}{lll} &\\ln \\left( {\\left(a-1\\right)}^{n}\\cdot \\prod_{i=1}^{n}{\\frac{1}{{{x}_{i}}^{a}}} \\right)& \\cr \\color{green}{\\checkmark}&=n\\cdot \\ln \\left( a-1 \\right)-a\\cdot \\sum_{i=1}^{n}{\\ln \\left( {x}_{i} \\right)}& \\cr \\end{array}\\]	[EMPTYCHAR, CHECKMARK]
Equiv	Pass	[binomial(n,k)+binomial(n,k+1),stackeq(n!/(k!(n-k)!)+n!/((k+1)!(n-k-1)!)),stackeq(n!/(k!(n-k)(n-k-1)!)+n!/((k+1)!(n-k-1)!)),stackeq(n!/(k!(n-k-1)!)(1/(n-k)+1/(k+1))),stackeq(n!/(k!(n-k-1)!)((n+1)/((n-k)(k+1)))),stackeq((n+1)n!/(k!(n-k-1)!)(1/((k+1)(n-k)))),stackeq((n+1)n!/((k+1)k!(n-k)(n-k-1)!)),stackeq(((n+1)!/((k+1)!)(1/((n-k)(n-k-1)!)))),stackeq((n+1)!/((k+1)!*(n-k)!)),stackeq(binomial(n+1,k+1))]	[]			1	1	\\[\\begin{array}{lll} &{{n}\\choose{k}}+{{n}\\choose{k+1}}& \\cr \\color{green}{\\checkmark}&=\\frac{n!}{k!\\cdot \\left(n-k\\right)!}+\\frac{n!}{\\left(k+1\\right)!\\cdot \\left(n-k-1\\right)!}& \\cr \\color{green}{\\checkmark}&=\\frac{n!}{k!\\cdot \\left(n-k\\right)\\cdot \\left(n-k-1\\right)!}+\\frac{n!}{\\left(k+1\\right)!\\cdot \\left(n-k-1\\right)!}& \\cr \\color{green}{\\checkmark}&=\\frac{n!}{k!\\cdot \\left(n-k-1\\right)!}\\cdot \\left(\\frac{1}{n-k}+\\frac{1}{k+1}\\right)& \\cr \\color{green}{\\checkmark}&=\\frac{n!}{k!\\cdot \\left(n-k-1\\right)!}\\cdot \\left(\\frac{n+1}{\\left(n-k\\right)\\cdot \\left(k+1\\right)}\\right)& \\cr \\color{green}{\\checkmark}&=\\frac{\\left(n+1\\right)\\cdot n!}{k!\\cdot \\left(n-k-1\\right)!}\\cdot \\left(\\frac{1}{\\left(k+1\\right)\\cdot \\left(n-k\\right)}\\right)& \\cr \\color{green}{\\checkmark}&=\\frac{\\left(n+1\\right)\\cdot n!}{\\left(k+1\\right)\\cdot k!\\cdot \\left(n-k\\right)\\cdot \\left(n-k-1\\right)!}& \\cr \\color{green}{\\checkmark}&=\\frac{\\left(n+1\\right)!}{\\left(k+1\\right)!}\\cdot \\left(\\frac{1}{\\left(n-k\\right)\\cdot \\left(n-k-1\\right)!}\\right)& \\cr \\color{green}{\\checkmark}&=\\frac{\\left(n+1\\right)!}{\\left(k+1\\right)!\\cdot \\left(n-k\\right)!}& \\cr \\color{green}{\\checkmark}&={{n+1}\\choose{k+1}}& \\cr \\end{array}\\]	[EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK]
Equiv	Pass	[(x-1)^2=(x-1)(x-1), stackeq(x^2-2x+1)]	[]			1	1	\\[\\begin{array}{lll}\\color{green}{\\checkmark}&{\\left(x-1\\right)}^2=\\left(x-1\\right)\\cdot \\left(x-1\\right)& \\cr \\color{green}{\\checkmark}&=x^2-2\\cdot x+1& \\cr \\end{array}\\]	[CHECKMARK, CHECKMARK]
Equiv	Pass	[(x-1)^2=(x-1)(x-1), stackeq(x^2-2x+2)]	[]			0	0	\\[\\begin{array}{lll}\\color{green}{\\checkmark}&{\\left(x-1\\right)}^2=\\left(x-1\\right)\\cdot \\left(x-1\\right)& \\cr \\color{red}{?}&=x^2-2\\cdot x+2& \\cr \\end{array}\\]	[CHECKMARK,QMCHAR]
Equiv	Pass	[(x-2)^2=(x-1)(x-1), stackeq(x^2-2x+1)]	[]			0	0	\\[\\begin{array}{lll}\\color{red}{?}&{\\left(x-2\\right)}^2=\\left(x-1\\right)\\cdot \\left(x-1\\right)& \\cr \\color{green}{\\checkmark}&=x^2-2\\cdot x+1& \\cr \\end{array}\\]	[QMCHAR, CHECKMARK]
Equiv	Pass	[4^((n+1)+1)-1= 44^(n+1)-1,stackeq(4(4^(n+1)-1)+3)]	[]			1	1	\\[\\begin{array}{lll}\\color{green}{\\checkmark}&4^{n+1+1}-1=4\\cdot 4^{n+1}-1& \\cr \\color{green}{\\checkmark}&=4\\cdot \\left(4^{n+1}-1\\right)+3& \\cr \\end{array}\\]	[CHECKMARK, CHECKMARK]
