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.

AlgEquiv

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
AlgEquiv		1/0	1		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATAlgEquiv_STACKERROR_SAns.
AlgEquiv		1	1/0		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATAlgEquiv_STACKERROR_TAns.
AlgEquiv			(x-1)^2		-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.	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		x^2			-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.	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		x-1)^2	(x-1)^2		-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.	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.
	See docs on subscripts and different atoms.
AlgEquiv		x1	x_1		0
AlgEquiv		x_1	x[1]		0
AlgEquiv		x[1]	x1		0
	Predicates
AlgEquiv		integerp(3)	true		1			ATLogic_True.
AlgEquiv		integerp(3.1)	true		0
AlgEquiv		integerp(3)	false		0
AlgEquiv		integerp(3)	true		1			ATLogic_True.
AlgEquiv		lowesttermsp(x^2/x)	true		1			ATLogic_True.
AlgEquiv		lowesttermsp(-y/-x)	true		1			ATLogic_True.
AlgEquiv		lowesttermsp((x^2-1)/(x-1))	true		0
AlgEquiv		lowesttermsp((x^2-1)/(x+2))	true		1			ATLogic_True.
	Case sensitivity
AlgEquiv		X	x		0			ATAlgEquiv_WrongCase.
AlgEquiv		exdowncase(X)	x		1
AlgEquiv		exdowncase((X-1)^2)	x^2-2*x+1		1
	Permutations of variables (To do: a dedicated answer test with feedback)
AlgEquiv		Y=1+X	y=1+x		0			ATEquation_default
AlgEquiv		v+w+x+y+z	a+b+c+A+B		0
	Numbers
AlgEquiv		4^(-1/2)	1/2		1
AlgEquiv		4^(1/2)	sqrt(4)		1
	Mix of floats and rational numbers
AlgEquiv		0.5	1/2		1
AlgEquiv		0.33	1/3		0
AlgEquiv		452	4.52*10^2		0
AlgEquiv		5.1e-2	51/1000		1
AlgEquiv		0.333333333333333	1/3		0
AlgEquiv		(0.5+x)*2	2*x+1		1
	Complex numbers
AlgEquiv		sqrt(-1)	%i		1
AlgEquiv		%i	e^(i*pi/2)		1
AlgEquiv		(4*sqrt(3)*%i+4)^(1/5)	8^(1/5)*(cos(%pi/15)+%i*sin(%p i/15))		1
AlgEquiv		(4*sqrt(3)*%i+4)^(1/5)	rectform((4*sqrt(3)*%i+4)^(1/5 ))		1
AlgEquiv		(4*sqrt(3)*%i+4)^(1/5)	polarform((4*sqrt(3)*%i+4)^(1/ 5))		1
AlgEquiv		%i/sqrt(x)	sqrt(-1/x)		1
	Infinity
AlgEquiv		inf	inf		1
AlgEquiv		inf	-inf		0
AlgEquiv		2*inf	inf		0
AlgEquiv		0*inf	0		1
	Powers and roots
AlgEquiv		x^(1/2)	sqrt(x)		1
AlgEquiv		x	sqrt(x^2)		0
AlgEquiv		abs(x)	sqrt(x^2)		1
AlgEquiv		1/abs(x)^(1/3)	(abs(x)^(1/3)/abs(x))^(1/2)		1
AlgEquiv		sqrt((x-3)*(x-5))	sqrt(x-3)*sqrt(x-5)		0
AlgEquiv		1/sqrt(x)	sqrt(1/x)		1
AlgEquiv		x-1	(x^2-1)/(x+1)		1
AlgEquiv		2^((1/5.1)*t)	2^((1/5.1)*t)		1
AlgEquiv		2^((1/5.1)*t)	2^(0.196078431373*t)		0
AlgEquiv		a^b*a^c	a^(b+c)		1
AlgEquiv		(a^b)^c	a^(b*c)		0
AlgEquiv		(assume(a>0),(a^b)^c)	a^(b*c)		1
AlgEquiv		(assume(x>2),6*((x-2)^2)^k)	6*(x-2)^(2*k)		1
AlgEquiv		signum(-3)	-1		1
AlgEquiv		6*((x-2)^3)^k	6*(x-2)^(3*k)		1
AlgEquiv		(4*sqrt(3)*%i+4)^(1/5)	6^(1/5)*cos(%pi/15)-6^(1/5)*%i *sin(%pi/15)		0
AlgEquiv		2+2*sqrt(3+x)	2+sqrt(12+4*x)		1
AlgEquiv		6*e^(6*(y^2+x^2))+72*x^2*e^(6* (y^2+x^2))	(72*x^2+6)*e^(6*(y^2+x^2))		1
	Expressions with subscripts
AlgEquiv		a1	a_1		0
AlgEquiv		rho*z*V/(4*pi*epsilon[0]*(R^2+ z^2)^(3/2))	rho*z*V/(4*pi*epsilon[0]*(R^2+ z^2)^(3/2))		1
AlgEquiv		rho*z*V/(4*pi*epsilon[1]*(R^2+ z^2)^(3/2))	rho*z*V/(4*pi*epsilon[0]*(R^2+ z^2)^(3/2))		0
AlgEquiv		sqrt(k/m)*sqrt(m/k)	1		1
AlgEquiv		(2*pi)/(k/m)^(1/2)	(2*pi)/(k/m)^(1/2)		1
AlgEquiv		(2*pi)*(m/k)^(1/2)	(2*pi)/(k/m)^(1/2)		1
AlgEquiv		sqrt(2*x/10+1)	sqrt((2*x+10)/10)		1
AlgEquiv		((x+3)^2*(x+3))^(1/3)	((x+3)*(x^2+6*x+9))^(1/3)		1
	Need to factor internally.
AlgEquiv		((x+3)^2*(x+3))^(1/3)	((x+3)*(x^2+6*x+9))^(1/3)		1
	Polynomials and rational function
AlgEquiv		(x-1)^2	x^2-2*x+1		1
AlgEquiv		(x-1)*(x^2+x+1)	x^3-1		1
AlgEquiv		(x-1)^(-2)	1/(x^2-2*x+1)		1
AlgEquiv		1/(4*x-(%pi+sqrt(2)))	1/(x+1)		0
AlgEquiv		(x-a)^6000	(x-a)^6000		1
AlgEquiv		(a-x)^6000	(x-a)^6000		1
AlgEquiv		(4*a-x)^6000	(x-4*a)^6000		1
AlgEquiv		(x-a)^6000	(x-a)^5999		0
AlgEquiv		(k+8)/(k^2+4*k-12)	(k+8)/(k^2+4*k-12)		1
AlgEquiv		(k+7)/(k^2+4*k-12)	(k+8)/(k^2+4*k-12)		0
AlgEquiv		-(2*k+6)/(k^2+4*k-12)	-(2*k+6)/(k^2+4*k-12)		1
AlgEquiv		1/n-1/(n+1)	1/(n*(n+1))		1
AlgEquiv		0.5*x^2+3*x-1	x^2/2+3*x-1		1
AlgEquiv		14336000000*x^13+250265600000* x^12+1862860800000*x^11+762392 5760000*x^10+18290677760000*x^ 9+24744757985280*x^8+145672123 51488*x^7-3267871272960*x^6-64 08053107200*x^5+670406720000*x ^4+1179708800000*x^3-429244800 000*x^2+56696000000*x-26800000 00	512*(2*x+5)^7*(5*x-1)^5*(70*x+ 67)		1
AlgEquiv		14336000000*x^13+250265600000* x^12+1862860800000*x^11+762392 5760000*x^10+18290677760000*x^ 9+24744757985280*x^8+145672123 51488*x^7-3267871272960*x^6-64 08053107200*x^5+670406720000*x ^4+1179708800000*x^3-429244800 000*x^2+56696000000*x-26800000 01	512*(2*x+5)^7*(5*x-1)^5*(70*x+ 67)		0
AlgEquiv		14336000000*x^13	512*(2*x+5)^7*(5*x-1)^5*(70*x+ 67)		0
	Trig functions
AlgEquiv		cos(x)	cos(-x)		1
AlgEquiv		cos(x)^2+sin(x)^2	1		1
AlgEquiv		cos(x+y)	cos(x)*cos(y)-sin(x)*sin(y)		1
AlgEquiv		cos(x+y)	cos(x)*cos(y)+sin(x)*sin(y)		0
AlgEquiv		cos(x#pm#y)	cos(x)*cos(y)-(#pm#sin(x)*sin( y))		1			ATLogic_True.
AlgEquiv		sin(x#pm#y)	sin(x)*cos(y)#pm#cos(x)*sin(y)		1			ATLogic_True.
AlgEquiv		sin(x#pm#y)	cos(x)*sin(y)#pm#sin(x)*cos(y)		0
AlgEquiv		2*cos(x)^2-1	cos(2*x)		1
AlgEquiv		1.0*cos(1200*%pi*x)	cos(1200*%pi*x)		1
AlgEquiv		diff(tan(10*x)^2,x)	cos(6*x)		0
AlgEquiv		exp(%i*%pi)	-1		1
AlgEquiv		2*cos(2*x)+x+1	-sin(x)^2+3*cos(x)^2+x		1
AlgEquiv		(2*sec(2*t)^2-2)/2	-(sin(4*t)^2-2*sin(4*t)+cos(4* t)^2-1)*(sin(4*t)^2+2*sin(4*t) +cos(4*t)^2-1)/(sin(4*t)^2+cos (4*t)^2+2*cos(4*t)+1)^2		1
AlgEquiv		1+cosec(3*x)	1+csc(3*x)		1
AlgEquiv		1/(1+exp(-2*x))	tanh(x)/2+1/2		1
AlgEquiv		1+cosech(3*x)	1+csch(3*x)		1
AlgEquiv		-4*sec(4*z)^2*sin(6*z)-6*tan(4 *z)*cos(6*z)	-4*sec(4*z)^2*sin(6*z)-6*tan(4 *z)*cos(6*z)		1
AlgEquiv		-4*sec(4*z)^2*sin(6*z)-6*tan(4 *z)*cos(6*z)	4*sec(4*z)^2*sin(6*z)+6*tan(4* z)*cos(6*z)		0
AlgEquiv		csc(6*x)^2*(7*sin(6*x)*cos(7*x )-6*cos(6*x)*sin(7*x))	-(6*cos(6*x)*sin(7*x)-7*sin(6* x)*cos(7*x))/sin(6*x)^2		1
AlgEquiv		csc(6*x)^2*(7*sin(6*x)*cos(7*x )-6*cos(6*x)*sin(7*x))	(6*cos(6*x)*sin(7*x)-7*sin(6*x )*cos(7*x))/sin(6*x)^2		0
AlgEquiv		-(7*x^6+4*x^3)/sin(7*y+x^7+x^4 +1)^2	-(7*x^6+4*x^3)*csc(7*y+x^7+x^4 +1)^2		1
AlgEquiv		sin((2*%pi*n-%pi)/2)	-cos(n*%pi)		1
AlgEquiv		sin(x/2)/(1+tan(x)*tan(x/2))	sin(x/2)*cos(x)		1
AlgEquiv		(declare(n,integer),trigrat(si n((2*%pi*n-%pi)/2)))	-(-1)^n		1
AlgEquiv	!	cot(%pi/20)+cot(%pi/24)-cot(%p i/10)	sqrt(1)+sqrt(2)+sqrt(3)+sqrt(4 )+sqrt(5)+sqrt(6)		-3
AlgEquiv		trigeval(cot(%pi/20)+cot(%pi/2 4)-cot(%pi/10))	sqrt(1)+sqrt(2)+sqrt(3)+sqrt(4 )+sqrt(5)+sqrt(6)		1
AlgEquiv	!	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]		-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		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
AlgEquiv		1+x	taylor(1/(1-x),x,0,1)		1
AlgEquiv		1	taylor(1/(1-x),x,0,1)		0
	Logarithms
AlgEquiv		log(a^2*b)	2*log(a)+log(b)		1
AlgEquiv		(2*log(2*x)+x)/(2*x)	(log(2*x)+2)/(2*sqrt(x))		0
AlgEquiv		log(abs((x^2-9)))	log(abs(x-3))+log(abs(x+3))		0
AlgEquiv		lg(10^x)	x		1
AlgEquiv		lg(3^x,3)	x		1
AlgEquiv		lg(a^x,a)	x		1
AlgEquiv		1+lg(27,3)	4		1
AlgEquiv		1+lg(27,3)	3		0
AlgEquiv		lg(1/8,2)	-3		1
AlgEquiv		lg(root(x,n))	lg(x,10)/n		1
AlgEquiv		log(root(x,n))	lg(x,10)/n		0
AlgEquiv		x^log(y)	y^log(x)		1
	Hyperbolic trig
AlgEquiv		e^1-e^(-1)	2*sinh(1)		1
	Lists
AlgEquiv		x	[1,2,3]		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		[1,2]	[1,2,3]		0		Your list should have \(3\) elements, but it actually has \(2\).	ATList_wronglen.
AlgEquiv		[1,2,4]	[1,2,3]		0		The entries underlined in red below are those that are incorrect. \[\left[ 1 , 2 , {\color{red}{\underline{4}}} \right] \]	(ATList_wrongentries 3).
AlgEquiv		[1,x>2]	[1,2<x]		1
AlgEquiv		[1,2,[2-x<0,{1,2,2,2, 1,3}] ]	[1,2,[2-x<0,{1,2}]]		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		[(k+8)/(k^2+4*k-12),-(2*k+6)/( k^2+4*k-12)]	[(k+8)/(k^2+4*k-12),-(2*k+6)/( k^2+4*k-12)]		1
AlgEquiv		[1,2]	ntuple(1,2)		0		Your answer should be an expression, not an equation, inequality, list, set or matrix.	ATAlgEquiv_SA_not_expression.
	Rounding of floats
AlgEquiv		round(0.5)	0.0		1
AlgEquiv		round(1.5)	2.0		1
AlgEquiv		round(2.5)	2.0		1
AlgEquiv		round(12.5)	12.0		1
AlgEquiv		significantfigures(0.5,1)	0.5		1
AlgEquiv		significantfigures(1.5,1)	2.0		1
AlgEquiv		significantfigures(2.5,1)	3.0		1
AlgEquiv		significantfigures(3.5,1)	4.0		1
AlgEquiv		significantfigures(11.5,2)	12.0		1
AlgEquiv		1500	scientific_notation(1500,3)		1
AlgEquiv		1500	displaysci(1.5,2,3)		1
AlgEquiv		[3,3.1,3.14,3.142,3.1416,3.141 59,3.141593,3.1415927]	makelist(significantfigures(%p i,i),i,8)		1
	Sets
AlgEquiv		x	{1,2,3}		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		co(1,2)	{1,2,3}		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		{1,2}	{1,2,3}		0		Your set should have \(3\) different elements, but it actually has \(2\).	ATSet_wrongsz.
AlgEquiv		{2/4, 1/3}	{1/2, 1/3}		1
AlgEquiv		{A[1],A[2],A[4]}	{A[1],A[2],A[3]}		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		{A[1],A[2],A[3]}	{A[1],A[2],A[3]}		1
AlgEquiv		{1,2,4}	{1,2,3}		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		{1,x>4}	{4<x, 1}		1
AlgEquiv		{x-1=0,x>1 and 5>x}	{x>1 and x<5,x=1}		1
AlgEquiv		{x-1=0,x>1 and 5>x}	{x>1 and x<5,x=2}		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		{x-1=0,x>1 and 5>x}	{x>1 and x<3,x=1}		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	!	{-sqrt(2)/sqrt(3)}	{-2/sqrt(6)}		-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	!	{[-sqrt(2)/sqrt(3),0],[2/sqrt( 6),0]}	{[2/sqrt(6),0],[-2/sqrt(6),0]}		-3		The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{\left[ -\frac{\sqrt{2}}{\sqrt{3}} , 0 \right] \right \}\]	ATSet_wrongentries.
AlgEquiv		ev(radcan({-sqrt(2)/sqrt(3)}), simp)	ev(radcan({-2/sqrt(6)}),simp)		1
AlgEquiv		ev(radcan(ratsimp({(-sqrt(10)/ 2)-2,sqrt(10)/2-2},algebraic:t rue)),simp)	ev(radcan(ratsimp({(-sqrt(5)/s qrt(2))-2,sqrt(5)/sqrt(2)-2},a lgebraic:true)),simp)		1
AlgEquiv		{(2-2^(5/2))/2,(2^(5/2)+2)/2}	{1-2^(3/2),2^(3/2)+1}		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		ev(radcan({(2-2^(5/2))/2,(2^(5 /2)+2)/2}),simp)	{1-2^(3/2),2^(3/2)+1}		1
AlgEquiv		{(x-a)^6000}	{(a-x)^6000}		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		{(k+8)/(k^2+4*k-12),-(2*k+6)/( k^2+4*k-12)}	{(k+8)/(k^2+4*k-12),-(2*k+6)/( k^2+4*k-12)}		1
	Matrices
AlgEquiv		matrix([1,2],[2,3])	matrix([1,2],[2,3])		1
AlgEquiv		matrix([1,2],[2,3])	matrix([1,2,3],[2,3,3])		0		Your matrix should be \(2\) by \(3\), but it is actually \(2\) by \(2\).	ATMatrix_wrongsz_columns.
AlgEquiv		matrix([1,2],[2,3])	matrix([1,2],[2,5])		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		matrix([0.33,1],[1,1])	matrix([0.333,1],[1,1])		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		matrix([x+x,2],[2,x*x])	matrix([2*x,2],[2,x^2])		1
AlgEquiv		matrix([epsilon[0],2],[2,x^2])	matrix([epsilon[0],2],[2,x^2])		1
AlgEquiv		matrix([epsilon[2],2],[2,x^2])	matrix([epsilon[0],2],[2,x^3])		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		matrix([x>4,{1,x^2}],[[1,2] ,[1,3]])	matrix([4-x<0,{x^2, 1}],[[1 ,2],[1,3]])		1
AlgEquiv		matrix([x>4,{1,x^2}],[[1,2] ,[1,3]])	matrix([4-x<0,{x^2, 1}],[[1 ,2],[1,4]])		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		a	stackvector(a)		0
	Equations
AlgEquiv		1	x=1		0		Your answer should be an equation, but is not.	ATAlgEquiv_SA_not_equation.
AlgEquiv		x=1	x=1		1			ATEquation_sides
AlgEquiv		1=x	1=x		1			ATEquation_sides
AlgEquiv		1=x	x=1		1			ATEquation_sides_op
AlgEquiv		1=1	1=x		0			ATEquation_default
AlgEquiv		1=1	x=1		0			ATEquation_default
AlgEquiv		x=2	x=1		0			ATEquation_lhs_notrhs
AlgEquiv		2=x	x=1		0			ATEquation_default
AlgEquiv		x=x	y=y		1			ATEquation_zero
AlgEquiv		x+y=1	y=1-x		1
AlgEquiv		2*x+2*y=1	y=0.5-x		1			ATEquation_ratio
AlgEquiv		1/x+1/y=2	y = x/(2*x-1)		1			ATEquation_ratio
AlgEquiv		y=sin(2*x)	y/2=cos(x)*sin(x)		1			ATEquation_ratio
AlgEquiv		y=(x-a)^6000	y=(x-a)^6000		1			ATEquation_sides
AlgEquiv		y=(x-a)^5999	y=(x-a)^6000		0			ATEquation_lhs_notrhs
AlgEquiv		y=(a-x)^6000	y=(x-a)^6000		1			ATEquation_sides
AlgEquiv		y=(a-x)^5999	y=(x-a)^5999		0			ATEquation_lhs_notrhs
AlgEquiv		y=(a-x)^59999	y=(x-a)^5999		0			ATEquation_lhs_notrhs
AlgEquiv		x+y=i	y=i-x		1
AlgEquiv		(1+%i)*(x+y)=0	y=-x		1
AlgEquiv		s^2*%e^(s*t)=0	s^2=0		0			ATEquation_default
AlgEquiv		0=-x+y/A+(y-z)/B	0=x-y/A-(y-z)/B		1
AlgEquiv		x^6000-x^6001=x^5999	x^5999*(1-x+x^2)=0		1			ATEquation_ratio
AlgEquiv		x^6000-x^6001=x^5999	x^5999*(1-x+x^3)=0		0			ATEquation_default
AlgEquiv		258552*x^7*(81*x^8+1)^398	x^3*(x^4+1)^399		0
AlgEquiv		Ia*(R1+R2+R3)-Ib*R3=0	-Ia*(R1+R2+R3)+Ib*R3=0		1
AlgEquiv		a=0 or b=0	a*b=0		1			ATEquation_sides
AlgEquiv		a*b=0	a=0 or b=0		1			ATEquation_sides
AlgEquiv		a*x=a*y	x=y		0			ATEquation_default
AlgEquiv		a*x=a*y	a=0 or x=y		1			ATEquation_ratio
	Unary Equations
AlgEquiv		1	stackeq(1)		1
AlgEquiv		stackeq(1)	1		1
AlgEquiv		stackeq(1)	0		0
	Equations: Loose/gain roots with nth powers of each side.
AlgEquiv		x=y	x^2=y^2		0			ATEquation_default
AlgEquiv		(x-2)^2=0	x=2		0			ATEquation_default
AlgEquiv		4*x^2-71*x+220 = 0 or 14*x^2-9 1*x+140 = 0	x = 5/2 or x = 4 or x = 55/4		0			ATEquation_default
AlgEquiv		4*x^2-71*x+220 = 0 or 14*x^2-9 1*x+140 = 0	x = 5/2 or x = 4 or x=4 or x = 55/4		1			ATEquation_sides
AlgEquiv		x^2=4	x=2 or x=-2		1			ATEquation_ratio
AlgEquiv		a^3*b^3=0	a=0 or b=0		0			ATEquation_default
AlgEquiv		a^3*b^3=0	a*b=0		0			ATEquation_default
AlgEquiv		(x-y)*(x+y)=0	x^2=y^2		1			ATEquation_ratio
AlgEquiv		x=1	(x-1)^3=0		0			ATEquation_default
AlgEquiv		sqrt(x)=sqrt(y)	x=y		0			ATEquation_default
AlgEquiv		x=sqrt(a)	x^2=a		0			ATEquation_default
AlgEquiv		(x-sqrt(a))*(x+sqrt(a))=0	x^2=a		1			ATEquation_ratio
AlgEquiv		(x-%i*sqrt(a))*(x+%i*sqrt(a))= 0	x^2=-a		1			ATEquation_ratio
AlgEquiv		(x-%i*sqrt(abs(a)))*(x+%i*sqrt (abs(a)))=0	x^2=-abs(a)		1			ATEquation_ratio
AlgEquiv		y=sqrt(1-x^2)	x^2+y^2=1		0			ATEquation_default
AlgEquiv		(y-sqrt(1-x^2))*(y+sqrt(1-x^2) )=0	x^2+y^2=1		1			ATEquation_ratio
AlgEquiv		(y-sqrt((1-x)*(1+x)))*(y+sqrt( (1-x)*(1+x)))=0	x^2+y^2=1		1			ATEquation_ratio
AlgEquiv		(x-1)*(x+1)*(y-1)*(y+1)=0	y^2+x^2=1+x^2*y^2		1			ATEquation_ratio
	Equations: edge cases. Teacher must enter an equation, all or none here.
AlgEquiv		all	x=x		1			ATEquation_zero
AlgEquiv		true	x=x		1			ATEquation_zero
AlgEquiv		x=x	all		1			ATEquation_zero
AlgEquiv		all	all		1			ATEquation_zero
AlgEquiv		true	all		1			ATEquation_zero
AlgEquiv		a=a	x=x		1			ATEquation_zero
AlgEquiv		false	x=x		0			ATEquation_zero_fail
AlgEquiv		false	all		0			ATEquation_zero_fail
AlgEquiv		none	all		0			ATEquation_zero_fail
AlgEquiv		all	none		0			ATEquation_empty_fail
AlgEquiv		2=3	1=4		1			ATEquation_empty
AlgEquiv		none	1=2		1			ATEquation_empty
AlgEquiv		false	1=2		1			ATEquation_empty
AlgEquiv		none	none		1			ATEquation_empty
AlgEquiv		false	none		1			ATEquation_empty
AlgEquiv		3=0	none		1			ATEquation_empty
AlgEquiv		0=3	none		1			ATEquation_empty
AlgEquiv		all	1=2		0			ATEquation_empty_fail
AlgEquiv		true	1=2		0			ATEquation_empty_fail
AlgEquiv		{}	1=2		0		Your answer should be an equation, but is not.	ATAlgEquiv_SA_not_equation.
AlgEquiv		[]	1=2		0		Your answer should be an equation, but is not.	ATAlgEquiv_SA_not_equation.
AlgEquiv		{}	none		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		x^2	cc(1,3)		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		%union(oo(1,2),oo(3,4))	%union(oo(1,2),oo(3,4))		1			ATRealSet_true.
AlgEquiv		%union(oc(1,2),co(2,3))	oo(1,3)		1			ATRealSet_true.
AlgEquiv		%union(oc(1,2),co(2,3))	cc(1,3)		0			ATRealSet_false.
AlgEquiv		{-1,1}	%union({-1,1})		1			ATRealSet_true.
AlgEquiv		{1,3}	cc(1,3)		0			ATRealSet_false.
AlgEquiv		%intersection(oc(-1,1),co(1,2) )	%union({1})		1			ATRealSet_true.
AlgEquiv		oo(-inf,1)	oo(-inf,1)		1			ATRealSet_true.
AlgEquiv		oo(-1,inf)	oo(0,inf)		0			ATRealSet_false.
AlgEquiv		%union(oc(-inf,0),oo(-1,4))	oo(-inf,4)		1			ATRealSet_true.
AlgEquiv		%union(oo(-inf,1),oo(-1,inf))	oo(-inf,inf)		1			ATRealSet_true.
AlgEquiv		all	oo(-inf,inf)		1			ATRealSet_true.
AlgEquiv		co(1,2)	1 <= x nounand x<2		0		Your answer should be an equation, inequality or a logical combination of many of these, but is not.	ATAlgEquiv_SA_not_logic.
AlgEquiv		1 <= x nounand x<2	co(1,2)		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		minf <= x	co(minf,inf)		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		-inf <= x	co(minf,inf)		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		x <= inf	oc(minf,inf)		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		minf <= x	oo(minf,inf)		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		single_variable_solver_real(mi nf <= x)	co(minf,inf)		1			ATRealSet_true.
AlgEquiv		single_variable_solver_real(-i nf <= x)	co(minf,inf)		1			ATRealSet_true.
AlgEquiv		single_variable_solver_real(x <= inf)	oc(minf,inf)		1			ATRealSet_true.
AlgEquiv		single_variable_solver_real(mi nf <= x)	oo(minf,inf)		0			ATRealSet_false.
	Complex numbers
AlgEquiv		a=b/%i	%i*a=b		1			ATEquation_num_i
AlgEquiv		b/%i=a	%i*a=b		1			ATEquation_num_i
AlgEquiv		b=a/%i	%i*a=b		0			ATEquation_lhs_notrhs_op
AlgEquiv		a*(2+%i)=b	a=b/(2+%i)		1			ATEquation_ratio
AlgEquiv		a*(2+%i)=b	a=b*(2-%i)/5		1			ATEquation_num_i
AlgEquiv		a*(2+%i)=b	a=b*(2-%i)/4		0			ATEquation_default
AlgEquiv		i	disp_complex(0,1)		0
	Absolute value in equations
AlgEquiv		abs(x)=abs(y)	x=y		0			ATEquation_default
AlgEquiv		abs(x)=abs(y)	x=y or x=-y		1
AlgEquiv		abs(x)=abs(y)	(x-y)*(x+y)=0		1
	Functions
AlgEquiv		f(x):=1/0	f(x):=x^2		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	TEST_FAILED
AlgEquiv		1	f(x):=x^2		0		Your answer should be a function, defined using the operator :=, but is not.	ATAlgEquiv_SA_not_function.
AlgEquiv		f(x)=x^2	f(x):=x^2		0		Your answer should be a function, defined using the operator :=, but is not.	ATAlgEquiv_SA_not_function.
AlgEquiv		f(x):=x^2	f(x,y):=x^2+y^2		0			ATFunction_length_args. ATFunction_false.
AlgEquiv		f(x):=x^2	f(x)=x^2		0		Your answer should be an equation, but is not.	ATAlgEquiv_SA_not_equation.
AlgEquiv		f(x):=x^2	f(x):=x^2		1			ATFunction_true.
AlgEquiv		f(x):=x^2	f(x):=sin(x)		0			ATFunction_false.
AlgEquiv		g(x):=x^2	f(x):=x^2		0			ATFunction_wrongname. ATFunction_true.
AlgEquiv		f(y):=y^2	f(x):=x^2		1			ATFunction_arguments_different. ATFunction_true.
AlgEquiv		f(a,b):=a^2+b^2	f(x,y):=x^2+y^2		1			ATFunction_arguments_different. ATFunction_true.
	Inequalities
AlgEquiv		1	x>1		0		Your answer should be an inequality, but is not.	ATAlgEquiv_SA_not_inequality.
AlgEquiv		x=1	x>1 and x<5		0		You have entered an equation, but an equation is not expected here. You may have typed something like "y=2*x+1" when you only needed to type "2*x+1".	ATAlgEquiv_TA_not_equation.
AlgEquiv		x<1	x>1		0		Your inequality appears to be backwards.	ATInequality_backwards.
AlgEquiv		1<x	x>1		1
AlgEquiv		a<b	b>a		1
AlgEquiv		2<2*x	x>1		1
AlgEquiv		-2>-2*x	x>1		1
AlgEquiv		x>1	x<=1		0		Your inequality should not be strict! Your inequality appears to be backwards.	ATInequality_strict. ATInequality_backwards.
AlgEquiv		x>=2	x<2		0		Your inequality should be strict, but is not! Your inequality appears to be backwards.	ATInequality_nonstrict. ATInequality_backwards.
AlgEquiv		x>=1	x>2		0		Your inequality should be strict, but is not!	ATInequality_nonstrict.
AlgEquiv		x>1	x>1		1
AlgEquiv		x>=1	x>=1		1
AlgEquiv		x>2	x>1		0
AlgEquiv		1<x	x>1		1
AlgEquiv		2*x>=x^2	x^2<=2*x		1
AlgEquiv		2*x>=x^2	x^2<=2*x		1
AlgEquiv		3*x^2<9*a	x^2-3*a<0		1
AlgEquiv		x^2>4	x>2 or x<-2		1			ATLogic_True.
AlgEquiv		1<x or x<-3	x<-3 or 1<x		1			ATLogic_True.
AlgEquiv		1<x or x<-3	x<-1 or 3<x		0
AlgEquiv		x>1 and x<5	x>1 and x<5		1			ATLogic_True.
AlgEquiv		x>1 and x<5	5>x and 1<x		1			ATLogic_True.
AlgEquiv		not (x<=2 and -2<=x)	x>2 or -2>x		1			ATLogic_True.
AlgEquiv		x>2 or -2>x	not (x<=2 and -2<=x)		1			ATLogic_True.
AlgEquiv		x>=1 or 1<=x	x>=1		1
AlgEquiv		x>=1 and x<=1	x=1		1			ATInequality_solver.
AlgEquiv		(x>4 and x<5) or (x<- 4 and x>-5) or (x+5>0 an d x<-4)	(x>-5 and x<-4) or (x> ;4 and x<5)		1			ATLogic_True.
AlgEquiv		(x>4 and x<5) or (x<- 4 and x>-5) or (x+5>0 an d x<-4)	(x>-5 and x<-4) or (x> ;8 and x<5)		0
AlgEquiv		(x < 0 nounor x >= 1) no unand x <= 3	x < 0 or (x >= 1 and x & lt;= 3)		1			ATLogic_True.
AlgEquiv		(x < 0 nounor x >= 1) no unand x <= 3	x < 0 or x >= 1 and x &l t;= 3		1			ATLogic_True.
AlgEquiv		(x < 0 nounor x >= 1) no unand x <= 3	x < 0 or (x >= 1 and x & lt;= 3)		1			ATLogic_True.
AlgEquiv		(x < 0 nounor x >= 1) no unand x <= 3	(x < 0 or x >= 1) and x <= 3		1			ATLogic_True.
AlgEquiv		(x < 0 nounor x >= 1) no unand x <= 3	x < 0 or (x >= 1 and x & lt;= 3)		1			ATLogic_True.
AlgEquiv		natural_domain(1/x^2)	natural_domain(1/x)		1			ATRealSet_true.
AlgEquiv		x^4>=0	x^2>=0		1
AlgEquiv		x^4>=16	x^2>=4		1
AlgEquiv		x^4>=16	x^2>=4		1
AlgEquiv		-3<=x	-3<=x nounand x<=3		0
AlgEquiv		{2,-2}	x>2 nounor -2>x		0		Your answer should be an equation, inequality or a logical combination of many of these, but is not.	ATAlgEquiv_SA_not_logic.
AlgEquiv		x^2<4	x<2 nounand x>-2		1			ATLogic_Solver_True.
AlgEquiv		x^2<6	x<2 nounand x>-2		0
AlgEquiv		x>1 nounand x<-1	false		1			ATLogic_Solver_True.
AlgEquiv		x>1 nounand x<3	true		0
AlgEquiv		x>1 nounor x<3	true		1			ATLogic_Solver_True.
AlgEquiv		x>1 nounor x<3	all		1			ATLogic_Solver_True.
AlgEquiv		abs(x)<1	abs(x)<1		1
AlgEquiv		abs(x)<1	abs(x)<2		0
AlgEquiv		abs(x)<1	abs(x)>1		0		Your inequality appears to be backwards.	ATInequality_backwards.
AlgEquiv	!	abs(x)<2	-2<x and x<2		-3
AlgEquiv	!	-2<x and x<2	abs(x)<2		-3
AlgEquiv		abs(x)<2	-1<x and x<1		0
AlgEquiv		x^2<=9	abs(x)<3		0
AlgEquiv	!	x^2<=9	abs(x)<=3		-3
AlgEquiv	!	x^6<1	abs(x)<1		-3
AlgEquiv	!	abs(x)>1	x<-1 or x>1		-3
AlgEquiv		minf < x	minf <= x		0		Your inequality should not be strict!	ATInequality_strict.
AlgEquiv		x>minf	minf < x		1
AlgEquiv		x>-inf	minf < x		1
AlgEquiv		x<2*inf	x<inf		0
AlgEquiv		minf < x nounand x <1	x<1		1
AlgEquiv		minf < x nounand x <1	x<2		0
	Maxima and infinity
AlgEquiv		2*inf	inf		0
AlgEquiv		-inf	minf		0
	Not equal to
AlgEquiv		x#1	x#1		1			ATLogic_True.
AlgEquiv		x#(1+1)	x#2		1			ATLogic_True.
AlgEquiv		1#x	x#1		1			ATLogic_True.
AlgEquiv		x#2	x-2#0		1			ATLogic_True.
AlgEquiv		[x#2]	[x-2#0]		1
AlgEquiv		x-3#0	x#2		0
AlgEquiv		x#2	x<2 nounor x>2		1			ATLogic_Solver_True.
AlgEquiv		x^2-3#1	x<-2 nounor (x<-2 and x& lt;2) nounor 2<x		0
AlgEquiv		x^2-3#1	x<-2 nounor (-2<x and x& lt;2) nounor 2<x		1			ATLogic_Solver_True.
AlgEquiv		x#1	x#0		0
	Surds
AlgEquiv		sqrt(12)	2*sqrt(3)		1
AlgEquiv		sqrt(11+6*sqrt(2))	3+sqrt(2)		1
AlgEquiv		(19601-13860*sqrt(2))^(7/4)	(5*sqrt(2)-7)^7		1
AlgEquiv		(19601-13861*sqrt(2))^(7/4)	(5*sqrt(2)-7)^7		0
AlgEquiv		(19601-13861*sqrt(2))^(7/4)	(5*sqrt(2)-7)^7		0
AlgEquiv		sqrt(2*log(26)+4-2*log(2))	sqrt(2*log(13)+4)		1
AlgEquiv		sqrt(2)*sqrt(3)+2*(sqrt(2/3))* x-(2/3)*(sqrt(2/3))*x^2+(4/9)* (sqrt(2/3))*x^3	4*sqrt(6)*x^3/27-(2*sqrt(6)*x^ 2)/9+(2*sqrt(6)*x)/3+sqrt(6)		1
	Factorials and binomials
AlgEquiv		(n+1)*n!	(n+1)!		1
AlgEquiv		n/n!	1/(n-1)!		1
AlgEquiv		n/n!	1/(n+1)!		0
AlgEquiv		n!/(k!*(n-k)!)	binomial(n,k)		1
AlgEquiv	!	binomial(n,k)+binomial(n,k+1)	binomial(n+1,k+1)		-3
AlgEquiv		binomial(n,k)+binomial(n,k+1)	binomial(n+1,k)		0
AlgEquiv		binomial(n,k)	binomial(n,n-k)		1
AlgEquiv		175!*56!/(55!*176!)	17556/55176		1
	Unevaluated derviatives
AlgEquiv		3*s*diff(q(s),s)	3*s*diff(q(s),s)		1
	Sums and products
AlgEquiv		sum(k^n,n,0,3)	sum(k^n,n,0,3)		1
AlgEquiv		1+k+k^2+k^3	sum(k^n,n,0,3)		1
AlgEquiv		1+k+k^2	sum(k^n,n,0,3)		0
AlgEquiv		n*(n+1)*(2*n+1)/6	sum(k^2,k,1,n)		1
AlgEquiv		sum((k+1)^2,k,0,n-1)	sum(k^2,k,1,n)		1
AlgEquiv		product(cos(k*x),k,1,3)	product(cos(k*x),k,1,3)		1
AlgEquiv		cos(x)*cos(2*x)*cos(3*x)	product(cos(k*x),k,1,3)		1
AlgEquiv		cos(x)*cos(2*x)	product(cos(k*x),k,1,3)		0
	Scientific units are ignored
AlgEquiv		9.81*m/s^2	stackunits(9.81,m/s^2)		1
AlgEquiv		6*stackunits(1,m)	stackunits(6,m)		1
AlgEquiv		stackunits(2,m)^2	stackunits(4,m^2)		1
AlgEquiv		stackunits(2,s)^2	stackunits(4,m^2)		0
	Maxima does not simplify -inf (I agree!)
AlgEquiv		-inf	minf		0
	These currently fail
AlgEquiv	!	2/%i*ln(sqrt((1+z)/2)+%i*sqrt( (1-z)/2))	-%i*ln(z+%i*sqrt(1-z^2))		-3
AlgEquiv	!	abs(x^2-4)/(abs(x-2)*abs(x+2))	1		-3
AlgEquiv	!	abs(x^2-4)	abs(x-2)*abs(x+2)		-3
AlgEquiv	!	(-1)^n*cos(x)^n	(-cos(x))^n		-3
AlgEquiv	!	(sqrt(108)+10)^(1/3)-(sqrt(108 )-10)^(1/3)	2		-3
AlgEquiv	!	(sqrt(2+sqrt(2))+sqrt(2-sqrt(2 )))/(2*sqrt(2))	sqrt(sqrt(2)+2)/2		-3
AlgEquiv	!	sqrt(2*x*sqrt(x^2+1)+2*x^2+1)- sqrt(x^2+1)-x	0		-3
AlgEquiv	!	(77+20*sqrt(13))^(1/6)-(77-20* sqrt(13))^(1/6)	1		-3
AlgEquiv	!	(930249+416020*sqrt(5))^(1/30) -(930249-416020*sqrt(5))^(1/30 )	1		-3
AlgEquiv	!	cos(2*%pi/17)	(-1+sqrt(17)+sqrt(34-2*sqrt(17 )))/16+(2*sqrt(17+3*sqrt(17)-s qrt(34-2*sqrt(17))-2*sqrt(34+2 *sqrt(17))))/16		-3
AlgEquiv	!	(41-sqrt(511))/2	(sqrt((4*(cos((1/2*(acos((61/1 040*sqrt(130)))-atan(11/3))))) ^(2))+21)-(2*cos((1/2*(acos((6 1/1040*sqrt(130)))-atan(11 / 3 ))))))^(2)		-3
AlgEquiv	!	a*(1+sqrt(2))=b	a=b*(sqrt(2)-1)/3		-3			ATEquation_default
	This is only equivalent for x>=0...
AlgEquiv	!	atan(1/2)	%pi/2-atan(2)		-3
	This is true for all x...
AlgEquiv	!	asinh(x)	ln(x+sqrt(x^2+1))		-3
	Logical expressions
AlgEquiv		true and false	false		1			ATLogic_True.
AlgEquiv		true or false	false		0
AlgEquiv		A and B	B and A		1			ATLogic_True.
AlgEquiv		A and B	C and A		0
AlgEquiv		A and B=C	C=B and A		1			ATLogic_True.
AlgEquiv		A and (B and C)	A and B and C		1			ATLogic_True.
AlgEquiv		A and (B or C)	A and (B or C)		1			ATLogic_True.
AlgEquiv		(A and B) or (A and C)	A and (B or C)		1			ATLogic_True.
AlgEquiv		-(b#pm#sqrt(b^2-4*a*c))	-b#pm#sqrt(b^2-4*a*c)		1			ATLogic_True.
AlgEquiv		x=-b#pm#c^2	x=c^2-b or x=-c^2-b		1			ATLogic_True.
AlgEquiv		x#pm#a = y#pm#b	x#pm#a = y#pm#b		1			ATEquation_sides
AlgEquiv		x#pm#a = y#pm#b	x#pm#a = y#pm#c		0			ATEquation_lhs_notrhs
AlgEquiv		not(A) and not(B)	not(A or B)		1			ATLogic_True.
AlgEquiv		not(A) and not(B)	not(A and B)		0
AlgEquiv		not(A) or B	boolean_form(A implies B)		1
AlgEquiv		not(A) or B	A implies B		1			ATLogic_True.
AlgEquiv		not(A) and B	A implies B		0
AlgEquiv		(not A and B) or (not B and A)	A xor B		1			ATLogic_True.
AlgEquiv		(A and B) or (not A and not B)	A xnor B		1			ATLogic_True.
AlgEquiv		{not(A) or B,A and B}	{A implies B,A and B}		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		{A implies B,A and B}	{not(A) and B,A and B}		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		diff(x^2,x)	2*x		1
AlgEquiv		diff(x^2,x)	'diff(x^2,x)		1
AlgEquiv		noundiff(x^2,x)	2*x		1
AlgEquiv		diff(y,x)	0		1
AlgEquiv		noundiff(y,x)	0		1
AlgEquiv		diff(y(x),x)	0		0
AlgEquiv		diff(y(x),x)	diff(y,x)		0
AlgEquiv		diff(y,x)	diff(y,x,2)		1
	Basic support for strings
AlgEquiv		"Hello"	"Hello"		1			ATAlgEquiv_String
AlgEquiv		"hello"	"Hello"		0			ATAlgEquiv_String
AlgEquiv		W	"Hello"		0		Your answer should be a string, but is not.	ATAlgEquiv_SA_not_string.
AlgEquiv		"Hello"	x^2		0		Your answer should be an expression, not an equation, inequality, list, set or matrix.	ATAlgEquiv_SA_not_expression.