Equiv	Pass	[2x+3y=6 and 4x+9y=15,2x+3y=6 and -2x=-3,3+3y=6 and 2*x=3,y=1 and x=3/2]	[]			1	1	\\[\\begin{array}{lll} &\\left\\{\\begin{array}{l}2\\cdot x+3\\cdot y=6\\cr 4\\cdot x+9\\cdot y=15\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}2\\cdot x+3\\cdot y=6\\cr -2\\cdot x=-3\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}3+3\\cdot y=6\\cr 2\\cdot x=3\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}y=1\\cr x=\\frac{3}{2}\\cr \\end{array}\\right.& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[2x+3y=6 and 4x+9y=15,2x+3y=6 and -2x=-3,3+3y=6 and 2*x=3,y=1 and x=3]	[]			0	0	\\[\\begin{array}{lll} &\\left\\{\\begin{array}{l}2\\cdot x+3\\cdot y=6\\cr 4\\cdot x+9\\cdot y=15\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}2\\cdot x+3\\cdot y=6\\cr -2\\cdot x=-3\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}3+3\\cdot y=6\\cr 2\\cdot x=3\\cr \\end{array}\\right.& \\cr \\color{red}{?}&\\left\\{\\begin{array}{l}y=1\\cr x=3\\cr \\end{array}\\right.& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR,QMCHAR]
Equiv	Pass	[x^2+y^2=8 and x=y, 2*x^2=8 and y=x, x^2=4 and y=x, x= #pm#2 and y=x, (x= 2 and y=x) or (x=-2 and y=x), (x=2 and y=2) or (x=-2 and y=-2)]	[]			1	1	\\[\\begin{array}{lll} &\\left\\{\\begin{array}{l}x^2+y^2=8\\cr x=y\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}2\\cdot x^2=8\\cr y=x\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}x^2=4\\cr y=x\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}x= \\pm 2\\cr y=x\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&x=2\\,{\\mbox{ and }}\\, y=x\\,{\\mbox{ or }}\\, x=-2\\,{\\mbox{ and }}\\, y=x& \\cr \\color{green}{\\Leftrightarrow}&x=2\\,{\\mbox{ and }}\\, y=2\\,{\\mbox{ or }}\\, x=-2\\,{\\mbox{ and }}\\, y=-2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x^2+y^2=5 and xy=2, x^2+y^2-5=0 and xy-2=0, x^2-2xy+y^2-1=0 and x^2+2xy+y^2-9=0, (x-y)^2-1=0 and (x+y)^2-3^2=0, (x-y=1 and x+y=3) or (x-y=-1 and x+y=3) or (x-y=1 and x+y=-3) or (x-y=-1 and x+y=-3), (x=1 and y=2) or (x=2 and y=1) or (x=-2 and y=-1) or (x=-1 and y=-2)]	[]			1	1	\\[\\begin{array}{lll} &\\left\\{\\begin{array}{l}x^2+y^2=5\\cr x\\cdot y=2\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}x^2+y^2-5=0\\cr x\\cdot y-2=0\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}x^2-2\\cdot x\\cdot y+y^2-1=0\\cr x^2+2\\cdot x\\cdot y+y^2-9=0\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}{\\left(x-y\\right)}^2-1=0\\cr {\\left(x+y\\right)}^2-3^2=0\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&x-y=1\\,{\\mbox{ and }}\\, x+y=3\\,{\\mbox{ or }}\\, x-y=-1\\,{\\mbox{ and }}\\, x+y=3\\,{\\mbox{ or }}\\, x-y=1\\,{\\mbox{ and }}\\, x+y=-3\\,{\\mbox{ or }}\\, x-y=-1\\,{\\mbox{ and }}\\, x+y=-3& \\cr \\color{green}{\\Leftrightarrow}&x=1\\,{\\mbox{ and }}\\, y=2\\,{\\mbox{ or }}\\, x=2\\,{\\mbox{ and }}\\, y=1\\,{\\mbox{ or }}\\, x=-2\\,{\\mbox{ and }}\\, y=-1\\,{\\mbox{ or }}\\, x=-1\\,{\\mbox{ and }}\\, y=-2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[4x^2+7xy+4y^2=4 and y=x-4, 4x^2+7x(x-4)+4(x-4)^2-4=0 and y=x-4, 15x^2-60x+60=0 and y=x-4, (x-2)^2=0 and y=x-4, x=2 and y=x-4, x=2 and y=-2]	[]			1	1	\\[\\begin{array}{lll} &\\left\\{\\begin{array}{l}4\\cdot x^2+7\\cdot x\\cdot y+4\\cdot y^2=4\\cr y=x-4\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}4\\cdot x^2+7\\cdot x\\cdot \\left(x-4\\right)+4\\cdot {\\left(x-4\\right)}^2-4=0\\cr y=x-4\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}15\\cdot x^2-60\\cdot x+60=0\\cr y=x-4\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}{\\left(x-2\\right)}^2=0\\cr y=x-4\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}x=2\\cr y=x-4\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}x=2\\cr y=-2\\cr \\end{array}\\right.& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[a^2=b and a^2=1, b=a^2 and (a=1 or a=-1), (b=1 and a=1) or (b=1 and a=-1)]	[]			1	1	\\[\\begin{array}{lll} &\\left\\{\\begin{array}{l}a^2=b\\cr a^2=1\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}b=a^2\\cr a=1\\,{\\mbox{ or }}\\, a=-1\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&b=1\\,{\\mbox{ and }}\\, a=1\\,{\\mbox{ or }}\\, b=1\\,{\\mbox{ and }}\\, a=-1& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[a^2=b and x=1, b=a^2 and x=1]	[]			1	1	\\[\\begin{array}{lll} &\\left\\{\\begin{array}{l}a^2=b\\cr x=1\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}b=a^2\\cr x=1\\cr \\end{array}\\right.& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR]
Equiv	Pass	[a^2=b and b^2=a, b=a^2 and a^4=a, b=a^2 and a^4-a=0, b=a^2 and a(a-1)(a^2+a+1)=0, b=a^2 and (a=0 or a=1 or a^2+a+1=0), (b=0 and a=0) or (b=1 and a=1)]	[]	[assumereal]		1	1	\\[\\begin{array}{lll}\\color{blue}{(\\mathbb{R})}&\\left\\{\\begin{array}{l}a^2=b\\cr b^2=a\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}b=a^2\\cr a^4=a\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}b=a^2\\cr a^4-a=0\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}b=a^2\\cr a\\cdot \\left(a-1\\right)\\cdot \\left(a^2+a+1\\right)=0\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}b=a^2\\cr a=0\\,{\\mbox{ or }}\\, a=1\\,{\\mbox{ or }}\\, a^2+a+1=0\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&b=0\\,{\\mbox{ and }}\\, a=0\\,{\\mbox{ or }}\\, b=1\\,{\\mbox{ and }}\\, a=1& \\cr \\end{array}\\]	[ASSUMEREALVARS, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[2x^3-9x^2+10x-3,stacklet(x,1),21^3-91^2+101-3,stackeq(0),"So",2x^3-9x^2+10x-3,stackeq((x-1)(2x^2-7x+3)),stackeq((x-1)(2x-1)*(x-3))]	[]			0	0	\\[\\begin{array}{lll} &2\\cdot x^3-9\\cdot x^2+10\\cdot x-3& \\cr &\\mbox{Let }x = 1& \\cr \\color{green}{\\Leftrightarrow}&2\\cdot 1^3-9\\cdot 1^2+10\\cdot 1-3& \\cr \\color{green}{\\checkmark}&=0& \\cr &\\mbox{So}& \\cr &2\\cdot x^3-9\\cdot x^2+10\\cdot x-3& \\cr \\color{green}{\\checkmark}&=\\left(x-1\\right)\\cdot \\left(2\\cdot x^2-7\\cdot x+3\\right)& \\cr \\color{green}{\\checkmark}&=\\left(x-1\\right)\\cdot \\left(2\\cdot x-1\\right)\\cdot \\left(x-3\\right)& \\cr \\end{array}\\]	[EMPTYCHAR, EMPTYCHAR, EQUIVCHAR, CHECKMARK, EMPTYCHAR, EMPTYCHAR, CHECKMARK, CHECKMARK]
Equiv	Pass	[2x^2+x>=6, 2x^2+x-6>=0, (2x-3)(x+2)>= 0,((2x-3)>=0 and (x+2)>=0) or ((2x-3)<=0 and (x+2)<=0), (x>=3/2 and x>=-2) or (x<=3/2 and x<=-2), x>=3/2 or x <=-2]	[]			1	1	\\[\\begin{array}{lll} &2\\cdot x^2+x\\geq 6& \\cr \\color{green}{\\Leftrightarrow}&2\\cdot x^2+x-6\\geq 0& \\cr \\color{green}{\\Leftrightarrow}&\\left(2\\cdot x-3\\right)\\cdot \\left(x+2\\right)\\geq 0& \\cr \\color{green}{\\Leftrightarrow}&2\\cdot x-3\\geq 0\\,{\\mbox{ and }}\\, x+2\\geq 0\\,{\\mbox{ or }}\\, 2\\cdot x-3\\leq 0\\,{\\mbox{ and }}\\, x+2\\leq 0& \\cr \\color{green}{\\Leftrightarrow}&x\\geq \\frac{3}{2}\\,{\\mbox{ and }}\\, x\\geq -2\\,{\\mbox{ or }}\\, x\\leq \\frac{3}{2}\\,{\\mbox{ and }}\\, x\\leq -2& \\cr \\color{green}{\\Leftrightarrow}&x\\geq \\frac{3}{2}\\,{\\mbox{ or }}\\, x\\leq -2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[2x^2+x>=6, 2x^2+x-6>=0, (2x-3)(x+2)>= 0,((2x-3)>=0 and (x+2)>=0) or ((2x-3)<=0 and (x+2)<=0), (x>=3/2 and x>=-2) or (x<=3/2 and x<=-2), x>=3/2 or x <=-2]	[]			1	1	\\[\\begin{array}{lll} &2\\cdot x^2+x\\geq 6& \\cr \\color{green}{\\Leftrightarrow}&2\\cdot x^2+x-6\\geq 0& \\cr \\color{green}{\\Leftrightarrow}&\\left(2\\cdot x-3\\right)\\cdot \\left(x+2\\right)\\geq 0& \\cr \\color{green}{\\Leftrightarrow}&2\\cdot