AlgEquivNouns

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
AlgEquivNouns		1/0	1		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATAlgEquivNouns_STACKERROR_SAns.
AlgEquivNouns		1	1/0		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATAlgEquivNouns_STACKERROR_TAns.
AlgEquivNouns			(x-1)^2		-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.	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		x^2			-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.	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		x-1)^2	(x-1)^2		-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.	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		diff(x^2,x)	2*x		1
AlgEquivNouns		diff(x^2,x)	'diff(x^2,x)		0
AlgEquivNouns		diff(x^2,x)	'diff(x^2,x)		0
AlgEquivNouns		'diff(y,x)	noundiff(y,x)		1
AlgEquivNouns		diff(y,x)	0		1
AlgEquivNouns		'diff(y,x)	0		0
AlgEquivNouns		noundiff(y,x)	0		0
AlgEquivNouns		diff(y(x),x)	0		0
AlgEquivNouns		'diff(y,x,1)	'diff(y,x,2)		0
AlgEquivNouns		'diff(y(x),x)	'diff(y,x)		0
AlgEquivNouns		subst(y,y(x),'diff(y,x)+y =1)	'diff(y,x)+y=1		1			ATEquation_sides
AlgEquivNouns		subst(y,y(x),'diff(y(x),x )+y(x)=1)	'diff(y,x)+y=1		1			ATEquation_sides
AlgEquivNouns		subst(y(x),y,'diff(y,x)+y =1)	'diff(y(x),x)+y(x)=1		1			ATEquation_sides
AlgEquivNouns		subst(y(x),y,'diff(y,x)+y =1)	'diff(y,x)+y=1		0			ATEquation_default
AlgEquivNouns		subst(y(x),y,'diff(y(x),x )+y(x)=1)	'diff(y,x)+y=1		-1	TEST_FAILED	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		y_x	'diff(y,x)		0
	Partials
AlgEquivNouns		noundiff(f,x,1,y,1)	noundiff(noundiff(f,x),y)		1
AlgEquivNouns		noundiff(noundiff(f,y),x)	noundiff(noundiff(f,x),y)		1
AlgEquivNouns		noundiff(noundiff(f,x),x)	noundiff(f,x,2)		1
	Differential equations
AlgEquivNouns		noundiff(H,x,2) = -R/T	noundiff(H,x,2) + R/T = 0		1			ATEquation_ratio
AlgEquivNouns		'diff(H,x,2) = -R/T	noundiff(H,x,2) + R/T = 0		1			ATEquation_ratio
AlgEquivNouns		y(t)=int(s^2,s,0,t)	y(t)=t^3/3		1			ATEquation_sides
AlgEquivNouns		y(t)='int(s^2,s,0,t)	y(t)=t^3/3		0			ATEquation_lhs_notrhs
AlgEquivNouns		y(t)='int(s^2,s,0,t)	y(t)=nounint(s^2,s,0,t)		1			ATEquation_sides
	Logic nouns are still evaluated
AlgEquivNouns		true nounand false	false		1			ATLogic_True.

SubstEquiv

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
SubstEquiv		1/0	x^2-2*x+1		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSubstEquiv_STACKERROR_SAns.
SubstEquiv		x^2	x^2-2*x+1	[1/0]	-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSubstEquiv_STACKERROR_Opt.
SubstEquiv		x^2	x^2-2*x+1	x	-1		The option to this answer test must be a list. This is an error. Please contact your teacher.	ATSubstEquiv_Opt_List.
SubstEquiv		x^2+1	x^2+1		1
SubstEquiv		x^2+1	x^3+1		0
SubstEquiv		x^2+1	x^3+1		0
SubstEquiv		X^2+1	x^2+1		1		Your answer would be correct if you used the following substitution of variables. \[\left[ X=x \right] \]	ATSubstEquiv_Subst [X = x].
SubstEquiv		x^2+y	a^2+b		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		x^2+y/z	a^2+c/b		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		y=x^2	a^2=b		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		{x=1,y=2}	{x=2,y=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		cos(a*x)/(x*(ln(x)))	cos(a*y)/(y*(ln(y)))		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		cos(a*x)/(x*(ln(x)))	cos(x*a)/(a*(ln(a)))		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		cos(a*x)/(x*(ln(x)))	cos(a*x)/(x(ln(x)))		0
SubstEquiv		cos(a*x)/(x*(ln(x)))	cos(a*y)/(y(ln(y)))		0
SubstEquiv		x+1>y	y+1>x		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		x+1>y	x<y+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		matrix([1,A^2+A+1],[2,0])	matrix([1,x^2+x+1],[2,0])		1		Your answer would be correct if you used the following substitution of variables. \[\left[ A=x \right] \]	ATSubstEquiv_Subst [A = x].
SubstEquiv		matrix([B,A^2+A+1],[2,C])	matrix([y,x^2+x+1],[2,z])		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		matrix([B,A^2+A+1],[2,C])	matrix([y,x^2+x+1],[2,x])		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		[x^2+1,x^2]	[A^2+1,A^2]		1		Your answer would be correct if you used the following substitution of variables. \[\left[ x=A \right] \]	ATSubstEquiv_Subst [x = A].
SubstEquiv		[x^2-1,x^2]	[A^2+1,A^2]		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		[A,B,C]	[B,C,A]		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		[A,B,C]	[B,B,A]		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		[1,[A,B],C]	[1,[a,b],C]		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		{x^2+1,x^2}	{A^2+1,A^2}		1		Your answer would be correct if you used the following substitution of variables. \[\left[ x=A \right] \]	ATSubstEquiv_Subst [x = A].
SubstEquiv		{x^2-1,x^2}	{A^2+1,A^2}		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		{A+1,B^2,C}	{B,C+1,A^2}		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		{1,{A,B},C}	{1,{a,b},C}		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		A*cos(t)+B*sin(t)	P*cos(t)+Q*sin(t)		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		A*cos(t)+B*sin(t)	P*cos(x)+Q*sin(x)		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		A*cos(t)+B*sin(t)	P*cos(x)+Q*sin(x)	[x]	0
SubstEquiv		A*cos(t)+B*sin(t)	P*cos(x)+Q*sin(x)	[t]	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		A*cos(t)*e^x+B*sin(t)*e^x+C*si n(2*x)+D*cos(2*x)	P*cos(t)*e^x+Q*sin(t)*e^x+R*si n(2*x)+S*cos(2*x)	[x,t]	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].
SubstEquiv		sqrt(2*g*y)	sqrt(2*g*x)		1		Your answer would be correct if you used the following substitution of variables. \[\left[ g=g , y=x \right] \]	ATSubstEquiv_Subst [g = g,y = x].
SubstEquiv		sqrt(2*g*y)	sqrt(2*g*x)	[g]	1		Your answer would be correct if you used the following substitution of variables. \[\left[ y=x \right] \]	ATSubstEquiv_Subst [y = x].

EqualComAss

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
EqualComAss		1/0	0		-1			ATEqualComAss_STACKERROR_SAns.
EqualComAss		0	1/0		-1			ATEqualComAss_STACKERROR_TAns.
	Numbers
EqualComAss		2/4	1/2		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		3^2	8		0			ATEqualComAss (AlgEquiv-false).
EqualComAss		3^2	9		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		cos(0)	1		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		4^(1/2)	2		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		1/3^(1/2)	(1/3)^(1/2)		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		sqrt(3)/3	(1/3)^(1/2)		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		sqrt(3)	3^(1/2)		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		2*sqrt(2)	sqrt(8)		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		2*2^(1/2)	sqrt(8)		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		sqrt(2)/4	1/sqrt(8)		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		1/sqrt(2)	2^(1/2)/2		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		4.0	4		0			ATEqualComAss (AlgEquiv-true).
	Case sensitivity
EqualComAss		X	x		0			ATEqualComAss (AlgEquiv-false)ATAlgEquiv_WrongCase.
EqualComAss		exdowncase(X)	x		1
EqualComAss		exdowncase((X-1)^2)	x^2-2*x+1		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		exdowncase(X^2-2*X+1)	x^2-2*x+1		1
	Powers
EqualComAss		a^2/b^3	a^2*b^(-3)		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		lg(a^x,a)	x		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		x^(2/4)	x^(1/2)		0			ATEqualComAss (AlgEquiv-true).
	Simple polynomials
EqualComAss		1+2*x	x*2+1		1
EqualComAss		1+x	2*x+1		0			ATEqualComAss (AlgEquiv-false).
EqualComAss		1+x+x	2*x+1		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		(x+y)+z	z+x+y		1
EqualComAss		x*x	x^2		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		(x+5)*x	x*(5+x)		1
EqualComAss		x*(x+5)	5*x+x^2		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		(1-x)^2	(x-1)^2		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		(a-x)^6000	(x-a)^6000		0			ATEqualComAss (AlgEquiv-true).
	Expressions with subscripts
EqualComAss		rho*z*V/(4*pi*epsilon[0]*(R^2+ z^2)^(3/2))	rho*z*V/(4*pi*epsilon[0]*(R^2+ z^2)^(3/2))		1
EqualComAss		rho*z*V/(4*pi*epsilon[1]*(R^2+ z^2)^(3/2))	rho*z*V/(4*pi*epsilon[0]*(R^2+ z^2)^(3/2))		0			ATEqualComAss (AlgEquiv-false).
	Unary minus
EqualComAss		-1+2	2-1		1
EqualComAss		-1*2+3*4	3*4-1*2		1
EqualComAss		(-1*2)+3*4	10		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		-1*2+3*4	3*4-1*2		1
EqualComAss		x*(-y)	-x*y		1
EqualComAss		x*(-y)	-(x*y)		1
EqualComAss		(-x)*(-x)	x*x		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		(-x)*(-x)	x^2		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		-1/4*%pi*i	-(%i*%pi)/4		0			ATEqualComAss (AlgEquiv-true).
	Rational expressions
EqualComAss		1/2	3/6		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		1/(1+2*x)	1/(2*x+1)		1
EqualComAss		2/(4+2*x)	1/(x+2)		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		(a*b)/c	a*(b/c)		1
EqualComAss		((x+1)/(x*(x-1)))*(x-1)	((x+1)*(x-1))/(x*(x-1))		1
EqualComAss		(-x)/y	-(x/y)		1
EqualComAss		x/(-y)	-(x/y)		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		-1/(1-x)	1/(x-1)		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		1/2*1/x	1/(2*x)		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		(k+8)/(k^2+4*k-12)	(k+8)/(k^2+4*k-12)		1
EqualComAss		(k+8)/(k^2+4*k-12)	(k+8)/((k-2)*(k+6))		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		(k+7)/(k^2+4*k-12)	(k+8)/(k^2+4*k-12)		0			ATEqualComAss (AlgEquiv-false).
EqualComAss		-(2*k+6)/(k^2+4*k-12)	-(2*k+6)/(k^2+4*k-12)		1
EqualComAss		(a+b)/1	(b+a)/1		1
	No simplicifcation here
EqualComAss		1*x	x		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		23+0*x	23		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		x+0	x		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		x^1	x		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		(1/2)*(a+b)	(a+b)/2		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		1/3*logbase(27,6)	logbase(27,6)/3		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		1/3*lg(27,6)	lg(27,6)/3		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		lg(root(x, n))	lg(x, 10)/n		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		exp(x)	%e^x		1
EqualComAss		exp(x)^2	%e^(2*x)		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		exp(x)^2	(%e^(x))^2		1
EqualComAss		1/3*i	i/3		0			ATEqualComAss (AlgEquiv-true).
	Complex numbers
EqualComAss		%i	e^(i*pi/2)		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		(4*sqrt(3)*%i+4)^(1/5)	rectform((4*sqrt(3)*%i+4)^(1/5 ))		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		(4*sqrt(3)*%i+4)^(1/5)	8^(1/5)*(cos(%pi/15)+%i*sin(%p i/15))		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		(4*sqrt(3)*%i+4)^(1/5)	polarform((4*sqrt(3)*%i+4)^(1/ 5))		0			ATEqualComAss (AlgEquiv-true).
	Equations
EqualComAss		y=x	x=y		1
EqualComAss		x+1	y=2*x+1		0		Your answer should be an equation, but is not.	ATEqualComAss ATAlgEquiv_SA_not_equation.
EqualComAss		y=1+2*x	y=2*x+1		1
EqualComAss		y=x+x+1	y=1+2*x		0			ATEqualComAss (AlgEquiv-true).
	Logic
EqualComAss		A and B	B and A		1
EqualComAss		A or B	B or A		1
EqualComAss		A or B	B and A		0			ATEqualComAss (AlgEquiv-false).
EqualComAss		not(true)	false		0			ATEqualComAss (AlgEquiv-true).
	Sets
EqualComAss		{2*x+1,2}	{2, 1+x*2}		1
EqualComAss		2	{2}		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		{2*x+1, 1+1}	{2, 1+x*2}		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		{1,2}	{1,{2}}		0			ATEqualComAss (AlgEquiv-false)ATSet_wrongentries.
EqualComAss		{4,3}	{3,4}		1
EqualComAss		{4,4}	{4}		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		{-1,1,-1}	{-1,-1,1}		1
EqualComAss		{-1,1,-1}	{-1,1}		0			ATEqualComAss (AlgEquiv-true).
	Lists
EqualComAss		[2*x+1,2]	[1+x*2,2]		1
EqualComAss		[x+x+1, 1+1]	[1+x*2,2]		0			ATEqualComAss (AlgEquiv-true).
	Matrices
EqualComAss		matrix([1,2],[2,3])	matrix([1,2],[2,3])		1
EqualComAss		matrix([1,2],[2,3])	matrix([1,2,3],[2,3,3])		0			ATEqualComAss (AlgEquiv-false)ATMatrix_wrongsz_columns.
EqualComAss		matrix([1,2],[2,3])	matrix([1,2],[2,5])		0			ATEqualComAss (AlgEquiv-false)ATMatrix_wrongentries.
EqualComAss		matrix([1,2],[2,2+1])	matrix([1,2],[2,3])		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		matrix([x+x, 1],[1, 1])	matrix([2*x, 1],[1, 1])		0			ATEqualComAss (AlgEquiv-true).
	Sums and products
EqualComAss		sum(k^n,n,0,3)	sum(k^n,n,0,3)		1
EqualComAss		1+k+k^2+k^3	sum(k^n,n,0,3)		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		sum(k,k,0,1+n)	sum(k,k,0,n+1)		1
EqualComAss		(n+1)*(n+2)/2	sum(k,k,0,n+1)		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		product(cos(k*x),k,1,3)	product(cos(k*x),k,1,3)		1
EqualComAss		cos(x)*cos(2*x)*cos(3*x)	product(cos(k*x),k,1,3)		0			ATEqualComAss (AlgEquiv-true).
	Inequalities are not commutative under this test
EqualComAss		-6/5 > x	x < -6/5		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		x<1 and -3<x	-3<x and x<1		1
EqualComAss		1>x and -3<x	-3<x and x<1		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		make_less_ineq(-6/5 > x)	x < -6/5		1
EqualComAss		make_less_ineq(1>x and -3&l t;x)	-3<x and x<1		1
EqualComAss		make_less_ineq(6/3 > x)	x < 2		0			ATEqualComAss (AlgEquiv-true).
	Unary Equations
EqualComAss		1	stackeq(1)		1
EqualComAss		stackeq(1)	1		1
EqualComAss		stackeq(1+1)	2		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		stackeq(1)	0		0			ATEqualComAss (AlgEquiv-false).
EqualComAss		lowesttermsp(1/3)	true		1
EqualComAss		lowesttermsp(2/6)	true		0			ATEqualComAss (AlgEquiv-false).
EqualComAss		lowesttermsp(x^2/x)	true		0			ATEqualComAss (AlgEquiv-false).
EqualComAss		lowesttermsp(-y/-x)	true		0			ATEqualComAss (AlgEquiv-false).
EqualComAss		lowesttermsp((x^2-1)/(x-1))	true		0			ATEqualComAss (AlgEquiv-false).
EqualComAss		lowesttermsp((x^2-1)/(x+2))	true		1
	Bad things in denominators
EqualComAss		rationalized(1+sqrt(3)/3)	true		1
EqualComAss		rationalized(1+1/sqrt(3))	[sqrt(3)]		1
EqualComAss		rationalized(1/sqrt(3))	[sqrt(3)]		1
EqualComAss		rationalized(1/sqrt(2)+i/sqrt( 2))	[sqrt(2),sqrt(2)]		1
EqualComAss		rationalized(sqrt(2)/2+1/sqrt( 3))	[sqrt(3)]		1
EqualComAss		rationalized(1/sqrt(2)+1/sqrt( 3))	[sqrt(2),sqrt(3)]		1
EqualComAss		rationalized(1/(1+i))	[i]		1
EqualComAss		rationalized(1/(1+1/root(3,2)) )	[root(3,2)]		1
	Differential Equations
EqualComAss		diff(y,x)	0		1
EqualComAss		diff(x^2,x)	2*x		1
EqualComAss		noundiff(x^2,x)	2*x		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		diff(y,x)	'diff(y,x)		0			ATEqualComAss (AlgEquiv-true).
EqualComAss		noundiff(y,x)	'diff(y,x)		1
EqualComAss		'diff(y(x),x)	'diff(y(x),x,1)		1
EqualComAss		noundiff(y(x),x)=-x/4	4*noundiff(y(x),x)+x=0		0			ATEqualComAss (AlgEquiv-true).