x-3\\geq 0\\,{\\mbox{ and }}\\, x+2\\geq 0\\,{\\mbox{ or }}\\, 2\\cdot x-3\\leq 0\\,{\\mbox{ and }}\\, x+2\\leq 0& \\cr \\color{green}{\\Leftrightarrow}&x\\geq \\frac{3}{2}\\,{\\mbox{ and }}\\, x\\geq -2\\,{\\mbox{ or }}\\, x\\leq \\frac{3}{2}\\,{\\mbox{ and }}\\, x\\leq -2& \\cr \\color{green}{\\Leftrightarrow}&x\\geq \\frac{3}{2}\\,{\\mbox{ or }}\\, x\\leq -2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[2x^2+x>=6, 2x^2+x-6>=0, (2x-3)(x+2)>= 0,((2x-3)>=0 and (x+2)>=0) or ((2x-3)<=0 and (x+2)<=0), (x>=3/2 and x>=-2) or (x<=3/2 and x<=-2), x>=3/2 or x <=2]	[]			0	0	\\[\\begin{array}{lll} &2\\cdot x^2+x\\geq 6& \\cr \\color{green}{\\Leftrightarrow}&2\\cdot x^2+x-6\\geq 0& \\cr \\color{green}{\\Leftrightarrow}&\\left(2\\cdot x-3\\right)\\cdot \\left(x+2\\right)\\geq 0& \\cr \\color{green}{\\Leftrightarrow}&2\\cdot x-3\\geq 0\\,{\\mbox{ and }}\\, x+2\\geq 0\\,{\\mbox{ or }}\\, 2\\cdot x-3\\leq 0\\,{\\mbox{ and }}\\, x+2\\leq 0& \\cr \\color{green}{\\Leftrightarrow}&x\\geq \\frac{3}{2}\\,{\\mbox{ and }}\\, x\\geq -2\\,{\\mbox{ or }}\\, x\\leq \\frac{3}{2}\\,{\\mbox{ and }}\\, x\\leq -2& \\cr \\color{red}{?}&x\\geq \\frac{3}{2}\\,{\\mbox{ or }}\\, x\\leq 2& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR,QMCHAR]
Equiv	Pass	[x^2>=9 and x>3, x^2-9>=0 and x>3, (x>=3 or x<=-3) and x>3, x>3]	[]			1	1	\\[\\begin{array}{lll} &\\left\\{\\begin{array}{l}x^2\\geq 9\\cr x > 3\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}x^2-9\\geq 0\\cr x > 3\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}x\\geq 3\\,{\\mbox{ or }}\\, x\\leq -3\\cr x > 3\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&x > 3& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[-x^2+ax+a-3<0, a-3<x^2-ax, a-3<(x-a/2)^2-a^2/4, a^2/4+a-3<(x-a/2)^2, a^2+4a-12<4(x-a/2)^2, (a-2)(a+6)<4(x-a/2)^2, "This inequality is required to be true for all x.", "So it must be true when the right hand side takes its minimum value.", "This happens for x=a/2.", (a-2)*(a+6)<0, ((a-2)<0 and (a+6)>0) or ((a-2)>0 and (a+6)<0), (a<2 and a>-6) or (a>2 and a<-6), (-6<a and a<2) or false, (-6<a and a<2)]	[]			0	0	\\[\\begin{array}{lll} &-x^2+a\\cdot x+a-3 < 0& \\cr \\color{green}{\\Leftrightarrow}&a-3 < x^2-a\\cdot x& \\cr \\color{green}{\\Leftrightarrow}&a-3 < {\\left(x-\\frac{a}{2}\\right)}^2-\\frac{a^2}{4}& \\cr \\color{green}{\\Leftrightarrow}&\\frac{a^2}{4}+a-3 < {\\left(x-\\frac{a}{2}\\right)}^2& \\cr \\color{green}{\\Leftrightarrow}&a^2+4\\cdot a-12 < 4\\cdot {\\left(x-\\frac{a}{2}\\right)}^2& \\cr \\color{green}{\\Leftrightarrow}&\\left(a-2\\right)\\cdot \\left(a+6\\right) < 4\\cdot {\\left(x-\\frac{a}{2}\\right)}^2& \\cr &\\mbox{This inequality is required to be true for all x.}& \\cr &\\mbox{So it must be true when the right hand side takes its minimum value.}& \\cr &\\mbox{This happens for x=a/2.}& \\cr &\\left(a-2\\right)\\cdot \\left(a+6\\right) < 0& \\cr \\color{green}{\\Leftrightarrow}&a-2 < 0\\,{\\mbox{ and }}\\, a+6 > 0\\,{\\mbox{ or }}\\, a-2 > 0\\,{\\mbox{ and }}\\, a+6 < 0& \\cr \\color{green}{\\Leftrightarrow}&a < 2\\,{\\mbox{ and }}\\, a > -6\\,{\\mbox{ or }}\\, a > 2\\,{\\mbox{ and }}\\, a < -6& \\cr \\color{green}{\\Leftrightarrow}&-6 < a\\,{\\mbox{ and }}\\, a < 2\\,{\\mbox{ or }}\\, \\mathbf{False}& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}-6 < a\\cr a < 2\\cr \\end{array}\\right.& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EMPTYCHAR, EMPTYCHAR, EMPTYCHAR, EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x-2>0 and x(x-2)<15,x>2 and x^2-2x-15<0,x>2 and (x-5)*(x+3)<0,x>2 and ((x<5 and x>-3) or (x>5 and x<-3)),x>2 and (x<5 and x>-3),x>2 and x<5]	[]			1	1	\\[\\begin{array}{lll} &\\left\\{\\begin{array}{l}x-2 > 0\\cr x\\cdot \\left(x-2\\right) < 15\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}x > 2\\cr x^2-2\\cdot x-15 < 0\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}x > 2\\cr \\left(x-5\\right)\\cdot \\left(x+3\\right) < 0\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}x > 2\\cr x < 5\\,{\\mbox{ and }}\\, x > -3\\,{\\mbox{ or }}\\, x > 5\\,{\\mbox{ and }}\\, x < -3\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}x > 2\\cr x < 5\\,{\\mbox{ and }}\\, x > -3\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}x > 2\\cr x < 5\\cr \\end{array}\\right.& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x-2>0 and x(x-2)<15,x>2 and x^2-2x-15<0,x>2 and (x-5)*(x+3)<0,x>2 and ((x<5 and x>-3) or (x>5 and x<-3)),x>7 and (x<5 and x>-3),x>2 and x<5]	[]			0	0	\\[\\begin{array}{lll} &\\left\\{\\begin{array}{l}x-2 > 0\\cr x\\cdot \\left(x-2\\right) < 15\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}x > 2\\cr x^2-2\\cdot x-15 < 0\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}x > 2\\cr \\left(x-5\\right)\\cdot \\left(x+3\\right) < 0\\cr \\end{array}\\right.& \\cr \\color{green}{\\Leftrightarrow}&\\left\\{\\begin{array}{l}x > 2\\cr x < 5\\,{\\mbox{ and }}\\, x > -3\\,{\\mbox{ or }}\\, x > 5\\,{\\mbox{ and }}\\, x < -3\\cr \\end{array}\\right.& \\cr \\color{red}{?}&\\left\\{\\begin{array}{l}x > 7\\cr x < 5\\,{\\mbox{ and }}\\, x > -3\\cr \\end{array}\\right.& \\cr \\color{red}{?}&\\left\\{\\begin{array}{l}x > 2\\cr x < 5\\cr \\end{array}\\right.& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR,QMCHAR,QMCHAR]
Equiv	Pass	[x^2 + (a-2)x + a = 0,(x + (a-2)/2)^2 -((a-2)/2)^2 + a = 0,(x + (a-2)/2)^2 =(a-2)^2/4 - a,"This has real roots iff",(a-2)^2/4-a >=0,a^2-4a+4-4a >=0,a^2-8a+4>=0,(a-4)^2-16+4>=0,(a-4)^2>=12,a-4>=sqrt(12) or a-4<= -sqrt(12),"Ignoring the negative solution.",a>=sqrt(12)+4,"Using external domain information that a is an integer.",a>=8]	[]			0	0	\\[\\begin{array}{lll} &x^2+\\left(a-2\\right)\\cdot x+a=0& \\cr \\color{green}{\\Leftrightarrow}&{\\left(x+\\frac{a-2}{2}\\right)}^2-{\\left(\\frac{a-2}{2}\\right)}^2+a=0& \\cr \\color{green}{\\Leftrightarrow}&{\\left(x+\\frac{a-2}{2}\\right)}^2=\\frac{{\\left(a-2\\right)}^2}{4}-a& \\cr &\\mbox{This has real roots iff}& \\cr &\\frac{{\\left(a-2\\right)}^2}{4}-a\\geq 0& \\cr \\color{green}{\\Leftrightarrow}&a^2-4\\cdot a+4-4\\cdot a\\geq 0& \\cr \\color{green}{\\Leftrightarrow}&a^2-8\\cdot a+4\\geq 0& \\cr \\color{green}{\\Leftrightarrow}&{\\left(a-4\\right)}^2-16+4\\geq 0& \\cr \\color{green}{\\Leftrightarrow}&{\\left(a-4\\right)}^2\\geq 12& \\cr \\color{green}{\\Leftrightarrow}&a-4\\geq \\sqrt{12}\\,{\\mbox{ or }}\\, a-4\\leq -\\sqrt{12}& \\cr &\\mbox{Ignoring the negative solution.}& \\cr &a\\geq \\sqrt{12}+4& \\cr &\\mbox{Using external domain information that a is an integer.}& \\cr &a\\geq 8& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EMPTYCHAR, EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EMPTYCHAR, EMPTYCHAR, EMPTYCHAR, EMPTYCHAR]