EqualComAssRules

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
EqualComAssRules		1/0	0	[]	-1			ATEqualComAssRules_STACKERROR_SAns.
EqualComAssRules		0	1/0	[]	-1			ATEqualComAssRules_STACKERROR_TAns.
EqualComAssRules		0+a	a		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test.	STACKERROR_OPTION.
EqualComAssRules		0+a	a	x	-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		0+a	a	[x]	-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		0+a	a	[intMul,intFac]	-1		The option to this answer test contains incompatible rules. This is an error. Please contact your teacher.	ATEqualComAssRules_Opt_Incompatible.
	Basic cases
EqualComAssRules		1+1	3	[zeroAdd]	0			ATEqualComAssRules (AlgEquiv-false).
EqualComAssRules		1+1	2	[zeroAdd]	0
EqualComAssRules		1+1	2	[testdebug,zero Add]	0			ATEqualComAssRules: [1 nounadd 1,2].
EqualComAssRules		0+a	a	[zeroAdd]	1
EqualComAssRules		a+0	a	[zeroAdd]	1
EqualComAssRules		1*a	a	[testdebug,zero Add]	0			ATEqualComAssRules: [1 nounmul a,a].
EqualComAssRules		1*a	a	[oneMul]	1
EqualComAssRules		1*a	a	ID_TRANS	1
EqualComAssRules		a/1	a	ID_TRANS	1
EqualComAssRules		0*a	0	ID_TRANS	1
EqualComAssRules		0-1*i	-i	ID_TRANS	1
EqualComAssRules		0-i	-i	ID_TRANS	1
EqualComAssRules		2+1*i	2+i	ID_TRANS	1
EqualComAssRules		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
EqualComAssRules		%e^x	exp(x)	[testdebug,ID_T RANS]	1			ATEqualComAssRules: [%e nounpow x,%e nounpow x].
EqualComAssRules		12*%e^((2*(%pi/2)*%i)/2)	12*exp(%i*(%pi/2))	ID_TRANS	0
EqualComAssRules		12*%e^((2*(%pi/2)*%i)/2)	12*exp(%i*(%pi/2))	[ID_TRANS,[negN eg,negDiv,negOr d],[recipMul,di vDiv,divCancel] ,[intAdd,intMul ,intPow]]	1
EqualComAssRules		0^(1-1)	0	ID_TRANS	0			ATEqualComAssRules_STACKERROR_SAns.
EqualComAssRules		0*a	0	delete(zeroMul, ID_TRANS)	0
EqualComAssRules		-(-a)	a	[negNeg]	1
EqualComAssRules		-(-(-a))	-a	[negNeg]	1
EqualComAssRules		-(-(-a))	a	[testdebug,negN eg]	0			ATEqualComAssRules (AlgEquiv-false).
EqualComAssRules		3/(-x)	-3/x	ID_TRANS	0
EqualComAssRules		3/(-x)	-3/x	[testdebug,ID_T RANS]	0			ATEqualComAssRules: [3 nounmul UNARY_RECIP UNARY_MINUS nounmul x,UNARY_MINUS nounmul 3 nounmul UNARY_RECIP x].
EqualComAssRules		-x*(x+1)	x*(-x-1)	[negDist]	1
EqualComAssRules		-x*(x-1)	x*(1-x)	NEG_TRANS	1
EqualComAssRules		-x*(x-1)	x*(1-x)	NEG_TRANS	1
EqualComAssRules		-5*x*(3-x)	5*x*(x-3)	NEG_TRANS	1
EqualComAssRules		-x*(x-1)*(x+1)	x*(x-1)*(-x-1)	NEG_TRANS	1
EqualComAssRules		-x*(x-1)*(x+1)	x*(1-x)*(x+1)	NEG_TRANS	1
EqualComAssRules		-x*(y-1)*(x-1)	x*(1-x)*(y-1)	NEG_TRANS	1
EqualComAssRules		-x*(y-1)*(x-1)	x*(x-1)*(1-y)	NEG_TRANS	1
EqualComAssRules		(x-y)*(y-x)	-(x-y)*(x-y)	NEG_TRANS	1
EqualComAssRules		(x-y)*(y-x)	-(x-y)^2	[testdebug,NEG_ TRANS]	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		-x*(x-1)*(x+1)	x*(1-x)*(x+1)	[testdebug,negD ist,negNeg]	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		-x*(y-1)*(x-1)	x*(x-1)*(1-y)	[testdebug,negD ist,negNeg]	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		3/(-x)	-3/x	[negDiv]	1
EqualComAssRules		3/(-x)	ev(-3,simp)/x	[negDiv]	1
EqualComAssRules		(-a)/(-x)	-(-a/x)	[testdebug,ID_T RANS]	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		(-a)/(-x)	-(-a/x)	[negDiv]	1
EqualComAssRules		(-a)/(-x)	a/x	[testdebug,negD iv]	0			ATEqualComAssRules: [UNARY_MINUS nounmul UNARY_MINUS nounmul a nounmul UNARY_RECIP x,a nounmul UNARY_RECIP x].
EqualComAssRules		(-a)/(-x)	a/x	[negDiv,negNeg]	1
EqualComAssRules		1/(-x)	(-1)/x	[negDiv]	1
EqualComAssRules		1/(-x)	ev(-1,simp)/x	[negDiv]	1
EqualComAssRules		(2/-3)*(x-y)	-(2/3)*(x-y)	[negDiv]	1
EqualComAssRules		(2/-3)*(x-y)	(2/3)*(y-x)	[negDiv]	0
EqualComAssRules		(2/-3)*(x-y)	(2/3)*(y-x)	[negDiv,negOrd]	1
EqualComAssRules		-2/(1-x)	2/(x-1)	[testdebug,negD iv]	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		1/2*3/x	3/(2*x)	[testdebug,ID_T RANS]	0			ATEqualComAssRules: [3 nounmul (UNARY_RECIP 2) nounmul UNARY_RECIP x,3 nounmul UNARY_RECIP 2 nounmul x].
EqualComAssRules		1/2*3/x	3/(2*x)	[ID_TRANS,recip Mul]	1
EqualComAssRules		5/2*3/x	15/(2*x)	[testdebug,ID_T RANS,recipMul]	0			ATEqualComAssRules: [3 nounmul 5 nounmul UNARY_RECIP 2 nounmul x,15 nounmul UNARY_RECIP 2 nounmul x].
EqualComAssRules		-(x-y)	y-x	[negOrd]	1
EqualComAssRules		5/2*3/x	15/(2*x)	[ID_TRANS,recip Mul,intMul]	1
EqualComAssRules		(3+2)*x+x	5*x+x	[ID_TRANS,intAd d]	1
EqualComAssRules		(3-5)*x+x	-2*x+x	[ID_TRANS,intAd d]	1
EqualComAssRules		7*x*(-3*x)	-21*x*x	[ID_TRANS,intMu l]	1
EqualComAssRules		(-7*x)*(-3*x)	21*x*x	[testdebug,ID_T RANS,intMul]	0			ATEqualComAssRules: [UNARY_MINUS nounmul UNARY_MINUS nounmul 21 nounmul x nounmul x,21 nounmul x nounmul x].
EqualComAssRules		(-7*x)*(-3*x)	21*x*x	[ID_TRANS,intMu l,negNeg]	1
	ev(a/b/c, simp)=a/(b*c)
EqualComAssRules		a/b/c	a/(b*c)	[testdebug,ID_T RANS]	0			ATEqualComAssRules: [a nounmul (UNARY_RECIP b) nounmul UNARY_RECIP c,a nounmul UNARY_RECIP b nounmul c].
EqualComAssRules		a/b/c	a/(b*c)	[ID_TRANS,recip Mul]	1
EqualComAssRules		(a/b)/c	a/(b*c)	[ID_TRANS,recip Mul]	1
	ev(a/(b/c), simp)=(a*c)/b
EqualComAssRules		a/(b/c)	(a*c)/b	[testdebug,ID_T RANS]	0			ATEqualComAssRules: [a nounmul UNARY_RECIP b nounmul UNARY_RECIP c,a nounmul c nounmul UNARY_RECIP b].
EqualComAssRules		a/(b/c)	(a*c)/b	[testdebug,ID_T RANS,recipMul]	0			ATEqualComAssRules: [a nounmul UNARY_RECIP b nounmul UNARY_RECIP c,a nounmul c nounmul UNARY_RECIP b].
EqualComAssRules		a/(b/c)	(a*c)/b	[ID_TRANS,divDi v]	1
EqualComAssRules		A*a/(B*b/c)	A*(a*c)/(B*b)	[ID_TRANS,divDi v]	1
EqualComAssRules		A*a/(B*b/c)*1/d	A*(a*c)/(B*b)*1/d	[ID_TRANS,divDi v]	1
EqualComAssRules		D*A*a/(B*b/c)*1/d	A*(a*c)/(B*b)*D/d	[ID_TRANS,divDi v]	1
EqualComAssRules		A*a/(B*b/c)*1/d	A*(a*c)/(B*b*d)	[testdebug,ID_T RANS,divDiv]	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		A*a/(B*b/c)*1/d	A*(a*c)/(B*b*d)	[ID_TRANS,divDi v,recipMul]	1
EqualComAssRules		A/(B/(C/D))	A*C/(B*D)	[testdebug,ID_T RANS,divDiv]	0			ATEqualComAssRules: [A nounmul C nounmul (UNARY_RECIP B) nounmul UNARY_RECIP D,A nounmul C nounmul UNARY_RECIP B nounmul D].
EqualComAssRules		A/(B/(C/D))	A*C/(B*D)	[ID_TRANS,divDi v,recipMul]	1
EqualComAssRules		18	2*3^2	[intFac]	1
EqualComAssRules		0+%i*(-(1/27))	-(%i/27)	[[zeroAdd,zeroM ul,oneMul,onePo w,idPow,zeroPow ,zPow,oneDiv],[ negNeg,negDiv,n egOrd],[recipMu l,divDiv,divCan cel],[intAdd,in tMul,intPow]]	1
EqualComAssRules		x=sqrt(3)+2	x=3^(1/2)+2	[ID_TRANS,sqrtR em]	1
EqualComAssRules		x=sqrt(3)+2 nounor x=-sqrt(3)- 2	x=3^(1/2)+2 nounor x=-3^(1/2)- 2	ID_TRANS	0
EqualComAssRules		x=sqrt(3)+2 nounor x=-sqrt(3)- 2	x=3^(1/2)+2 nounor x=-3^(1/2)- 2	[ID_TRANS,sqrtR em]	1
EqualComAssRules		x=sqrt(3)+2 nounor x=-sqrt(3)+ 7	x=3^(1/2)+2 nounor x=-3^(1/2)- 2	[ID_TRANS,sqrtR em]	0			ATEqualComAssRules (AlgEquiv-false)ATEquation_default.
EqualComAssRules		1/sqrt(3)	1/3^(1/2)	[ID_TRANS,sqrtR em]	1
EqualComAssRules		1/sqrt(3)	3^(-1/2)	[ID_TRANS,sqrtR em]	0

CasEqual

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

SameType

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
SameType		1/0	1		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSameType_STACKERROR_SAns.
SameType		1	1/0		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSameType_STACKERROR_TAns.
	Numbers
SameType		4^(-1/2)	1/2		1
	Lists
SameType		x	[1,2,3]		0
SameType		[1,2]	[1,2,3]		1
SameType		[1,x>2]	[1,2<x]		1
SameType		[1,x,3]	[1,2<x,4]		0
	Sets
SameType		x	{1,2,3}		0
SameType		{1,2}	{1,2,3}		1
	Matrices
SameType		matrix([1,2],[2,3])	matrix([1,2],[2,3])		1
SameType		[[1,2],[2,3]]	matrix([1,2],[2,3])		0
SameType		matrix([1,2],[2,3])	matrix([1,2,3],[2,3,3])		1
SameType		matrix([x>4,{1,x^2}],[[1,2] ,[1,3]])	matrix([4-x<0,{x^2, 1}],[[1 ,2],[1,3]])		1
SameType		matrix([x>4,[1,x^2]],[[1,2] ,[1,3]])	matrix([4-x<0,{x^2, 1}],[[1 ,2],[1,4]])		0
	Equations
SameType		1	x=1		0
SameType		x=1	x=1		1
	Inequalities
SameType		1	x>1		0
SameType		x>2	x>1		1
SameType		x>1	x>=1		1
SameType		x>1 and x<3	x>=1		1
SameType		{x>1,x<3}	x>=1		0
SameType		sqrt(2)*sqrt(3)+2*(sqrt(2/3))* x-(2/3)*(sqrt(2/3))*x^2+(4/9)* (sqrt(2/3))*x^3	4*sqrt(6)*x^3/27-(2*sqrt(6)*x^ 2)/9+(2*sqrt(6)*x)/3+sqrt(6)		1

SysEquiv

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
	Basic tests
SysEquiv		1/0	[(x-1)*(x+1)=0]		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSysEquiv_STACKERROR_SAns.
SysEquiv		[(x-1)*(x+1)=0]	1/0		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSysEquiv_STACKERROR_TAns.
SysEquiv		1	[(x-1)*(x+1)=0]		0		Your answer should be a list, but it is not!	ATSysEquiv_SA_not_list.
SysEquiv		[(x-1)*(x+1)=0]	1		0		The teacher's answer is not a list. Please contact your teacher.	ATSysEquiv_SB_not_list.
SysEquiv		[1]	[90=v*t,90=(v+5)*(t-1/4)]		0		Your answer should be a list of equations, but it is not!	ATSysEquiv_SA_not_eq_list.
SysEquiv		[(x-1)*(x+1)=0]	[1]		0		The teacher's answer is not a list of equations, but should be.	ATSysEquiv_SB_not_eq_list.
SysEquiv		[x^2]	[(x-1)*(x+1)=0]		0		Your answer should be a list of equations, but it is not!	ATSysEquiv_SA_not_eq_list.
SysEquiv		[90=v*t^t,90=(v+5)*(t-1/4)]	[90=v*t,90=(v+5)*(t-1/4)]		0		One or more of your equations is not a polynomial!	ATSysEquiv_SA_not_poly_eq_list.
SysEquiv		[90=v*t,90=(v+5)*(t-1/4)]	[90=v*t^t,90=(v+5)*(t-1/4)]		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		[x^2=1]	[(x-1)*(x+1)=0]		1
SysEquiv		[x^2+y^2=4,y=x]	[y=x,y^2=2]		1
SysEquiv		[x^2+y^2=2,y=x]	[y=x,y^2=2]		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		[x=1]	[(x-1)*(x+1)=0,(x-1)*(x-3)=0]		1			ATSysEquiv_SA_Completely_solved.
SysEquiv		[3*a+b-c=2, a-b+2*c=5,b+c=5]	[a=1,b=2,c=3]		1
SysEquiv		[a=1,b=2,c=3]	[3*a+b-c=2, a-b+2*c=5,b+c=5]		1			ATSysEquiv_SA_Completely_solved.
SysEquiv		[x^2=1]	[(x-1)*(x+1)*(x-2)=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		[x=1,y=-1]	[(x-1)*(y+1)=0]		0			ATSysEquiv_SA_Not_completely_solved.
SysEquiv		[x=1]	[(x-1)*(x+1)=0]		0			ATSysEquiv_SA_Not_completely_solved.
SysEquiv		[x=1]	[(x-1)*(x+1)*y=0]		0			ATSysEquiv_SA_Not_completely_solved.
SysEquiv		[90=v*t,90=(v+5)*(t-1/4)]	[90=v*t,90=(v+5)*(t-1/4)]		1
SysEquiv		[90=v*t,90=(v+5)*(t*x-1/4)]	[90=v*t,90=(v+5)*(t-1/4)]		0		Your answer includes too many variables!	ATSysEquiv_SA_extra_variables.
SysEquiv		[90=v*t,90=(v+5)*(t-1/4)]	[90=v*t,90=(v+5)*(t*x-1/4)]		0		Your answer is missing one or more variables!	ATSysEquiv_SA_missing_variables.
SysEquiv		[90=v*t]	[90=v*t,90=(v+5)*(t-1/4)]		0		The equations in your system appear to be correct, but you need others besides.	ATSysEquiv_SA_system_underdetermined.
SysEquiv		[90=v*t,90=(v+5)*(t-1/4),90=(v +6)*(t-1/5)]	[90=v*t,90=(v+5)*(t-1/4)]		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		[90=v*t,90=(v+5)*(t-1/4),90=(v +6)*(t-1/5),90=(v+7)*(t-1/4),9 0=(v+8)*(t-1/3)]	[90=v*t,90=(v+5)*(t-1/4)]		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		[b^2=a,a=9]	[x^2=y,y=9]		0		Your answer uses the wrong variables!	ATSysEquiv_SA_wrong_variables.
SysEquiv		[x^2=4]	[x^2=4,y=9]		0		Your answer is missing one or more variables!	ATSysEquiv_SA_missing_variables.
SysEquiv		[d=90,d=v*t,d=(v+5)*(t-1/4)]	[90=v*t,90=(v+5)*(t-1/4)]		0		Your answer includes too many variables!	ATSysEquiv_SA_extra_variables.
SysEquiv		stack_eval_assignments([d=90,d =v*t,d=(v+5)*(t-1/4)])	[90=v*t,90=(v+5)*(t-1/4)]		1

Sets

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
Sets		{1/0}	{0}		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSets_STACKERROR_SAns.
Sets		{0}	{1/0}		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATSets_STACKERROR_TAns.
Sets		x	{1,2,3}		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		{1,2}	x		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		{1,2}	{1,2,3}		0		The following are missing from your set. \[\left \{3 \right \}\]	ATSets_missingentries.
Sets		{1,2,4}	{1,2}		0		These entries should not be elements of your set. \[\left \{4 \right \}\]	ATSets_wrongentries.
Sets		{1,2,2+2}	{1,2}		0		These entries should not be elements of your set. \[\left \{4 \right \}\]	ATSets_wrongentries.
Sets		{5,1,2,4}	{1,2,3}		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		{2/4, 1/3}	{1/2, 1/3}		1
	Duplicate entries
Sets		{1,2,1}	{1,2}		1		Your set appears to contain duplicate entries!	ATSets_duplicates.
Sets		{1,2,1+1}	{1,2}		1		Your set appears to contain duplicate entries!	ATSets_duplicates.
Sets		{1,2,1+1}	{1,2,3}		0		Your set appears to contain duplicate entries! The following are missing from your set. \[\left \{3 \right \}\]	ATSets_duplicates. ATSets_missingentries.
Sets		{(x-a)^6000}	{(a-x)^6000}		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

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
Expanded		1/0	0		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATExpanded_STACKERROR_SAns.
Expanded		x>2	x^2-2*x+1		0		Your answer should be an expression, not an equation, inequality, list, set or matrix.	ATExpanded_SA_not_expression.
Expanded		x^2-1	0		1			ATExpanded_TRUE.
Expanded		2*(x-1)	0		0			ATExpanded_FALSE.
Expanded		(x-1)*(x+1)	0		0			ATExpanded_FALSE.
Expanded		(x-a)*(x-b)	0		0			ATExpanded_FALSE.
Expanded		x^2-(a+b)*x+a*b	0		0			ATExpanded_FALSE.
Expanded		x^2-a*x-b*x+a*b	0		1			ATExpanded_TRUE.
Expanded		cos(2*x)	0		1			ATExpanded_TRUE.
Expanded		p+1	0		1			ATExpanded_TRUE.
Expanded		(p+1)*(p-1)	0		0			ATExpanded_FALSE.
Expanded		3+2*sqrt(3)	0		1			ATExpanded_TRUE.
Expanded		3+sqrt(12)	0		1			ATExpanded_TRUE.
Expanded		(1+sqrt(5))*(1-sqrt(3))	0		0			ATExpanded_FALSE.
	This fails, but you are never going to ask students to do this anyway...
Expanded	!	(a-x)^6000	0		-2			ATExpanded_TRUE.