Equiv	Pass	["Set P(n) be the statement that",sum(k^2,k,1,n) = n(n+1)(2n+1)/6, "Then P(1) is the statement", 1^2 = 1(1+1)(21+1)/6, 1 = 1, "So P(1) holds. Now assume P(n) is true.",sum(k^2,k,1,n) = n(n+1)(2n+1)/6,sum(k^2,k,1,n) +(n+1)^2= n(n+1)(2n+1)/6 +(n+1)^2,sum(k^2,k,1,n+1)= (n+1)(n(2n+1) +6(n+1))/6,sum(k^2,k,1,n+1)= (n+1)(2n^2+7n+6)/6,sum(k^2,k,1,n+1)= (n+1)(n+1+1)(2(n+1)+1)/6]	[]			0	0	\\[\\begin{array}{lll} &\\mbox{Set P(n) be the statement that}& \\cr &\\sum_{k=1}^{n}{k^2}=\\frac{n\\cdot \\left(n+1\\right)\\cdot \\left(2\\cdot n+1\\right)}{6}& \\cr &\\mbox{Then P(1) is the statement}& \\cr &1^2=\\frac{1\\cdot \\left(1+1\\right)\\cdot \\left(2\\cdot 1+1\\right)}{6}& \\cr \\color{green}{\\Leftrightarrow}&1=1& \\cr &\\mbox{So P(1) holds. Now assume P(n) is true.}& \\cr &\\sum_{k=1}^{n}{k^2}=\\frac{n\\cdot \\left(n+1\\right)\\cdot \\left(2\\cdot n+1\\right)}{6}& \\cr \\color{green}{\\Leftrightarrow}&\\sum_{k=1}^{n}{k^2}+{\\left(n+1\\right)}^2=\\frac{n\\cdot \\left(n+1\\right)\\cdot \\left(2\\cdot n+1\\right)}{6}+{\\left(n+1\\right)}^2& \\cr \\color{green}{\\Leftrightarrow}&\\sum_{k=1}^{n+1}{k^2}=\\frac{\\left(n+1\\right)\\cdot \\left(n\\cdot \\left(2\\cdot n+1\\right)+6\\cdot \\left(n+1\\right)\\right)}{6}& \\cr \\color{green}{\\Leftrightarrow}&\\sum_{k=1}^{n+1}{k^2}=\\frac{\\left(n+1\\right)\\cdot \\left(2\\cdot n^2+7\\cdot n+6\\right)}{6}& \\cr \\color{green}{\\Leftrightarrow}&\\sum_{k=1}^{n+1}{k^2}=\\frac{\\left(n+1\\right)\\cdot \\left(n+1+1\\right)\\cdot \\left(2\\cdot \\left(n+1\\right)+1\\right)}{6}& \\cr \\end{array}\\]	[EMPTYCHAR, EMPTYCHAR, EMPTYCHAR, EMPTYCHAR, EQUIVCHAR, EMPTYCHAR, EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[(n+1)^2+sum(k^2,k,1,n) = (n+1)^2+(n(n+1)(2n+1))/6, sum(k^2,k,1,n+1) = ((n+1)(n(2n+1)+6(n+1)))/6, sum(k^2,k,1,n+1) = ((n+1)(2n^2+7n+6))/6, sum(k^2,k,1,n+1) = ((n+1)(n+2)(2*(n+1)+1))/6]	[]			1	1	\\[\\begin{array}{lll} &{\\left(n+1\\right)}^2+\\sum_{k=1}^{n}{k^2}={\\left(n+1\\right)}^2+\\frac{n\\cdot \\left(n+1\\right)\\cdot \\left(2\\cdot n+1\\right)}{6}& \\cr \\color{green}{\\Leftrightarrow}&\\sum_{k=1}^{n+1}{k^2}=\\frac{\\left(n+1\\right)\\cdot \\left(n\\cdot \\left(2\\cdot n+1\\right)+6\\cdot \\left(n+1\\right)\\right)}{6}& \\cr \\color{green}{\\Leftrightarrow}&\\sum_{k=1}^{n+1}{k^2}=\\frac{\\left(n+1\\right)\\cdot \\left(2\\cdot n^2+7\\cdot n+6\\right)}{6}& \\cr \\color{green}{\\Leftrightarrow}&\\sum_{k=1}^{n+1}{k^2}=\\frac{\\left(n+1\\right)\\cdot \\left(n+2\\right)\\cdot \\left(2\\cdot \\left(n+1\\right)+1\\right)}{6}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[conjugate(a)conjugate(b),stacklet(a,x+iy),stacklet(b,r+is),stackeq(conjugate(x+iy)conjugate(r+is)),stackeq((x-iy)(r-is)),stackeq((xr-ys)-i(yr+xs)),stackeq(conjugate((xr-ys)+i(yr+xs))),stackeq(conjugate((x+iy)(r+is))),stacklet(x+iy,a),stacklet(r+is,b),stackeq(conjugate(a*b))]	[]			1	1	\\[\\begin{array}{lll} &a^\\star\\cdot b^\\star& \\cr &\\mbox{Let }a = x+\\mathrm{i}\\cdot y& \\cr &\\mbox{Let }b = r+\\mathrm{i}\\cdot s& \\cr \\color{green}{\\checkmark}&=\\left(x+\\mathrm{i}\\cdot y\\right)^\\star\\cdot \\left(r+\\mathrm{i}\\cdot s\\right)^\\star& \\cr \\color{green}{\\checkmark}&=\\left(x-\\mathrm{i}\\cdot y\\right)\\cdot \\left(r-\\mathrm{i}\\cdot s\\right)& \\cr \\color{green}{\\checkmark}&=x\\cdot r-y\\cdot s-\\mathrm{i}\\cdot \\left(y\\cdot r+x\\cdot s\\right)& \\cr \\color{green}{\\checkmark}&=\\left(x\\cdot r-y\\cdot s+\\mathrm{i}\\cdot \\left(y\\cdot r+x\\cdot s\\right)\\right)^\\star& \\cr \\color{green}{\\checkmark}&=\\left(\\left(x+\\mathrm{i}\\cdot y\\right)\\cdot \\left(r+\\mathrm{i}\\cdot s\\right)\\right)^\\star& \\cr &\\mbox{Let }x+\\mathrm{i}\\cdot y = a& \\cr &\\mbox{Let }r+\\mathrm{i}\\cdot s = b& \\cr \\color{green}{\\checkmark}&=\\left(a\\cdot b\\right)^\\star& \\cr \\end{array}\\]	[EMPTYCHAR, EMPTYCHAR, EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, EMPTYCHAR, EMPTYCHAR, CHECKMARK]
Equiv	Pass	[nounint(xe^x,x,-inf,0),nounlimit(nounint(xe^x,x,t,0),t,-inf),nounlimit(e^t-te^t-1,t,-inf),nounlimit(e^t,t,-inf)+nounlimit(-te^t,t,-inf)+nounlimit(-1,t,-inf),-1]	[]			1	1	\\[\\begin{array}{lll} &\\int_{-\\infty }^{0}{x\\cdot e^{x}\\;\\mathrm{d}x}& \\cr \\color{green}{\\Leftrightarrow}&\\lim_{t\\rightarrow -\\infty }{\\int_{t}^{0}{x\\cdot e^{x}\\;\\mathrm{d}x}}& \\cr \\color{green}{\\Leftrightarrow}&\\lim_{t\\rightarrow -\\infty }{e^{t}-t\\cdot e^{t}-1}& \\cr \\color{green}{\\Leftrightarrow}&\\lim_{t\\rightarrow -\\infty }{e^{t}}+\\lim_{t\\rightarrow -\\infty }{\\left(-t\\right)\\cdot e^{t}}+\\lim_{t\\rightarrow -\\infty }{-1}& \\cr \\color{green}{\\Leftrightarrow}&-1& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[noundiff(x^2,x),stackeq(nounlimit(((x+h)^2-x^2)/h,h,0)),stackeq(nounlimit(2x+h,h,0)),stackeq(2x)]	[]			1	1	\\[\\begin{array}{lll} &\\frac{\\mathrm{d}}{\\mathrm{d} x} x^2& \\cr \\color{green}{\\checkmark}&=\\lim_{h\\rightarrow 0}{\\frac{{\\left(x+h\\right)}^2-x^2}{h}}& \\cr \\color{green}{\\checkmark}&=\\lim_{h\\rightarrow 0}{2\\cdot x+h}& \\cr \\color{green}{\\checkmark}&=2\\cdot x& \\cr \\end{array}\\]	[EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK]
Equiv	Pass	[-12+3noundiff(y(x),x)+8-8noundiff(y(x),x)=0,-5*noundiff(y(x),x)=4,noundiff(y(x),x)=-4/5]	[]	[calculus]		1	1	\\[\\begin{array}{lll} &-12+3\\cdot \\left(\\frac{\\mathrm{d}}{\\mathrm{d} x} y\\left(x\\right)\\right)+8-8\\cdot \\left(\\frac{\\mathrm{d}}{\\mathrm{d} x} y\\left(x\\right)\\right)=0& \\cr \\color{green}{\\Leftrightarrow}&-5\\cdot \\left(\\frac{\\mathrm{d}}{\\mathrm{d} x} y\\left(x\\right)\\right)=4& \\cr \\color{green}{\\Leftrightarrow}&\\left(\\frac{\\mathrm{d}}{\\mathrm{d} x} y\\left(x\\right)\\right)=\\frac{-4}{5}& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[x^2+1,x^3/3+x,x^2+1,x^3/3+x+c]	[]	[calculus]		1	1	\\[\\begin{array}{lll} &x^2+1& \\cr \\color{blue}{\\int\\ldots\\mathrm{d}x}&\\frac{x^3}{3}+x& \\cr \\color{blue}{\\frac{\\mathrm{d}}{\\mathrm{d}x}\\ldots}&x^2+1& \\cr \\color{blue}{\\int\\ldots\\mathrm{d}x}&\\frac{x^3}{3}+x+c& \\cr \\end{array}\\]	[EMPTYCHAR,INTCHAR(x),DIFFCHAR(x),INTCHAR(x)]
Equiv	Pass	[3x^(3/2)-2/x,(9sqrt(x))/2+2/x^2,3*x^(3/2)-2/x+c]	[]	[calculus]		1	1	\\[\\begin{array}{lll} &3\\cdot x^{\\frac{3}{2}}-\\frac{2}{x}&{\\color{blue}{{x \\not\\in {\\left \\{0 \\right \\}}}}}\\cr \\color{blue}{\\frac{\\mathrm{d}}{\\mathrm{d}x}\\ldots}&\\frac{9\\cdot \\sqrt{x}}{2}+\\frac{2}{x^2}&{\\color{blue}{{x \\in {\\left( 0,\\, \\infty \\right)}}}}\\cr \\color{blue}{\\int\\ldots\\mathrm{d}x}&3\\cdot x^{\\frac{3}{2}}-\\frac{2}{x}+c& \\cr \\end{array}\\]	[EMPTYCHAR,DIFFCHAR(x),INTCHAR(x)]
Equiv	Pass	[x^2+1,stackeq(x^3/3+x),stackeq(x^2+1),stackeq(x^3/3+x+c)]	[]	[calculus]		0	0	\\[\\begin{array}{lll} &x^2+1& \\cr \\color{red}{?}&=\\frac{x^3}{3}+x& \\cr \\color{red}{?}&=x^2+1& \\cr \\color{red}{?}&=\\frac{x^3}{3}+x+c& \\cr \\end{array}\\]	[EMPTYCHAR,QMCHAR,QMCHAR,QMCHAR]
Equiv	Pass	[diff(x^2sin(x),x),stackeq(x^2diff(sin(x),x)+diff(x^2,x)sin(x)),stackeq(x^2cos(x)+2xsin(x))]	[]	[calculus]		1	1	\\[\\begin{array}{lll} &\\cos \\left( x \\right)\\cdot x^2+2\\cdot x\\cdot \\sin \\left( x \\right)& \\cr \\color{green}{\\checkmark}&=x^2\\cdot \\cos \\left( x \\right)+2\\cdot x\\cdot \\sin \\left( x \\right)& \\cr \\color{green}{\\checkmark}&=x^2\\cdot \\cos \\left( x \\right)+2\\cdot x\\cdot \\sin \\left( x \\right)& \\cr \\end{array}\\]	[EMPTYCHAR, CHECKMARK, CHECKMARK]