FacForm

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
FacForm		1/0	0	x	-1			ATFacForm_STACKERROR_SAns.
FacForm		0	1/0	x	-1			ATFacForm_STACKERROR_TAns.
FacForm		0	0	1/0	-1			ATFacForm_STACKERROR_Opt.
	Trivial cases
FacForm		2	2	x	1			ATFacForm_int_true.
FacForm		6	6	x	1			ATFacForm_int_true.
FacForm		1/3	1/3	x	1			ATFacForm_true.
FacForm		3*x^2	3*x^2	x	1			ATFacForm_true.
FacForm		4*x^2	4*x^2	x	1			ATFacForm_true.
	Linear integer factors
FacForm		2*(x-1)	2*x-2	x	1			ATFacForm_true.
FacForm		2*x-2	2*x-2	x	0		Your answer is not factored. You need to take out a common factor.	ATFacForm_notfactored.
FacForm		2*(x+1)	2*x-2	x	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		2*x+2	2*x-2	x	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		2*(x+0.5)	2*x+1	x	1			ATFacForm_default_true.
	Linear factors
FacForm		t*(2*x+1)	t*(2*x+1)	x	1			ATFacForm_true.
FacForm		t*x+t	t*(x+1)	x	0		Your answer is not factored.	ATFacForm_notfactored.
FacForm		6*s*t+10*s	2*s*(3*t+5)	t	0		Your answer is not factored.	ATFacForm_notfactored.
	Quadratic, with no const
FacForm		2*x*(x-3)	2*x^2-6*x	x	1			ATFacForm_true.
FacForm		2*(x^2-3*x)	2*x*(x-3)	x	0		Your answer is not factored. You could still do some more work on the term \(x^2-3\cdot x\).	ATFacForm_notfactored.
FacForm		x*(2*x-6)	2*x*(x-3)	x	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		(x+2)*(x+3)	(x+2)*(x+3)	x	1			ATFacForm_true.
FacForm		(x+2)*(2*x+6)	2*(x+2)*(x+3)	x	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		(z*x+z)*(2*x+6)	2*z*(x+1)*(x+3)	x	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		(x+t)*(x-t)	x^2-t^2	x	1			ATFacForm_true.
FacForm		t^2-1	(t-1)*(t+1)	t	0		Your answer is not factored.	ATFacForm_notfactored.
FacForm		t^2+1	t^2+1	t	1			ATFacForm_true.
FacForm		v^2+1	v^2+1	v	1			ATFacForm_true.
FacForm		v^2-1	v^2-1	v	0		Your answer is not factored.	ATFacForm_notfactored.
FacForm		-(3*w-4*v+9*u)*(3*w+4*v-u)	-(3*w-4*v+9*u)*(3*w+4*v-u)	v	1			ATFacForm_true.
FacForm		-6*k*(4*b-k-1)	6*k*(1+k-4*b)	k	1			ATFacForm_default_true.
FacForm		-2*3*k*(4*b-k-1)	6*k*(1+k-4*b)	k	1			ATFacForm_true.
FacForm		-(6*k*(4*b-k-1))	6*k*(1+k-4*b)	k	1			ATFacForm_default_true.
FacForm		-(6*a*(4*b-a-1))	6*a*(1+a-4*b)	a	1			ATFacForm_true.
FacForm		-(6*a*(4*b-a-1))	6*a*(-(4*b)+a+1)	a	1			ATFacForm_true.
FacForm		x*(x-4+4/x)	x^2-4*x+4	x	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		(2-x)*(3-x)	(x-2)*(x-3)	x	1			ATFacForm_true.
FacForm		(1-x)^2	(x-1)^2	x	1			ATFacForm_true.
FacForm		(1-x)*(1-x)	(x-1)^2	x	1			ATFacForm_true.
FacForm		-(1-x)^2	-(x-1)^2	x	1			ATFacForm_true.
FacForm		(1-x)^2	(x-1)^2	x	1			ATFacForm_true.
FacForm		4*(1-x/2)^2	(x-2)^2	x	1			ATFacForm_default_true.
FacForm		-3*(x-4)*(x+1)	-3*x^2+9*x+12	x	1			ATFacForm_true.
FacForm		3*(-x+4)*(x+1)	-3*x^2+9*x+12	x	1			ATFacForm_true.
FacForm		3*(4-x)*(x+1)	-3*x^2+9*x+12	x	1			ATFacForm_true.
	Cubics
FacForm		(x-1)*(x^2+x+1)	x^3-1	x	1			ATFacForm_true.
FacForm		x^3-x+1	x^3-x+1	x	1			ATFacForm_true.
FacForm		7*x^3-7*x+7	7*(x^3-x+1)	x	0		Your answer is not factored. You need to take out a common factor.	ATFacForm_notfactored.
FacForm		(1-x)*(2-x)*(3-x)	-x^3+6*x^2-11*x+6	x	1			ATFacForm_true.
FacForm		(2-x)*(2-x)*(3-x)	-x^3+7*x^2-16*x+12	x	1			ATFacForm_true.
FacForm		(2-x)^2*(3-x)	-x^3+7*x^2-16*x+12	x	1			ATFacForm_true.
FacForm		(x^2-4*x+4)*(3-x)	-x^3+7*x^2-16*x+12	x	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		(x^2-3*x+2)*(3-x)	-x^3+6*x^2-11*x+6	x	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		3*y^3-6*y^2-24*y	3*(y-4)*y*(y+2)	y	0		Your answer is not factored. You need to take out a common factor.	ATFacForm_notfactored.
FacForm		3*(y^3-2*y^2-8*y)	3*(y-4)*y*(y+2)	y	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		3*y*(y^2-2*y-8)	3*(y-4)*y*(y+2)	y	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		3*(y^2-4*y)*(y+2)	3*(y-4)*y*(y+2)	y	0		Your answer is not factored. You could still do some more work on the term \(y^2-4\cdot y\).	ATFacForm_notfactored.
FacForm		(y-4)*y*(3*y+6)	3*(y-4)*y*(y+2)	y	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		(a-x)^6000	(a-x)^6000	x	1			ATFacForm_true.
FacForm		(x-a)^6000	(a-x)^6000	x	1			ATFacForm_true.
	Needs flattening
FacForm		2*a*(a*b-1)	2*a*(a*b-1)	a	1			ATFacForm_true.
FacForm		(2*a)*(a*b-1)	2*a*(a*b-1)	a	1			ATFacForm_true.
FacForm		3*x*(7*y-3)*(7*y+3)	3*x*(7*y-3)*(7*y+3)	x	1			ATFacForm_true.
FacForm		3*x*(7*y-3)*(7*y+3)	3*x*(7*y-3)*(7*y+3)	y	1			ATFacForm_true.
	Not polynomials in a variable
FacForm		(sin(x)+1)*(sin(x)-1)	sin(x)^2-1	sin(x)	1			ATFacForm_true.
FacForm		(cos(t)-sqrt(2))^2	cos(t)^2-2*sqrt(2)*cos(t)+2	cos(t)	1			ATFacForm_true.
FacForm		7	7	x	1			ATFacForm_int_true.
	Factors over other fields
FacForm		24*(x-1/4)	24*x-6	x	1			ATFacForm_default_true.
FacForm		(x-sqrt(2))*(x+sqrt(2))	x^2-2	x	1			ATFacForm_true.
FacForm		x^2-2	x^2-2	x	1			ATFacForm_true.
FacForm		(%i*x-2*%i)	%i*(x-2)	x	0		Your answer is not factored.	ATFacForm_notfactored.
FacForm		%i*(x-2)	(%i*x-2*%i)	x	1			ATFacForm_true.
FacForm		(x-%i)*(x+%i)	x^2+1	x	1			ATFacForm_true.
FacForm		(x-1)*(x+(1+sqrt(3)*%i)/2)*(x+ (1-sqrt(3)*%i)/2)	x^3-1	x	1			ATFacForm_default_true.

CompSquare

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
CompSquare		1/0	0		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test.	STACKERROR_OPTION.
CompSquare		1/0	0	x	-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATCompSquare_STACKERROR_SAns.
CompSquare		0	1/0	x	-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATCompSquare_STACKERROR_TAns.
CompSquare		0	0	1/0	-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATCompSquare_STACKERROR_Opt.
	Category errors.
CompSquare		1	(x-1)^2+1	x	0		Your answer should depend on the variable \(x\) but it does not!	ATCompSquare_SA_not_depend_var.
CompSquare		(t-1)^2+1	(x-1)^2+1	x	0		Your answer should depend on the variable \(x\) but it does not!	ATCompSquare_SA_not_depend_var.
CompSquare		(x-1)^2+1=0	(x-1)^2+1	x	0		Your answer should be an expression, not an equation, inequality, list, set or matrix.	ATCompSquare_STACKERROR_LIST.
CompSquare		sin(x-1)+a-1	(x-1)^2+1	x	0			ATCompSquare_false_not_AlgEquiv.
	Trivial cases
CompSquare		1	1	x	1			ATCompSquare_true_trivial.
CompSquare		x-a	x-a	x	1			ATCompSquare_true_trivial.
CompSquare		x^2	x^2	x	1			ATCompSquare_true.
CompSquare		x^2-1	(x-1)*(x+1)	x	1			ATCompSquare_true.
CompSquare		(x-1)^2*k	(x-1)^2*k	x	1			ATCompSquare_true.
CompSquare		(x-1)^2/k	(x-1)^2/k	x	1			ATCompSquare_true.
	Normal cases
CompSquare		(x-1)^2+1	(x-1)^2+1	x	1			ATCompSquare_true.
CompSquare		(1-x)^2+1	(x-1)^2+1	x	1			ATCompSquare_true.
CompSquare		(X-1)^2+1	(x-1)^2+1	x	0		Your answer should depend on the variable \(x\) but it does not!	ATCompSquare_SA_not_depend_var.
CompSquare		9*(x-1)^2+1	(3*x-3)^2+1	x	1			ATCompSquare_true.
CompSquare		-(x-1)^2	-(x-1)^2	x	1			ATCompSquare_true.
CompSquare		-(1-x)^2	-(x-1)^2	x	1			ATCompSquare_true.
CompSquare		-(x-1)^2+3	-(x-1)^2+3	x	1			ATCompSquare_true.
CompSquare		-(1-x)^2+3	-(x-1)^2+3	x	1			ATCompSquare_true.
CompSquare		-4*(x-1)^2+3	-4*(x-1)^2+3	x	1			ATCompSquare_true.
CompSquare		-4*(x-1)^2+3	-(2*x-2)^2+3	x	1			ATCompSquare_true.
CompSquare		3-4*(x-1)^2	-(2*x-2)^2+3	x	1			ATCompSquare_true.
CompSquare		(x-1)^2+1	(x+1)^2+1	x	0		Your answer appears to be in the correct form, but is not equivalent to the correct answer.	ATCompSquare_true_not_AlgEquiv.
CompSquare		(x-a^2)^2+1+b	(x-a^2)^2+1+b	x	1			ATCompSquare_true.
CompSquare		x^2-2*x+2	(x-1)^2+1	x	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		x+1	(x-1)^2+1	x	0			ATCompSquare_false_not_AlgEquiv.
CompSquare		a*(x-1)^2+1	a*(x-1)^2+1	x	1			ATCompSquare_true.
CompSquare		-a*(x-1)^2+1	1-a*(x-1)^2	x	1			ATCompSquare_true.
	Not simple variable
CompSquare		(sin(x)-1)^2+1	(sin(x)-1)^2+1	sin(x)	1			ATCompSquare_true.
CompSquare		(x^2-1)^2+1	(x^2-1)^2+1	x^2	1			ATCompSquare_true.
CompSquare		(y-1)^2+1	(y-1)^2+1	y	1			ATCompSquare_true.
CompSquare		(y+1)^2+1	(y-1)^2+1	y	0		Your answer appears to be in the correct form, but is not equivalent to the correct answer.	ATCompSquare_true_not_AlgEquiv.
CompSquare		(x-1)^2+1	(sin(x)-1)^2+1	sin(x)	0		Your answer should depend on the variable \({\it facdum}\) but it does not!	ATCompSquare_SA_not_depend_var.

PropLogic

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
PropLogic		1/0	0		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATPropLogic_STACKERROR_SAns.
PropLogic		0	1/0		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATPropLogic_STACKERROR_TAns.
PropLogic		true	true		1
PropLogic		true	false		0
PropLogic		A implies B	not(A) or B		1
PropLogic		(a and b and c) xor (a and b) xor (a and c) xor a xor true	(a implies b) or c		1