Equiv	Pass	[y(x)cos(x)+y(x)^2 = 6x,cos(x)diff(y(x),x)+2y(x)diff(y(x),x)-y(x)sin(x) = 6,(cos(x)+2y(x))diff(y(x),x) = y(x)sin(x)+6,diff(y(x),x) = (y(x)sin(x)+6)/(cos(x)+2*y(x))]	[]	[calculus]		1	1	\\[\\begin{array}{lll} &y\\left(x\\right)\\cdot \\cos \\left( x \\right)+y^2\\left(x\\right)=6\\cdot x& \\cr \\color{blue}{\\frac{\\mathrm{d}}{\\mathrm{d}x}\\ldots}&\\cos \\left( x \\right)\\cdot \\left(\\frac{\\mathrm{d}}{\\mathrm{d} x} y\\left(x\\right)\\right)+2\\cdot y\\left(x\\right)\\cdot \\left(\\frac{\\mathrm{d}}{\\mathrm{d} x} y\\left(x\\right)\\right)+\\left(-y\\left(x\\right)\\right)\\cdot \\sin \\left( x \\right)=6& \\cr \\color{green}{\\Leftrightarrow}&\\left(\\cos \\left( x \\right)+2\\cdot y\\left(x\\right)\\right)\\cdot \\left(\\frac{\\mathrm{d}}{\\mathrm{d} x} y\\left(x\\right)\\right)=y\\left(x\\right)\\cdot \\sin \\left( x \\right)+6& \\cr \\color{green}{\\Leftrightarrow}&\\left(\\frac{\\mathrm{d}}{\\mathrm{d} x} y\\left(x\\right)\\right)=\\frac{y\\left(x\\right)\\cdot \\sin \\left( x \\right)+6}{\\cos \\left( x \\right)+2\\cdot y\\left(x\\right)}& \\cr \\end{array}\\]	[EMPTYCHAR,DIFFCHAR(x), EQUIVCHAR, EQUIVCHAR]
Equiv	Pass	[nounint(s^2+1,s),stackeq(s^3/3+s+c)]	[]	[calculus]		1	1	\\[\\begin{array}{lll} &\\int {s^2+1}{\\;\\mathrm{d}s}& \\cr \\color{blue}{\\int\\ldots\\mathrm{d}s}&=\\frac{s^3}{3}+s+c& \\cr \\end{array}\\]	[EMPTYCHAR,INTCHAR(s)]
Equiv	Pass	[nounint(x^3log(x),x),x^4/4log(x)-1/4nounint(x^3,x),x^4/4log(x)-x^4/16]	[]	[calculus]		0	0	\\[\\begin{array}{lll} &\\int {x^3\\cdot \\ln \\left( x \\right)}{\\;\\mathrm{d}x}& \\cr \\color{green}{\\Leftrightarrow}&\\frac{x^4}{4}\\cdot \\ln \\left( x \\right)-\\frac{1}{4}\\cdot \\int {x^3}{\\;\\mathrm{d}x}& \\cr \\color{red}{\\cdots +c\\quad ?}&\\frac{x^4}{4}\\cdot \\ln \\left( x \\right)-\\frac{x^4}{16}&{\\color{blue}{{x \\in {\\left( 0,\\, \\infty \\right)}}}}\\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR,PLUSC]
Equiv	Pass	[nounint(x^3log(x),x),x^4/4log(x)-1/4nounint(x^3,x),x^4/4log(x)-x^4/16+c]	[]	[calculus]		1	1	\\[\\begin{array}{lll} &\\int {x^3\\cdot \\ln \\left( x \\right)}{\\;\\mathrm{d}x}& \\cr \\color{green}{\\Leftrightarrow}&\\frac{x^4}{4}\\cdot \\ln \\left( x \\right)-\\frac{1}{4}\\cdot \\int {x^3}{\\;\\mathrm{d}x}& \\cr \\color{blue}{\\int\\ldots\\mathrm{d}x}&\\frac{x^4}{4}\\cdot \\ln \\left( x \\right)-\\frac{x^4}{16}+c& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR,INTCHAR(x)]
Equiv	Pass	[noundiff(y,x)-2/xy=x^3sin(3x),1/x^2noundiff(y,x)-2/x^3y=xsin(3x),noundiff(y/x^2,x)=xsin(3x),y/x^2 = nounint(xsin(3x),x),y/x^2=(sin(3x)-3xcos(3*x))/9+c]	[]	[calculus]		1	1	\\[\\begin{array}{lll} &\\frac{\\mathrm{d} y}{\\mathrm{d} x}-\\frac{2}{x}\\cdot y=x^3\\cdot \\sin \\left( 3\\cdot x \\right)& \\cr \\color{green}{\\Leftrightarrow}&\\frac{1}{x^2}\\cdot \\left(\\frac{\\mathrm{d} y}{\\mathrm{d} x}\\right)-\\frac{2}{x^3}\\cdot y=x\\cdot \\sin \\left( 3\\cdot x \\right)& \\cr \\color{green}{\\Leftrightarrow}&\\left(\\frac{\\mathrm{d}}{\\mathrm{d} x} \\frac{y}{x^2}\\right)=x\\cdot \\sin \\left( 3\\cdot x \\right)& \\cr \\color{blue}{\\int\\ldots\\mathrm{d}x}&\\frac{y}{x^2}=\\int {x\\cdot \\sin \\left( 3\\cdot x \\right)}{\\;\\mathrm{d}x}& \\cr \\color{blue}{\\int\\ldots\\mathrm{d}x}&\\frac{y}{x^2}=\\frac{\\sin \\left( 3\\cdot x \\right)-3\\cdot x\\cdot \\cos \\left( 3\\cdot x \\right)}{9}+c& \\cr \\end{array}\\]	[EMPTYCHAR, EQUIVCHAR, EQUIVCHAR,INTCHAR(x),INTCHAR(x)]

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