Equiv

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
Equiv		x	[x^2=4,x=2 or x=-2]		-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		[x^2=4,x=2 or x=-2]	x		-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		[1/0]	[x^2=4,x=2 or x=-2]		-1			ATEquiv_STACKERROR_SAns.
Equiv		[x^2=4,x=2 or x=-2]	[1/0]		-1			ATEquiv_STACKERROR_TAns.
Equiv		[x^2=4,x=2 or x=-2]	[x^2=4,x=2 or x=-2]		1		\[\begin{array}{lll} &x^2=4& \cr \color{green}{\Leftrightarrow}&x=2\,{\mbox{ or }}\, x=-2& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR)
Equiv		[x^2=4,x=#pm#2,x=2 and x=-2]	[x^2=4,x=2 or x=-2]		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		[x^2=4,x=2]	[x^2=4,x=2 or x=-2]		0		\[\begin{array}{lll} &x^2=4& \cr \color{red}{\Leftarrow}&x=2& \cr \end{array}\]	(EMPTYCHAR,IMPLIEDCHAR)
Equiv		[x^2=4,x=2]	[x^2=4,x=2]	[assumepos]	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		[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		\[\begin{array}{lll} &x^2=4& \cr \color{green}{\Leftrightarrow}&x^2-4=0& \cr \color{green}{\Leftrightarrow}&\left(x-2\right)\cdot \left(x+2\right)=0& \cr \color{green}{\Leftrightarrow}&x=2\,{\mbox{ or }}\, x=-2& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR)
Equiv		[x^2=4,x= #pm#2, x=2 or x=-2]	[x^2=4,x=2 or x=-2]		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		[x^2-6*x+9=0,x=3]	[x^2-6*x+9=0,x=3]		1		\[\begin{array}{lll} &x^2-6\cdot x+9=0& \cr \color{green}{\mbox{(Same roots)}}&x=3& \cr \end{array}\]	(EMPTYCHAR,SAMEROOTS)
Equiv		[]	[]		1		\[\begin{array}{lll} &\left[ \right] & \cr \end{array}\]	(EMPTYCHAR)
Equiv		[x^2=-1]	[]		1		\[\begin{array}{lll} &x^2=-1& \cr \end{array}\]	(EMPTYCHAR)
Equiv		[x=x,all]	[]		1		\[\begin{array}{lll} &x=x& \cr \color{green}{\Leftrightarrow}&\mathbb{R}& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR)
Equiv		[x=x,true]	[]		1		\[\begin{array}{lll} &x=x& \cr \color{green}{\Leftrightarrow}&\mathbf{True}& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR)
Equiv		[x=x,false]	[]		0		\[\begin{array}{lll} &x=x& \cr \color{red}{?}&\mathbf{False}& \cr \end{array}\]	(EMPTYCHAR,QMCHAR)
Equiv		[1=1,all]	[]		1		\[\begin{array}{lll} &1=1& \cr \color{green}{\Leftrightarrow}&\mathbb{R}& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR)
Equiv		[1=1,true]	[]		1		\[\begin{array}{lll} &1=1& \cr \color{green}{\Leftrightarrow}&\mathbf{True}& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR)
Equiv		[0=0,all]	[]		1		\[\begin{array}{lll} &0=0& \cr \color{green}{\Leftrightarrow}&\mathbb{R}& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR)
Equiv		[0=0,true]	[]		1		\[\begin{array}{lll} &0=0& \cr \color{green}{\Leftrightarrow}&\mathbf{True}& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR)
Equiv		[1=2,false]	[]		1		\[\begin{array}{lll} &1=2& \cr \color{green}{\Leftrightarrow}&\mathbf{False}& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR)
Equiv		[1=2,none]	[]		1		\[\begin{array}{lll} &1=2& \cr \color{green}{\Leftrightarrow}&\emptyset& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR)
Equiv		[1=2,{}]	[]		1		\[\begin{array}{lll} &1=2& \cr \color{green}{\Leftrightarrow}&\left \{ \right \}& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR)
Equiv		[1=2,[]]	[]		1		\[\begin{array}{lll} &1=2& \cr \color{green}{\Leftrightarrow}&\left[ \right] & \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR)
Equiv		[x=1,X=1]	[]		0		\[\begin{array}{lll} &x=1& \cr \color{red}{?}&X=1& \cr \end{array}\]	(EMPTYCHAR,QMCHAR)
Equiv		[1/(x^2+1)=1/((x+%i)*(x-%i)),t rue]	[]		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		[2^2,stackeq(4)]	[]		1		\[\begin{array}{lll} &2^2& \cr \color{green}{\checkmark}&=4& \cr \end{array}\]	(EMPTYCHAR, CHECKMARK)
Equiv		[2^2,stackeq(3)]	[]		0		\[\begin{array}{lll} &2^2& \cr \color{red}{\Rightarrow}&=3& \cr \end{array}\]	(EMPTYCHAR,IMPLIESCHAR)
Equiv		[2^2,4]	[]		1		\[\begin{array}{lll} &2^2& \cr \color{green}{\Leftrightarrow}&4& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR)
Equiv		[2^2,3]	[]		0		\[\begin{array}{lll} &2^2& \cr \color{red}{\Rightarrow}&3& \cr \end{array}\]	(EMPTYCHAR,IMPLIESCHAR)
Equiv		[lg(64,4),lg(4^3,4),3*lg(4,4), 3]	[]		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		[lg(64,4),stackeq(lg(4^3,4)),s tackeq(3*lg(4,4)),stackeq(3)]	[]		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		[x=1 or x=2,x=1 or 2]	[]		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		[x=1 or x=2,x=1 and x=2]	[]		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		[x=1 and y=2,x=1 or y=2]	[]		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		[a=b,a^2=b^2]	[]		0		\[\begin{array}{lll} &a=b& \cr \color{red}{\Rightarrow}&a^2=b^2& \cr \end{array}\]	(EMPTYCHAR,IMPLIESCHAR)
Equiv		[a=b,sqrt(a)=sqrt(b)]	[]		0		\[\begin{array}{lll} &a=b& \cr \color{red}{\Leftarrow}&\sqrt{a}=\sqrt{b}& \cr \end{array}\]	(EMPTYCHAR,IMPLIEDCHAR)
Equiv		[a^2=b^2,a=b]	[]		0		\[\begin{array}{lll} &a^2=b^2& \cr \color{red}{\Leftarrow}&a=b& \cr \end{array}\]	(EMPTYCHAR,IMPLIEDCHAR)
Equiv		[a^2=b^2,a=b or a=-b]	[]		1		\[\begin{array}{lll} &a^2=b^2& \cr \color{green}{\Leftrightarrow}&a=b\,{\mbox{ or }}\, a=-b& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR)
Equiv		[a^2=b^2,a= #pm#b,a= b or a=-b ]	[]		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		[9*x^2/2-81*x/2+90=5*x^2/2-5*x -20 nounor 9*x^2/2-81*x/2+90=- (5*x^2/2-5*x-20),9*x^2-81*x+18 0=5*x^2-10*x-40 nounor 9*x^2-8 1*x+180=-5*x^2+10*x+40,4*x^2-7 1*x+220=0 nounor 14*x^2-91*x+1 40=0,x=(71 #pm# sqrt(71^2-4*4* 220))/(2*4) nounor x=(91 #pm# sqrt(91^2-4*14*140))/(2*14),x= 55/4 nounor x=4 nounor x=5/2]	[]		1		\[\begin{array}{lll} &\frac{9\cdot x^2}{2}-\frac{81\cdot x}{2}+90=\frac{5\cdot x^2}{2}-5\cdot x-20\,{\mbox{ or }}\, \frac{9\cdot x^2}{2}-\frac{81\cdot x}{2}+90=-\left(\frac{5\cdot x^2}{2}-5\cdot x-20\right)& \cr \color{green}{\Leftrightarrow}&9\cdot x^2-81\cdot x+180=5\cdot x^2-10\cdot x-40\,{\mbox{ or }}\, 9\cdot x^2-81\cdot x+180=-5\cdot x^2+10\cdot x+40& \cr \color{green}{\Leftrightarrow}&4\cdot x^2-71\cdot x+220=0\,{\mbox{ or }}\, 14\cdot x^2-91\cdot x+140=0& \cr \color{green}{\Leftrightarrow}&x=\frac{{71 \pm \sqrt{71^2-4\cdot 4\cdot 220}}}{2\cdot 4}\,{\mbox{ or }}\, x=\frac{{91 \pm \sqrt{91^2-4\cdot 14\cdot 140}}}{2\cdot 14}& \cr \color{green}{\mbox{(Same roots)}}&x=\frac{55}{4}\,{\mbox{ or }}\, x=4\,{\mbox{ or }}\, x=\frac{5}{2}& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR,SAMEROOTS)
Equiv		[a=b,abs(a)=abs(b),a=b]	[]		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		[abs(a)=abs(b),a=b or a=-b]	[]		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		[abs(a)=abs(b),a^2=b^2]	[]		1		\[\begin{array}{lll} &\left| a\right| =\left| b\right| & \cr \color{green}{\Leftrightarrow}&a^2=b^2& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR)
Equiv		[x^3=8,x=2]	[]		0		\[\begin{array}{lll} &x^3=8& \cr \color{red}{\Leftarrow}&x=2& \cr \end{array}\]	(EMPTYCHAR,IMPLIEDCHAR)
Equiv		[x^3=8,x=2]	[]	[assumereal]	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		[abs(x-1/2)+abs(x+1/2)=2,abs(x )=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		[a^2=9 and a>0,a=3]	[]		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		[T=2*pi*sqrt(L/g),T^2=4*pi^2*L /g,g=4*pi^2*L/T^2]	[]	[assumepos]	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		[a=b,a^2=b^2]	[]	[assumepos]	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		[a=b,sqrt(a)=sqrt(b)]	[]	[assumepos]	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		[a^2=b^2,a=b]	[]	[assumepos]	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		[a^2=b^2,a=b or a=-b]	[]	[assumepos]	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		[a=b,abs(a)=abs(b)]	[]	[assumepos]	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		[abs(a)=abs(b),a=b]	[]	[assumepos]	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		[abs(a)=abs(b),a=-b]	[]	[assumepos]	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		[abs(a)=abs(b),a=b or a=-b]	[]	[assumepos]	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		[x=abs(-2),x=2]	[]	[assumepos]	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		[abs(a)=abs(b),a^2=b^2]	[]	[assumepos]	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		[x^2=9,x=#pm#3,x=3 or x=-3,x=3 ]	[]	[assumepos]	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		[x^2=9,x=3]	[]	[assumepos]	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		[x^2=2,x=#pm#sqrt(2),x=sqrt(2) or x=-sqrt(2)]	[]	[assumepos]	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		[x^2=2,x=sqrt(2)]	[]	[assumepos]	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		[x^2 = a^2-b,x = sqrt(a^2-b)]	[]	[assumepos]	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		[2*(x-3) = 4*x-3*(x+2),2*x-6=x -6,x=0]	[]		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		[2*(x-3) = 5*x-3*(x+2),2*x-6=2 *x-6,0=0,all]	[]		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		[2*(x-3) = 5*x-3*(x+1),2*x-6=2 *x-3,0=3,{}]	[]		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		[a^2=b^2,a^2-b^2=0,(a-b)*(a+b) =0,a=b or a=-b]	[]		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		[a^3=b^3,a^3-b^3=0,(a-b)*(a^2+ a*b+b^2)=0,(a-b)=0,a=b]	[]		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		[a^3=b^3,a^3-b^3=0,(a-b)*(a^2+ a*b+b^2)=0,(a-b)=0 or (a^2+a*b +b^2)=0, a=b or (a+(1+%i*sqrt( 3))/2*b)*(a+(1-%i*sqrt(3))/2*b )=0, a=b or a=-(1+%i*sqrt(3))/ 2*b or a=-(1-%i*sqrt(3))/2*b]	[]		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		[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		\[\begin{array}{lll} &x^2-x=30& \cr \color{green}{\Leftrightarrow}&x^2-x-30=0& \cr \color{green}{\Leftrightarrow}&\left(x-6\right)\cdot \left(x+5\right)=0& \cr \color{green}{\Leftrightarrow}&x-6=0\,{\mbox{ or }}\, x+5=0& \cr \color{green}{\Leftrightarrow}&x=6\,{\mbox{ or }}\, x=-5& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR)
Equiv		[x^2=2,x^2-2=0,(x-sqrt(2))*(x+ sqrt(2))=0,x=sqrt(2) or x=-sqr t(2)]	[]		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		[x^2=2,x=#pm#sqrt(2),x=sqrt(2) or x=-sqrt(2)]	[]		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		[(2*x-7)^2=(x+1)^2,(2*x-7)^2 - (x+1)^2=0,(2*x-7+x+1)*(2*x-7-x -1)=0,(3*x-6)*(x-8)=0,x=2 or x =8]	[]		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		[x^2-6*x=-9,(x-3)^2=0,x-3=0,x= 3]	[]		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		[(2*x-7)^2=(x+1)^2,sqrt((2*x-7 )^2)=sqrt((x+1)^2),2*x-7=x+1,x =8]	[]		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		[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		\[\begin{array}{lll} &x^2-10\cdot x+9=0& \cr \color{green}{\Leftrightarrow}&{\left(x-5\right)}^2-16=0& \cr \color{green}{\Leftrightarrow}&{\left(x-5\right)}^2=16& \cr \color{green}{\Leftrightarrow}&x-5= \pm 4& \cr \color{green}{\Leftrightarrow}&x-5=4\,{\mbox{ or }}\, x-5=-4& \cr \color{green}{\Leftrightarrow}&x=1\,{\mbox{ or }}\, x=9& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR)
Equiv		[x^2-2*p*x-q=0,x^2-2*p*x=q,x^2 -2*p*x+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		\[\begin{array}{lll} &x^2-2\cdot p\cdot x-q=0& \cr \color{green}{\Leftrightarrow}&x^2-2\cdot p\cdot x=q& \cr \color{green}{\Leftrightarrow}&x^2-2\cdot p\cdot x+p^2=q+p^2& \cr \color{green}{\Leftrightarrow}&{\left(x-p\right)}^2=q+p^2& \cr \color{green}{\Leftrightarrow}&x-p= \pm \sqrt{q+p^2}& \cr \color{green}{\Leftrightarrow}&x-p=\sqrt{q+p^2}\,{\mbox{ or }}\, x-p=-\sqrt{q+p^2}& \cr \color{green}{\Leftrightarrow}&x=p+\sqrt{q+p^2}\,{\mbox{ or }}\, x=p-\sqrt{q+p^2}& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR)
Equiv		[x^2-10*x+7=0,(x-5)^2-18=0,(x- 5)^2=sqrt(18)^2,(x-5)^2-sqrt(1 8)^2=0,(x-5-sqrt(18))*(x-5+sqr t(18))=0,x=5-sqrt(18) or x=5+s qrt(18)]	[]		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		[9*x^2/2-81*x/2+90=5*x^2/2-5*x -20,4*x^2-71*x+220 = 0,x = (71 #pm# 39)/8,x=55/4 nounor x=4]	[]		1		\[\begin{array}{lll} &\frac{9\cdot x^2}{2}-\frac{81\cdot x}{2}+90=\frac{5\cdot x^2}{2}-5\cdot x-20& \cr \color{green}{\Leftrightarrow}&4\cdot x^2-71\cdot x+220=0& \cr \color{green}{\Leftrightarrow}&x=\frac{{71 \pm 39}}{8}& \cr \color{green}{\Leftrightarrow}&x=\frac{55}{4}\,{\mbox{ or }}\, x=4& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR)
Equiv		[x^2+2*a*x = 0, x*(x+2*a)=0, ( x+a-a)*(x+a+a)=0, (x+a)^2-a^2= 0]	[]		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		[x^3-1=0,(x-1)*(x^2+x+1)=0,x=1 ]	[]		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		[x^3-1=0,(x-1)*(x^2+x+1)=0,x=1 or x^2+x+1=0,x=1 or x = -(sqr t(3)*%i+1)/2 or x=(sqrt(3)*%i- 1)/2]	[]		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		[a*x^2+b*x+c=0 or a=0,a^2*x^2+ a*b*x+a*c=0,(a*x)^2+b*(a*x)+a* c=0, (a*x)^2+b*(a*x)+b^2/4-b^2 /4+a*c=0,(a*x+b/2)^2-b^2/4+a*c =0,(a*x+b/2)^2=b^2/4-a*c, a*x+ b/2= #pm#sqrt(b^2/4-a*c),a*x=- b/2+sqrt(b^2/4-a*c) or a*x=-b/ 2-sqrt(b^2/4-a*c), (a=0 or x=( -b+sqrt(b^2-4*a*c))/(2*a)) or (a=0 or x=(-b-sqrt(b^2-4*a*c)) /(2*a)), a^2=0 or x=(-b+sqrt(b ^2-4*a*c))/(2*a) or x=(-b-sqrt (b^2-4*a*c))/(2*a)]	[]		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		[a*x^2+b*x=-c,4*a^2*x^2+4*a*b* x+b^2=b^2-4*a*c,(2*a*x+b)^2=b^ 2-4*a*c,2*a*x+b=#pm#sqrt(b^2-4 *a*c),2*a*x=-b#pm#sqrt(b^2-4*a *c),x=(-b#pm#sqrt(b^2-4*a*c))/ (2*a)]	[]		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		[a*x^2+b*x=-c or a=0,4*a^2*x^2 +4*a*b*x+b^2=b^2-4*a*c,(2*a*x+ b)^2=b^2-4*a*c,2*a*x+b=#pm#sqr t(b^2-4*a*c),2*a*x=-b#pm#sqrt( b^2-4*a*c),x=(-b#pm#sqrt(b^2-4 *a*c))/(2*a) or a=0]	[]		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		[sqrt(3*x+4) = 2+sqrt(x+2), 3* x+4=4+4*sqrt(x+2)+(x+2),x-1=2* sqrt(x+2),x^2-2*x+1 = 4*x+8,x^ 2-6*x-7 = 0,(x-7)*(x+1) = 0,x= 7 or x=-1]	[]		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		[sqrt(3*x+4) = 2+sqrt(x+2), 3* x+4=4+4*sqrt(x+2)+(x+2),x-1=2* sqrt(x+2),x^2-2*x+1 = 4*x+8,x^ 2-6*x-7 = 0,(x-7)*(x+1) = 0,x= 7 or x=-1,x=7]	[]	[assumepos]	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		[x*(x-1)*(x-2)=0,x*(x-1)=0,x*( x-1)*(x-2)=0,x*(x^2-2)=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		[x^2-6*x=-9,x=3]	[]		1		\[\begin{array}{lll} &x^2-6\cdot x=-9& \cr \color{green}{\mbox{(Same roots)}}&x=3& \cr \end{array}\]	(EMPTYCHAR,SAMEROOTS)
Equiv		[x=1 nounor x=-2 nounor x=1,x^ 3-3*x=-2,x=1 nounor x=-2]	[]		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		[9*x^3-24*x^2+13*x=2,x=1/3 nou nor x=2]	[]		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		[(x-2)^43*(x+1/3)^60=0,(3*x+1) ^4*(x-2)^2=0,x=-1/3 nounor x=2 ]	[]		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		[2^x=4,x*log(2)=log(4),x=log(2 ^2)/log(2),x=2*log(2)/log(2),x =2]	[]		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		[x^log(y),stackeq(e^(log(x)*lo g(y))),stackeq(e^(log(y)*log(x ))),stackeq(y^log(x))]	[]		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		[lg(x+17,3)-2=lg(2*x,3),lg(x+1 7,3)-lg(2*x,3)=2,lg((x+17)/(2* x),3)=2,(x+17)/(2*x)=3^2,(x+17 )=18*x,17*x=17,x=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		[a=logbase(9,3),3^a=9,3^a=3^2, a=2]	[]		1		\[\begin{array}{lll} &a=\log_{3}\left(9\right)& \cr \color{green}{\Leftrightarrow}&3^{a}=9& \cr \color{green}{\Leftrightarrow}&3^{a}=3^2& \cr \color{green}{\Leftrightarrow}&a=2& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR)
Equiv		[x=(1+y/n)^n,x^(1/n)=(1+y/n),y /n=x^(1/n)-1,y=n*(x^(1/n)-1)]	[]		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		[a^3=b^3,a^3-b^3=0,(a-b)*(a^2+ a*b+b^2)=0,(a-b)=0,a=b]	[]	[assumereal]	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		[x^3-1=0,(x-1)*(x^2+x+1)=0,x=1 ]	[]	[assumereal]	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		[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		\[\begin{array}{lll}\color{blue}{(\mathbb{R})}&x^4=2& \cr \color{green}{\Leftrightarrow}&x^4-2=0& \cr \color{green}{\Leftrightarrow}&\left(x^2-\sqrt{2}\right)\cdot \left(x^2+\sqrt{2}\right)=0& \cr \color{green}{\Leftrightarrow}\, \color{blue}{(\mathbb{R})}&x^2=\sqrt{2}& \cr \color{green}{\Leftrightarrow}&x= \pm 2^{\frac{1}{4}}& \cr \end{array}\]	(ASSUMEREALVARS, EQUIVCHAR, EQUIVCHAR, EQUIVCHARREAL, EQUIVCHAR)
Equiv		[6*x-12=3*(x-2),6*x-12+3*(x-2) =0,9*x-18=0,x=2]	[]		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		[x^2-6*x+9=0,x^2-6*x=-9,x*(x-6 )=3*-3,x=3 or x-6=-3,x=3]	[]		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		[(x+3)*(2-x)=4,x+3=4 or (2-x)= 4,x=1 or x=-2]	[]		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		[(x-p)*(x-q)=0,x^2-p*x-q*x+p*q =0,1+q-x-p-p*q+p*x+x+q*x-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		\[\begin{array}{lll} &\left(x-p\right)\cdot \left(x-q\right)=0& \cr \color{green}{\Leftrightarrow}&x^2-p\cdot x+\left(-q\right)\cdot x+p\cdot q=0& \cr \color{green}{\Leftrightarrow}&1+q-x-p+\left(-p\right)\cdot q+p\cdot x+x+q\cdot x-x^2=1-p+q& \cr \color{green}{\Leftrightarrow}&\left(1+q-x\right)\cdot \left(1-p+x\right)=1-p+q& \cr \color{green}{\Leftrightarrow}&1+q-x=1-p+q\,{\mbox{ or }}\, 1-p+x=1-p+q& \cr \color{green}{\Leftrightarrow}&x=p\,{\mbox{ or }}\, x=q& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR)
Equiv		[a=b, a^2=a*b, a^2-b^2=a*b-b^2 , (a-b)*(a+b)=b*(a-b), a+b=b, 2*a=a, 1=2]	[]		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		[a=b or a=0, a^2=a*b, a^2-b^2= a*b-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		\[\begin{array}{lll} &a=b\,{\mbox{ or }}\, a=0& \cr \color{green}{\Leftrightarrow}&a^2=a\cdot b& \cr \color{green}{\Leftrightarrow}&a^2-b^2=a\cdot b-b^2& \cr \color{green}{\Leftrightarrow}&\left(a-b\right)\cdot \left(a+b\right)=b\cdot \left(a-b\right)& \cr \color{green}{\Leftrightarrow}&a+b=b\,{\mbox{ or }}\, a-b=0& \cr \color{green}{\Leftrightarrow}&2\cdot a=a\,{\mbox{ or }}\, a=b& \cr \color{green}{\Leftrightarrow}&2=1\,{\mbox{ or }}\, a=0\,{\mbox{ or }}\, a=b& \cr \color{green}{\Leftrightarrow}&a=0\,{\mbox{ or }}\, a=b& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR)
Equiv		[(x^2-4)/(x-2)=0,(x-2)*(x+2)/( x-2)=0,x+2=0,x=-2]	[]		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		[(x^2-4)/(x-2)=0,(x^2-4)=0,(x- 2)*(x+2)=0,x=-2 or x=2]	[]		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		[5*x/(2*x+1)-3/(x+1) = 1,5*x*( x+1)-3*(2*x+1)=(x+1)*(2*x+1),5 *x^2+5*x-6*x-3=2*x^2+3*x+1,3*x ^2-4*x-4=0,(x-2)*(3*x+2)=0,x=2 or x=-2/3]	[]		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		[(x+10)/(x-6)-5= (4*x-40)/(13- x),(x+10-5*(x-6))/(x-6)= (4*x- 40)/(13-x), (4*x-40)/(6-x)= (4 *x-40)/(13-x),6-x= 13-x,6= 13]	[]		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		[(x+5)/(x-7)-5= (4*x-40)/(13-x ),(x+5-5*(x-7))/(x-7)= (4*x-40 )/(13-x), (4*x-40)/(7-x)= (4*x -40)/(13-x),7-x= 13-x,7= 13]	[]		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		[(x+5)/(x-7)-5= (4*x-40)/(13-x ),(x+5-5*(x-7))/(x-7)= (4*x-40 )/(13-x), (4*x-40)/(7-x)= (4*x -40)/(13-x),7-x= 13-x or 4*x-4 0=0,7= 13 or 4*x=40,x=10]	[]		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		[a*x^2+b*x+c=0,a=0 nounand b=0 nounand c=0,a*x^2+b*x+c=0]	[]		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		[a*x^2+b*x+c=A*x^2+B*x+C,a=A n ounand b=B nounand c=C,a*x^2+b *x+c=A*x^2+B*x+C]	[]		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		[(x-1)*(x+4), stackeq(x^2-x+4* x-4),stackeq(x^2+3*x-4)]	[]		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		[(x-1)*(x+4), stackeq(x^2-x+4* x-4),stackeq(x^2+3*x-4)]	[]		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		[x^2-2,stackeq((x-sqrt(2))*(x+ sqrt(2)))]	[]		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		[x^2+4,stackeq((x-2*i)*(x+2*i) )]	[]		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		[x^2+2*a*x,x^2+2*a*x+a^2-a^2,( x+a)^2-a^2]	[]		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		[x^2+2*a*x,stackeq(x^2+2*a*x+a ^2-a^2),stackeq((x+a)^2-a^2)]	[]		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		[(y-z)/(y*z)+(z-x)/(z*x)+(x-y) /(x*y),(x*(y-z)+y*(z-x)+z*(x-y ))/(x*y*z),0]	[]		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		[(y-z)/(y*z)+(z-x)/(z*x)+(x-y) /(x*y),stackeq((x*(y-z)+y*(z-x )+z*(x-y))/(x*y*z)),stackeq(0) ]	[]		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		[2*(a^2*b^2+b^2*c^2+c^2*a^2)-( a^4+b^4+c^4),stackeq(4*a^2*b^2 -(a^4+b^4+c^4+2*a^2*b^2-2*b^2* c^2-2*c^2*a^2)),stackeq((2*a*b )^2-(b^2+a^2-c^2)^2,(2*a*b+b^2 +a^2-c^2)*(2*a*b-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		\[\begin{array}{lll} &2\cdot \left(a^2\cdot b^2+b^2\cdot c^2+c^2\cdot a^2\right)-\left(a^4+b^4+c^4\right)& \cr \color{green}{\checkmark}&=4\cdot a^2\cdot b^2-\left(a^4+b^4+c^4+2\cdot a^2\cdot b^2-2\cdot b^2\cdot c^2-2\cdot c^2\cdot a^2\right)& \cr \color{green}{\checkmark}&={\left(2\cdot a\cdot b\right)}^2-{\left(b^2+a^2-c^2\right)}^2& \cr \color{green}{\checkmark}&=\left({\left(a+b\right)}^2-c^2\right)\cdot \left(c^2-{\left(a-b\right)}^2\right)& \cr \color{green}{\checkmark}&=\left(a+b+c\right)\cdot \left(a+b-c\right)\cdot \left(c+a-b\right)\cdot \left(c-a+b\right)& \cr \end{array}\]	(EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK)
Equiv		[abs(x-1/2)+abs(x+1/2)-2,stack eq(abs(x)-1)]	[]		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		[11*sqrt(abs(x)+1)=25-x,11^2*( abs(x)+1)=(25-x)^2,11^2*abs(x) =(25-x)^2-11^2,11^4*x^2=((25-x )^2-11^2)^2, ((25-x)^2-11^2)^2 -11^4*x^2=0,((25-x)^2-11^2-11^ 2*x)*((25-x)^2-11^2+11^2*x)=0, (x^2-50*x+504-121*x)*(x^2-50*x +504+121*x)=0, (x-168)*(x-3)*( x+8)*(x+63)=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		[1/(x^2+1)=1/((x+%i)*(x-%i)), stackeq(1/(2*%i)*(1/(x-%i)-1/( x+%i)))]	[]		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		[((a-b)/(a^2+a*b))/((a^2-2*a*b +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		\[\begin{array}{lll} &\frac{\frac{a-b}{a^2+a\cdot b}}{\frac{a^2-2\cdot a\cdot b+b^2}{a^4-b^4}}& \cr \color{green}{\checkmark}&=\frac{\left(a-b\right)\cdot \left(a-b\right)\cdot \left(a+b\right)\cdot \left(a^2+b^2\right)}{a\cdot \left(a+b\right)\cdot {\left(a-b\right)}^2}& \cr \color{green}{\checkmark}&=\frac{a^2+b^2}{a}& \cr \color{green}{\checkmark}&=a+\frac{b^2}{a}& \cr \end{array}\]	(EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK)
Equiv		[a^4+4*b^4,stackeq((a^2)^2+4*a ^2*b^2+(2*b^2)^2-4*a^2*b^2),st ackeq((a^2+2*b^2)^2-(2*a*b)^2) ,stackeq((2*b^2-2*a*b+a^2)*(2* b^2+2*a*b+a^2))]	[]		1		\[\begin{array}{lll} &a^4+4\cdot b^4& \cr \color{green}{\checkmark}&={\left(a^2\right)}^2+4\cdot a^2\cdot b^2+{\left(2\cdot b^2\right)}^2-4\cdot a^2\cdot b^2& \cr \color{green}{\checkmark}&={\left(a^2+2\cdot b^2\right)}^2-{\left(2\cdot a\cdot b\right)}^2& \cr \color{green}{\checkmark}&=\left(2\cdot b^2-2\cdot a\cdot b+a^2\right)\cdot \left(2\cdot b^2+2\cdot a\cdot b+a^2\right)& \cr \end{array}\]	(EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK)
Equiv		[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		\[\begin{array}{lll} &\sum_{k=1}^{n+1}{k}& \cr \color{green}{\checkmark}&=\sum_{k=1}^{n}{k}+\left(n+1\right)& \cr \color{green}{\checkmark}&=\frac{n\cdot \left(n+1\right)}{2}+n+1& \cr \color{green}{\checkmark}&=\frac{\left(n+1\right)\cdot \left(n+1+1\right)}{2}& \cr \color{green}{\checkmark}&=\frac{\left(n+1\right)\cdot \left(n+2\right)}{2}& \cr \end{array}\]	(EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK)
Equiv		[log((a-1)^n*product(x_i^(-a), i,1,n)),stackeq(n*log(a-1)-a*s um(log(x_i),i,1,n))]	[]		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		[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		\[\begin{array}{lll} &{{n}\choose{k}}+{{n}\choose{k+1}}& \cr \color{green}{\checkmark}&=\frac{n!}{k!\cdot \left(n-k\right)!}+\frac{n!}{\left(k+1\right)!\cdot \left(n-k-1\right)!}& \cr \color{green}{\checkmark}&=\frac{n!}{k!\cdot \left(n-k\right)\cdot \left(n-k-1\right)!}+\frac{n!}{\left(k+1\right)!\cdot \left(n-k-1\right)!}& \cr \color{green}{\checkmark}&=\frac{n!}{k!\cdot \left(n-k-1\right)!}\cdot \left(\frac{1}{n-k}+\frac{1}{k+1}\right)& \cr \color{green}{\checkmark}&=\frac{n!}{k!\cdot \left(n-k-1\right)!}\cdot \left(\frac{n+1}{\left(n-k\right)\cdot \left(k+1\right)}\right)& \cr \color{green}{\checkmark}&=\frac{\left(n+1\right)\cdot n!}{k!\cdot \left(n-k-1\right)!}\cdot \left(\frac{1}{\left(k+1\right)\cdot \left(n-k\right)}\right)& \cr \color{green}{\checkmark}&=\frac{\left(n+1\right)\cdot n!}{\left(k+1\right)\cdot k!\cdot \left(n-k\right)\cdot \left(n-k-1\right)!}& \cr \color{green}{\checkmark}&=\frac{\left(n+1\right)!}{\left(k+1\right)!}\cdot \left(\frac{1}{\left(n-k\right)\cdot \left(n-k-1\right)!}\right)& \cr \color{green}{\checkmark}&=\frac{\left(n+1\right)!}{\left(k+1\right)!\cdot \left(n-k\right)!}& \cr \color{green}{\checkmark}&={{n+1}\choose{k+1}}& \cr \end{array}\]	(EMPTYCHAR, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK, CHECKMARK)
Equiv		[(x-1)^2=(x-1)*(x-1), stackeq( x^2-2*x+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		[(x-1)^2=(x-1)*(x-1), stackeq( x^2-2*x+2)]	[]		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		[(x-2)^2=(x-1)*(x-1), stackeq( x^2-2*x+1)]	[]		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		[4^((n+1)+1)-1= 4*4^(n+1)-1,st ackeq(4*(4^(n+1)-1)+3)]	[]		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		[2*x+3*y=6 and 4*x+9*y=15,2*x+ 3*y=6 and -2*x=-3,3+3*y=6 and 2*x=3,y=1 and x=3/2]	[]		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		[2*x+3*y=6 and 4*x+9*y=15,2*x+ 3*y=6 and -2*x=-3,3+3*y=6 and 2*x=3,y=1 and x=3]	[]		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		[x^2+y^2=8 and x=y, 2*x^2=8 an d 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		\[\begin{array}{lll} &\left\{\begin{array}{l}x^2+y^2=8\cr x=y\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}2\cdot x^2=8\cr y=x\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x^2=4\cr y=x\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x= \pm 2\cr y=x\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&x=2\,{\mbox{ and }}\, y=x\,{\mbox{ or }}\, x=-2\,{\mbox{ and }}\, y=x& \cr \color{green}{\Leftrightarrow}&x=2\,{\mbox{ and }}\, y=2\,{\mbox{ or }}\, x=-2\,{\mbox{ and }}\, y=-2& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR)
Equiv		[x^2+y^2=5 and x*y=2, x^2+y^2- 5=0 and x*y-2=0, x^2-2*x*y+y^2 -1=0 and x^2+2*x*y+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 an d 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		\[\begin{array}{lll} &\left\{\begin{array}{l}x^2+y^2=5\cr x\cdot y=2\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x^2+y^2-5=0\cr x\cdot y-2=0\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x^2-2\cdot x\cdot y+y^2-1=0\cr x^2+2\cdot x\cdot y+y^2-9=0\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}{\left(x-y\right)}^2-1=0\cr {\left(x+y\right)}^2-3^2=0\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&x-y=1\,{\mbox{ and }}\, x+y=3\,{\mbox{ or }}\, x-y=-1\,{\mbox{ and }}\, x+y=3\,{\mbox{ or }}\, x-y=1\,{\mbox{ and }}\, x+y=-3\,{\mbox{ or }}\, x-y=-1\,{\mbox{ and }}\, x+y=-3& \cr \color{green}{\Leftrightarrow}&x=1\,{\mbox{ and }}\, y=2\,{\mbox{ or }}\, x=2\,{\mbox{ and }}\, y=1\,{\mbox{ or }}\, x=-2\,{\mbox{ and }}\, y=-1\,{\mbox{ or }}\, x=-1\,{\mbox{ and }}\, y=-2& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR)
Equiv		[4*x^2+7*x*y+4*y^2=4 and y=x-4 , 4*x^2+7*x*(x-4)+4*(x-4)^2-4= 0 and y=x-4, 15*x^2-60*x+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		\[\begin{array}{lll} &\left\{\begin{array}{l}4\cdot x^2+7\cdot x\cdot y+4\cdot y^2=4\cr y=x-4\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}4\cdot x^2+7\cdot x\cdot \left(x-4\right)+4\cdot {\left(x-4\right)}^2-4=0\cr y=x-4\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}15\cdot x^2-60\cdot x+60=0\cr y=x-4\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}{\left(x-2\right)}^2=0\cr y=x-4\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x=2\cr y=x-4\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}x=2\cr y=-2\cr \end{array}\right.& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR)
Equiv		[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		\[\begin{array}{lll} &\left\{\begin{array}{l}a^2=b\cr a^2=1\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}b=a^2\cr a=1\,{\mbox{ or }}\, a=-1\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&b=1\,{\mbox{ and }}\, a=1\,{\mbox{ or }}\, b=1\,{\mbox{ and }}\, a=-1& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR)
Equiv		[a^2=b and x=1, b=a^2 and x=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		[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		\[\begin{array}{lll}\color{blue}{(\mathbb{R})}&\left\{\begin{array}{l}a^2=b\cr b^2=a\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}b=a^2\cr a^4=a\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}b=a^2\cr a^4-a=0\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}b=a^2\cr a\cdot \left(a-1\right)\cdot \left(a^2+a+1\right)=0\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&\left\{\begin{array}{l}b=a^2\cr a=0\,{\mbox{ or }}\, a=1\,{\mbox{ or }}\, a^2+a+1=0\cr \end{array}\right.& \cr \color{green}{\Leftrightarrow}&b=0\,{\mbox{ and }}\, a=0\,{\mbox{ or }}\, b=1\,{\mbox{ and }}\, a=1& \cr \end{array}\]	(ASSUMEREALVARS, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR)
Equiv		[2*x^3-9*x^2+10*x-3,stacklet(x ,1),2*1^3-9*1^2+10*1-3,stackeq (0),"So",2*x^3-9*x^2 +10*x-3,stackeq((x-1)*(2*x^2-7 *x+3)),stackeq((x-1)*(2*x-1)*( x-3))]	[]		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		[2*x^2+x>=6, 2*x^2+x-6>= 0, (2*x-3)*(x+2)>= 0,((2*x- 3)>=0 and (x+2)>=0) or ( (2*x-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		\[\begin{array}{lll} &2\cdot x^2+x\geq 6& \cr \color{green}{\Leftrightarrow}&2\cdot x^2+x-6\geq 0& \cr \color{green}{\Leftrightarrow}&\left(2\cdot x-3\right)\cdot \left(x+2\right)\geq 0& \cr \color{green}{\Leftrightarrow}&2\cdot x-3\geq 0\,{\mbox{ and }}\, x+2\geq 0\,{\mbox{ or }}\, 2\cdot x-3\leq 0\,{\mbox{ and }}\, x+2\leq 0& \cr \color{green}{\Leftrightarrow}&x\geq \frac{3}{2}\,{\mbox{ and }}\, x\geq -2\,{\mbox{ or }}\, x\leq \frac{3}{2}\,{\mbox{ and }}\, x\leq -2& \cr \color{green}{\Leftrightarrow}&x\geq \frac{3}{2}\,{\mbox{ or }}\, x\leq -2& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR)
Equiv		[2*x^2+x>=6, 2*x^2+x-6>= 0, (2*x-3)*(x+2)>= 0,((2*x- 3)>=0 and (x+2)>=0) or ( (2*x-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		\[\begin{array}{lll} &2\cdot x^2+x\geq 6& \cr \color{green}{\Leftrightarrow}&2\cdot x^2+x-6\geq 0& \cr \color{green}{\Leftrightarrow}&\left(2\cdot x-3\right)\cdot \left(x+2\right)\geq 0& \cr \color{green}{\Leftrightarrow}&2\cdot x-3\geq 0\,{\mbox{ and }}\, x+2\geq 0\,{\mbox{ or }}\, 2\cdot x-3\leq 0\,{\mbox{ and }}\, x+2\leq 0& \cr \color{green}{\Leftrightarrow}&x\geq \frac{3}{2}\,{\mbox{ and }}\, x\geq -2\,{\mbox{ or }}\, x\leq \frac{3}{2}\,{\mbox{ and }}\, x\leq -2& \cr \color{green}{\Leftrightarrow}&x\geq \frac{3}{2}\,{\mbox{ or }}\, x\leq -2& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR)
Equiv		[2*x^2+x>=6, 2*x^2+x-6>= 0, (2*x-3)*(x+2)>= 0,((2*x- 3)>=0 and (x+2)>=0) or ( (2*x-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		\[\begin{array}{lll} &2\cdot x^2+x\geq 6& \cr \color{green}{\Leftrightarrow}&2\cdot x^2+x-6\geq 0& \cr \color{green}{\Leftrightarrow}&\left(2\cdot x-3\right)\cdot \left(x+2\right)\geq 0& \cr \color{green}{\Leftrightarrow}&2\cdot x-3\geq 0\,{\mbox{ and }}\, x+2\geq 0\,{\mbox{ or }}\, 2\cdot x-3\leq 0\,{\mbox{ and }}\, x+2\leq 0& \cr \color{green}{\Leftrightarrow}&x\geq \frac{3}{2}\,{\mbox{ and }}\, x\geq -2\,{\mbox{ or }}\, x\leq \frac{3}{2}\,{\mbox{ and }}\, x\leq -2& \cr \color{red}{?}&x\geq \frac{3}{2}\,{\mbox{ or }}\, x\leq 2& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR,QMCHAR)
Equiv		[x^2>=9 and x>3, x^2-9&g t;=0 and x>3, (x>=3 or x <=-3) and x>3, x>3]	[]		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		[-x^2+a*x+a-3<0, a-3<x^2 -a*x, a-3<(x-a/2)^2-a^2/4, a^2/4+a-3<(x-a/2)^2, a^2+4* a-12<4*(x-a/2)^2, (a-2)*(a+ 6)<4*(x-a/2)^2, "This inequality is required to be t rue for all x.", "So it must be true when the righ t hand side takes its minimum value.", "This happe ns 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&l t;a and a<2) or false, (-6& lt;a and a<2)]	[]		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		[x-2>0 and x*(x-2)<15,x& gt;2 and x^2-2*x-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 an d (x<5 and x>-3),x>2 and x<5]	[]		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		[x-2>0 and x*(x-2)<15,x& gt;2 and x^2-2*x-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 an d (x<5 and x>-3),x>2 and x<5]	[]		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		[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- 4*a+4-4*a >=0,a^2-8*a+4> =0,(a-4)^2-16+4>=0,(a-4)^2& gt;=12,a-4>=sqrt(12) or a-4 <= -sqrt(12),"Ignoring the negative solution.", a>=sqrt(12)+4,"Using e xternal domain information tha t a is an integer.",a> =8]	[]		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		[x^2#1,x^2-1#0,(x-1)*(x+1)#0,x <-1 nounor (-1<x nounand x<1) nounor x>1]	[]		1		\[\begin{array}{lll} &x^2\neq 1& \cr \color{green}{\Leftrightarrow}&x^2-1\neq 0& \cr \color{green}{\Leftrightarrow}&\left(x-1\right)\cdot \left(x+1\right)\neq 0& \cr \color{green}{\Leftrightarrow}&x < -1\,{\mbox{ or }}\, -1 < x\,{\mbox{ and }}\, x < 1\,{\mbox{ or }}\, x > 1& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR)
Equiv		["Set P(n) be the stateme nt that",sum(k^2,k,1,n) = n*(n+1)*(2*n+1)/6, "Then P(1) is the statement", 1^2 = 1*(1+1)*(2*1+1)/6, 1 = 1 , "So P(1) holds. Now as sume P(n) is true.",sum(k ^2,k,1,n) = n*(n+1)*(2*n+1)/6, sum(k^2,k,1,n) +(n+1)^2= n*(n+ 1)*(2*n+1)/6 +(n+1)^2,sum(k^2, k,1,n+1)= (n+1)*(n*(2*n+1) +6* (n+1))/6,sum(k^2,k,1,n+1)= (n+ 1)*(2*n^2+7*n+6)/6,sum(k^2,k,1 ,n+1)= (n+1)*(n+1+1)*(2*(n+1)+ 1)/6]	[]		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		[(n+1)^2+sum(k^2,k,1,n) = (n+1 )^2+(n*(n+1)*(2*n+1))/6, sum(k ^2,k,1,n+1) = ((n+1)*(n*(2*n+1 )+6*(n+1)))/6, sum(k^2,k,1,n+1 ) = ((n+1)*(2*n^2+7*n+6))/6, s um(k^2,k,1,n+1) = ((n+1)*(n+2) *(2*(n+1)+1))/6]	[]		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		[conjugate(a)*conjugate(b),sta cklet(a,x+i*y),stacklet(b,r+i* s),stackeq(conjugate(x+i*y)*co njugate(r+i*s)),stackeq((x-i*y )*(r-i*s)),stackeq((x*r-y*s)-i *(y*r+x*s)),stackeq(conjugate( (x*r-y*s)+i*(y*r+x*s))),stacke q(conjugate((x+i*y)*(r+i*s))), stacklet(x+i*y,a),stacklet(r+i *s,b),stackeq(conjugate(a*b))]	[]		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		[nounint(x*e^x,x,-inf,0),nounl imit(nounint(x*e^x,x,t,0),t,-i nf),nounlimit(e^t-t*e^t-1,t,-i nf),nounlimit(e^t,t,-inf)+noun limit(-t*e^t,t,-inf)+nounlimit (-1,t,-inf),-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		[noundiff(x^2,x),stackeq(nounl imit(((x+h)^2-x^2)/h,h,0)),sta ckeq(nounlimit(2*x+h,h,0)),sta ckeq(2*x)]	[]		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		[-12+3*noundiff(y(x),x)+8-8*no undiff(y(x),x)=0,-5*noundiff(y (x),x)=4,noundiff(y(x),x)=-4/5 ]	[]	[calculus]	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		[x^2+1,x^3/3+x,x^2+1,x^3/3+x+c ]	[]	[calculus]	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		[3*x^(3/2)-2/x,(9*sqrt(x))/2+2 /x^2,3*x^(3/2)-2/x+c]	[]	[calculus]	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		[x^2+1,stackeq(x^3/3+x),stacke q(x^2+1),stackeq(x^3/3+x+c)]	[]	[calculus]	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		[diff(x^2*sin(x),x),stackeq(x^ 2*diff(sin(x),x)+diff(x^2,x)*s in(x)),stackeq(x^2*cos(x)+2*x* sin(x))]	[]	[calculus]	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		[y(x)*cos(x)+y(x)^2 = 6*x,cos( x)*diff(y(x),x)+2*y(x)*diff(y( x),x)-y(x)*sin(x) = 6,(cos(x)+ 2*y(x))*diff(y(x),x) = y(x)*si n(x)+6,diff(y(x),x) = (y(x)*si n(x)+6)/(cos(x)+2*y(x))]	[]	[calculus]	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		[nounint(s^2+1,s),stackeq(s^3/ 3+s+c)]	[]	[calculus]	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		[nounint(x^3*log(x),x),x^4/4*l og(x)-1/4*nounint(x^3,x),x^4/4 *log(x)-x^4/16]	[]	[calculus]	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		[nounint(x^3*log(x),x),x^4/4*l og(x)-1/4*nounint(x^3,x),x^4/4 *log(x)-x^4/16+c]	[]	[calculus]	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		[noundiff(y,x)-2/x*y=x^3*sin(3 *x),1/x^2*noundiff(y,x)-2/x^3* y=x*sin(3*x),noundiff(y/x^2,x) =x*sin(3*x),y/x^2 = nounint(x* sin(3*x),x),y/x^2=(sin(3*x)-3* x*cos(3*x))/9+c]	[]	[calculus]	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))

EquivFirst

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
EquivFirst		x	[x^2=4,x=2 or x=-2]		-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		[x^2=4,x=2 or x=-2]	x		-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		[1/0]	[x^2=4,x=2 or x=-2]		-1			ATEquivFirst_STACKERROR_SAns.
EquivFirst		[x^2=4,x=2 or x=-2]	[1/0]		-1			ATEquivFirst_STACKERROR_TAns.
EquivFirst		[x^2=4,x=2 or x=-2]	[x^2=4,x=2 or x=-2]		1		\[\begin{array}{lll} &x^2=4& \cr \color{green}{\Leftrightarrow}&x=2\,{\mbox{ or }}\, x=-2& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR)
EquivFirst		[x^2=9,x=3 or x=-3]	[x^2=4,x=2 or x=-2]		0		The first line in your argument must be "\(x^2=4\)".	ATEquivFirst_SA_wrong_start
EquivFirst		[x^2=4,x=2]	[x^2=4,x=2 or x=-2]		0		\[\begin{array}{lll} &x^2=4& \cr \color{red}{\Leftarrow}&x=2& \cr \end{array}\]	(EMPTYCHAR,IMPLIEDCHAR)
EquivFirst		[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		\[\begin{array}{lll} &x^2=4& \cr \color{green}{\Leftrightarrow}&x^2-4=0& \cr \color{green}{\Leftrightarrow}&\left(x-2\right)\cdot \left(x+2\right)=0& \cr \color{green}{\Leftrightarrow}&x=2\,{\mbox{ or }}\, x=-2& \cr \end{array}\]	(EMPTYCHAR, EQUIVCHAR, EQUIVCHAR, EQUIVCHAR)
EquivFirst		[x^2=4,x= #pm#2, x=2 or x=-2]	[x^2=4,x=2 or x=-2]		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		[x^2-6*x+9=0,x=3]	[x^2-6*x+9=0,x=3]		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		[x^2=4,x=2]	[x^2=4,x=2]	[assumepos]	1		\[\begin{array}{lll}\color{blue}{\mbox{Assume +ve vars}}&x^2=4& \cr \color{green}{\Leftrightarrow}&x=2& \cr \end{array}\]	(ASSUMEPOSVARS, EQUIVCHAR)

SingleFrac

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
SingleFrac		1/0	1/n		-1			ATSingleFrac_STACKERROR_SAns.
SingleFrac		0	1/0		-1			ATSingleFrac_STACKERROR_TAns.
SingleFrac		x=3	2		0		Your answer should be an expression, not an equation, inequality, list, set or matrix.	ATSingleFrac_SA_not_expression.
SingleFrac		3	3		1
SingleFrac		3	2		0		Your answer is not algebraically equivalent to the correct answer. You must have done something wrong.	ATSingleFrac_ret_exp.
SingleFrac		1/m	1/n		0		Your answer is not algebraically equivalent to the correct answer. You must have done something wrong.	ATSingleFrac_true. ATSingleFrac_ret_exp.
SingleFrac		1/n	1/n		1			ATSingleFrac_true.
SingleFrac		a+1/2	(2*a+1)/2		0		Your answer needs to be a single fraction of the form \( {a}\over{b} \).	ATSingleFrac_part.
SingleFrac		a+1/2	(2*a+1)/2		0		Your answer needs to be a single fraction of the form \( {a}\over{b} \).	ATSingleFrac_part.
SingleFrac		4/(x^2+2*x-24)+2/(x^2+4*x-12)	(6*x-16)/(x^3-28*x+48)		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		2*(1/n)	2/n		0		Your answer needs to be a single fraction of the form \( {a}\over{b} \).	ATSingleFrac_part.
SingleFrac		2/n	2/n		1			ATSingleFrac_true.
	Simple Mistakes
SingleFrac		2/(n+1)	1/(n+1)		0		Your answer is not algebraically equivalent to the correct answer. You must have done something wrong.	ATSingleFrac_true. ATSingleFrac_ret_exp.
SingleFrac		(2*n+1)/(n+2)	1/n		0		Your answer is not algebraically equivalent to the correct answer. You must have done something wrong.	ATSingleFrac_true. ATSingleFrac_ret_exp.
SingleFrac		(2*n)/(n*(n+2))	(2*n)/(n*(n+3))		0		Your answer is not algebraically equivalent to the correct answer. You must have done something wrong.	ATSingleFrac_true. ATSingleFrac_ret_exp.
SingleFrac		(x-1)/(x^2-1)	1/(x+1)		1			ATSingleFrac_true.
	Fractions within fractions
SingleFrac		(1/2)/(3/4)	2/3		0		Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction.	ATSingleFrac_div.
SingleFrac		(x-2)/4/(2/x^2)	(x-2)*x^2/8		0		Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction.	ATSingleFrac_div.
SingleFrac		1/(1-1/x)	x/(x-1)		0		Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction.	ATSingleFrac_div.
SingleFrac		(1+1/a)/a	(1+a)/a^2		0		Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction.	ATSingleFrac_div.
SingleFrac		a/(1+1/a)	a^2/(1+a)		0		Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction.	ATSingleFrac_div.
SingleFrac		(1+2*b/a)/c	(a+2*b)/(a*c)		0		Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction.	ATSingleFrac_div.
SingleFrac		c/(1+2*b/a)	a*c/(a+2*b)		0		Your answer contains fractions within fractions. You need to clear these and write your answer as a single fraction.	ATSingleFrac_div.
SingleFrac		a*c/(a+2*b)	a*c/(a+2*b)		1			ATSingleFrac_true.
	Negative cases
SingleFrac		-1/2	-1/2		1			ATSingleFrac_true.
SingleFrac		-1/2	-1/3		0		Your answer is not algebraically equivalent to the correct answer. You must have done something wrong.	ATSingleFrac_true. ATSingleFrac_ret_exp.
SingleFrac		-(1/2)	-1/2		1			ATSingleFrac_true.
SingleFrac		-a/b	-a/b		1			ATSingleFrac_true.
SingleFrac		(-a)/b	-a/b		1			ATSingleFrac_true.
SingleFrac		a/(-b)	-a/b		1			ATSingleFrac_true.
SingleFrac		-(a/b)	-a/b		1			ATSingleFrac_true.
SingleFrac		-(1/(n-1))	1/(1-n)		1			ATSingleFrac_true.
SingleFrac		a/(-1-1/a)	-a^2/(1+a)		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		((sqrt(5))^3 +6)/15	((sqrt(5))^3 +6)/15		1			ATSingleFrac_true.
SingleFrac		1/(1-sqrt(2))	1/(1-sqrt(2))		1			ATSingleFrac_true.
SingleFrac		((sqrt(5))^3+6)/15	((sqrt(5))^3+6)/15		1			ATSingleFrac_true.
SingleFrac		(5^(3/2)+6)/15	((sqrt(5))^3+6)/15		1			ATSingleFrac_true.

PartFrac

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

Diff

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
Diff		1/0	3*x^2		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test.	STACKERROR_OPTION.
Diff		0	1/0	(x	-1	TEST_FAILED	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		1/0	3*x^2	x	-1			ATDiff_STACKERROR_SAns.
Diff		0	1/0	x	-1			ATDiff_STACKERROR_TAns.
Diff		0	0	1/0	-1			ATDiff_STACKERROR_Opt.
	Basic tests
Diff		3*x^2	3*x^2	x	1			ATDiff_true.
Diff		3*X^2	3*x^2	x	0			ATDiff_var_SB_notSA.
Diff		x^4/4	3*x^2	x	0		It looks like you have integrated instead!	ATDiff_int.
Diff		x^4/4+1	3*x^2	x	0		It looks like you have integrated instead!	ATDiff_int.
Diff		x^4/4+c	3*x^2	x	0		It looks like you have integrated instead!	ATDiff_int.
Diff		y=x^4/4	x^4/4	x	0		Your answer should be an expression, not an equation, inequality, list, set or matrix.	ATDiff_SA_not_expression.
Diff		x^4/4	y=x^4/4	x	0
Diff		y=x^4/4	y=x^4/4	x	0		Your answer should be an expression, not an equation, inequality, list, set or matrix.	ATDiff_SA_not_expression.
Diff		6000*(x-a)^5999	6000*(x-a)^5999	x	1			ATDiff_true.
Diff		5999*(x-a)^5999	6000*(x-a)^5999	x	0
	Variable mismatch tests
Diff		y^2-2*y+1	x^2-2*x+1	x	0			ATDiff_var_SB_notSA.
Diff		x^2-2*x+1	y^2-2*y+1	x	0			ATDiff_var_SA_notSB.
Diff		y^2+2*y+1	x^2-2*x+1	z	0			ATDiff_var_notSASB_SAnceSB.
Diff		x^4/4	3*x^2	y	0
	Edge cases
Diff		e^x+c	e^x	x	0		It looks like you have integrated instead!	ATDiff_int.
Diff		e^x+2	e^x	x	0		It looks like you have integrated instead!	ATDiff_int.
Diff		n*x^n	n*x^(n-1)	x	-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. TIMEDOUT	ATDiff_STACKERROR_SAns.
Diff		n*x^n	(assume(n>0), n*x^(n-1))	x	0

Int

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
Int		1/0	1		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test.	STACKERROR_OPTION.
Int		1/0	1	x	-1			ATInt_STACKERROR_SAns.
Int		1	1/0	x	-1			ATInt_STACKERROR_TAns.
Int		0	0	1/0	-1			ATInt_STACKERROR_Opt.
Int		0	0	[x,1/0]	-1			ATInt_STACKERROR_Opt.
Int		0	0	[x,NOCONST,1/0]	-1			ATInt_STACKERROR_Opt.
	Basic tests
Int		x^3/3	x^3/3	x	0		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int		x^3/3+1	x^3/3	x	0		You need to add a constant of integration. This should be an arbitrary constant, not a number.	ATInt_const_int.
Int		x^3/3+c	x^3/3	x	1			ATInt_true.
Int		x^3/3+c+1	x^3/3	x	1			ATInt_true.
Int		x^3/3+3*c	x^3/3	x	1			ATInt_true.
Int		(x^3+c)/3	x^3/3	x	1			ATInt_true.
Int		x^3/3-c	x^3/3	x	1			ATInt_true.
Int		x^3/3+c+k	x^3/3	x	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		x^3/3+c^2	x^3/3	x	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		x^3/3*c	x^3/3	x	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		X^3/3+c	x^3/3	x	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		sin(2*x)	x^3/3	x	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		x^2/2-2*x+2+c	(x-2)^2/2	x	1			ATInt_true.
Int		(t-1)^5/5+c	(t-1)^5/5	t	1			ATInt_true.
Int		(v-1)^5/5+c	(v-1)^5/5	v	1			ATInt_true.
Int		cos(2*x)/2+1+c	cos(2*x)/2	x	1			ATInt_true.
Int		(x-a)^6001/6001+c	(x-a)^6001/6001	x	1			ATInt_true.
Int		(x-a)^6001/6001	(x-a)^6001/6001	x	0		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int		6000*(x-a)^5999	(x-a)^6001/6001	x	0		It looks like you have differentiated instead!	ATInt_diff.
Int		4*%e^(4*x)/(%e^(4*x)+1)	log(%e^(4*x)+1)+c	x	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		x^3/3+c	x^3/3+c	x	1			ATInt_true.
Int		x^2/2-2*x+2+c	(x-2)^2/2+k	x	1			ATInt_true.
	The teacher condones lack of constant, or numerical constant
Int		x^3/3	x^3/3	[x,NOCONST]	1			ATInt_const_condone.
Int		x^3/3+c	x^3/3	[x,NOCONST]	1			ATInt_true.
Int		x^2/2-2*x+2	(x-2)^2/2+k	[x,NOCONST]	1			ATInt_const_condone.
Int		x^3/3+1	x^3/3	[x,NOCONST]	1			ATInt_const_int_condone.
Int		x^3/3+c^2	x^3/3	[x,NOCONST]	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		n*x^n	n*x^(n-1)	x	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		n*x^n	(assume(n>0), n*x^(n-1))	x	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		exp(x)+c	exp(x)	x	1			ATInt_true.
Int		exp(x)	exp(x)	x	0		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int		exp(x)	exp(x)	[x,NOCONST]	1			ATInt_const_condone.
	Student differentiates by mistake
Int		2*x	x^3/3	x	0		It looks like you have differentiated instead!	ATInt_diff.
Int		2*x+c	x^3/3	x	0		It looks like you have differentiated instead!	ATInt_diff.
	Sloppy logs (teacher ignores abs(x) )
Int		ln(x)	ln(x)	x	0		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int		ln(x)	ln(x)	[x,NOCONST]	1			ATInt_const_condone.
Int		ln(x)+c	ln(x)+c	x	1			ATInt_true_equiv.
Int		ln(k*x)	ln(x)+c	x	1			ATInt_true_equiv.
	Fussy logs (teacher uses abs(x) )
Int		ln(x)	ln(abs(x))+c	x	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		ln(x)+c	ln(abs(x))+c	x	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		ln(x)	ln(abs(x))+c	[x, NOCONST]	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		ln(abs(x))	ln(abs(x))+c	x	0		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int		ln(abs(x))+c	ln(abs(x))+c	x	1			ATInt_true_equiv.
Int		ln(k*x)	ln(abs(x))+c	x	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		ln(k*abs(x))	ln(abs(x))+c	x	1			ATInt_true_equiv.
Int		ln(abs(k*x))	ln(abs(x))+c	x	1			ATInt_true_equiv.
	Teacher uses ln(k*abs(x))
Int		ln(x)	ln(k*abs(x))	x	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		ln(x)+c	ln(k*abs(x))	x	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		ln(abs(x))	ln(k*abs(x))	x	0		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int		ln(abs(x))+c	ln(k*abs(x))	x	1			ATInt_true_equiv.
Int		ln(k*x)	ln(k*abs(x))	x	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		ln(k*abs(x))	ln(k*abs(x))	x	1			ATInt_true_equiv.
	Other logs
Int		ln(x)+ln(a)	ln(k*abs(x+a))	x	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		log(x)^2-2*log(c)*log(x)+k	ln(c/x)^2	x	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		log(x)^2-2*log(c)*log(x)+k	ln(abs(c/x))^2	x	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		c-(log(2)-log(x))^2/2	-1/2*log(2/x)^2	x	1			ATInt_true_equiv.
Int	!	ln(abs(x+3))/2+c	ln(abs(2*x+6))/2+c	x	-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		log(abs(x-3))+log(abs(x+3))	log(abs(x-3))+log(abs(x+3))	x	0		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int		log(abs(x-3))+log(abs(x+3))+c	log(abs(x-3))+log(abs(x+3))	x	1			ATInt_true_equiv.
Int		log(abs(x-3))+log(abs(x+3))	log(x-3)+log(x+3)	x	0		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int		log(abs(x-3))+log(abs(x+3))+c	log(x-3)+log(x+3)	x	1			ATInt_true_equiv.
Int		log(x-3)+log(x+3)	log(x-3)+log(x+3)	x	0		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int		log(x-3)+log(x+3)+c	log(x-3)+log(x+3)	x	1			ATInt_true_equiv.
Int		log(x-3)+log(x+3)	log(abs(x-3))+log(abs(x+3))	x	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		log(x-3)+log(x+3)+c	log(abs(x-3))+log(abs(x+3))	x	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		log(abs((x-3)*(x+3)))+c	log(abs(x-3))+log(abs(x+3))	x	1			ATInt_true_equiv.
Int		log(abs((x^2-9)))+c	log(abs(x-3))+log(abs(x+3))	x	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		2*log(abs(x-2))-log(abs(x+2))+ (x^2+4*x)/2	-log(abs(x+2))+2*log(abs(x-2)) +(x^2+4*x)/2+c	x	0		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int		-log(abs(x+2))+2*log(abs(x-2)) +(x^2+4*x)/2+c	-log(abs(x+2))+2*log(abs(x-2)) +(x^2+4*x)/2+c	x	1			ATInt_true_equiv.
Int		-log(abs(x+2))+2*log(abs(x-2)) +(x^2+4*x)/2+c	-log((x+2))+2*log((x-2))+(x^2+ 4*x)/2	x	1			ATInt_true_equiv.
	Inconsistent log(abs())
Int		log(abs(x-3))+log((x+3))+c	log(x-3)+log(x+3)	x	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		log((v-3))+log(abs(v+3))+c	log(v-3)+log(v+3)	v	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		log((x-3))+log(abs(x+3))	log(x-3)+log(x+3)	x	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		2*log((x-2))-log(abs(x+2))+(x^ 2+4*x)/2	-log(abs(x+2))+2*log(abs(x-2)) +(x^2+4*x)/2	x	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		2*(sqrt(t)-5)-10*log((sqrt(t)- 5))+c	2*(sqrt(t)-5)-10*log((sqrt(t)- 5))+c	t	1			ATInt_true_equiv.
Int		2*(sqrt(t))-10*log((sqrt(t)-5) )+c	2*(sqrt(t)-5)-10*log((sqrt(t)- 5))+c	t	1			ATInt_true_differentconst.
Int		2*(sqrt(t)-5)-10*log((sqrt(t)- 5))+c	2*(sqrt(t)-5)-10*log(abs(sqrt( t)-5))+c	t	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		2*(sqrt(t))-10*log(abs(sqrt(t) -5))+c	2*(sqrt(t)-5)-10*log(abs(sqrt( t)-5))+c	t	1			ATInt_true_differentconst.
	Trig
Int		2*sin(x)*cos(x)	sin(2*x)+c	x	0		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int		2*sin(x)*cos(x)+k	sin(2*x)+c	x	1			ATInt_true.
Int		-2*cos(3*x)/3-3*cos(2*x)/2	-2*cos(3*x)/3-3*cos(2*x)/2+c	x	0		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int		-2*cos(3*x)/3-3*cos(2*x)/2+1	-2*cos(3*x)/3-3*cos(2*x)/2+c	x	0		You need to add a constant of integration. This should be an arbitrary constant, not a number.	ATInt_const_int.
Int		-2*cos(3*x)/3-3*cos(2*x)/2+c	-2*cos(3*x)/3-3*cos(2*x)/2+c	x	1			ATInt_true.
Int		(tan(2*t)-2*t)/2	-(t*sin(4*t)^2-sin(4*t)+t*cos( 4*t)^2+2*t*cos(4*t)+t)/(sin(4* t)^2+cos(4*t)^2+2*cos(4*t)+1)	t	0		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int		(tan(2*t)-2*t)/2+1	-(t*sin(4*t)^2-sin(4*t)+t*cos( 4*t)^2+2*t*cos(4*t)+t)/(sin(4* t)^2+cos(4*t)^2+2*cos(4*t)+1)	t	0		You need to add a constant of integration. This should be an arbitrary constant, not a number.	ATInt_const_int.
Int		(tan(2*t)-2*t)/2+c	-(t*sin(4*t)^2-sin(4*t)+t*cos( 4*t)^2+2*t*cos(4*t)+t)/(sin(4* t)^2+cos(4*t)^2+2*cos(4*t)+1)	t	1			ATInt_true.
Int		tan(x)-x+c	tan(x)-x	x	1			ATInt_true.
	Note the difference in feedback here, generated by the options.
Int		((5*%e^7*x-%e^7)*%e^(5*x))	((5*%e^7*x-%e^7)*%e^(5*x))/25+ c	x	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		((5*%e^7*x-%e^7)*%e^(5*x))	((5*%e^7*x-%e^7)*%e^(5*x))/25+ c	[x,x*%e^(5*x+7) ]	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		log(x-3)/6-log(x+3)/6+c	log(x-3)/6-log(x+3)/6	x	1			ATInt_true_equiv.
Int		asinh(x)	ln(x+sqrt(x^2+1))	x	0		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int		asinh(x)+c	ln(x+sqrt(x^2+1))	x	1			ATInt_true.
Int		-acoth(x/3)/3	log(x-3)/6-log(x+3)/6	x	0		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int		-acoth(x/3)/3	log(x-3)/6-log(x+3)/6	[x, NOCONST]	1			ATInt_true.
Int		-acoth(x/3)/3+c	log(x-3)/6-log(x+3)/6	x	1			ATInt_true.
Int		-acoth(x/3)/3+c	log(abs(x-3))/6-log(abs(x+3))/ 6	x	1			ATInt_true.
Int		log(x-a)/(2*a)-log(x+a)/(2*a)+ c	log(x-a)/(2*a)-log(x+a)/(2*a)	x	1			ATInt_true_equiv.
Int		-acoth(x/a)/a+c	log(x-a)/(2*a)-log(x+a)/(2*a)	x	1			ATInt_true.
Int		-acoth(x/a)/a+c	log(abs(x-a))/(2*a)-log(abs(x+ a))/(2*a)	x	1			ATInt_true.
Int		log(x-a)/(2*a)-log(x+a)/(2*a)+ c	log(abs(x-a))/(2*a)-log(abs(x+ a))/(2*a)	x	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		log(x-3)/6-log(x+3)/6+c	-acoth(x/3)/3	x	1			ATInt_true.
Int		log(abs(x-3))/6-log(abs(x+3))/ 6+c	-acoth(x/3)/3	x	1			ATInt_true.
Int		log(x-3)/6-log(x+3)/6	-acoth(x/3)/3	x	0		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int		atan(2*x-3)+c	atan(2*x-3)	x	1			ATInt_true.
Int		atan((x-2)/(x-1))+c	atan(2*x-3)	x	1			ATInt_true.
Int		atan((x-2)/(x-1))	atan(2*x-3)	x	0		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.
Int		atan((x-1)/(x-2))	atan(2*x-3)	x	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	!	2/3*sqrt(3)*(atan(sin(x)/(sqrt (3)*(cos(x)+1)))-(atan(sin(x)/ (cos(x)+1))))+x/sqrt(3)	2*atan(sin(x)/(sqrt(3)*(cos(x) +1)))/sqrt(3)	x	-3		You need to add a constant of integration, otherwise this appears to be correct. Well done.	ATInt_const.

GT

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
GT		1/0	1		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATGT_STACKERROR_SAns.
GT		1	1/0		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATGT_STACKERROR_TAns.
GT		1	1		0			ATGT_false.
GT		2	1		1			ATGT_true.
GT		1	2.1		0			ATGT_false.
GT		pi	3		1			ATGT_true.
GT		pi+2	5		1			ATGT_true.
	Infinity
GT		-inf	0		0			Not number
GT		inf	0		0			Not number

GTE

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
GTE		1/0	1		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATGTE_STACKERROR_SAns.
GTE		1	1/0		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATGTE_STACKERROR_TAns.
GTE		1	1		1			ATGTE_true.
GTE		2	1		1			ATGTE_true.
GTE		1	2.1		0			ATGTE_false.
GTE		pi	3		1			ATGTE_true.
GTE		pi+2	5		1			ATGTE_true.

NumRelative

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
	Basic tests
NumRelative		1/0	0		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATNumRelative_STACKERROR_SAns.
NumRelative		0	1/0		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATNumRelative_STACKERROR_TAns.
NumRelative		0	0	1/0	-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATNumRelative_STACKERROR_Opt.
NumRelative		0	(x		-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.	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		1.5	1.5	x	-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		1	0	(x	0
NumRelative		x=1.5	1.5		0		Your answer should be a floating point number, but is not.	ATNumerical_SA_not_number.
NumRelative		1.5	x=1.5		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		1.1	1		0
NumRelative		1.05	1		1
NumRelative		0.95	1		1
NumRelative		0.949	1		0
NumRelative		1.05e33	1e33		1
NumRelative		1.06e33	1e33		0
NumRelative		0.95e33	1e33		1
NumRelative		0.949e33	1e33		0
NumRelative		1.05e-33	1e-33		1
NumRelative		1.06e-33	1e-33		0
NumRelative		0.95e-33	1e-33		1
NumRelative		0.949e-33	1e-33		0
	Remove display dp etc.
NumRelative		1	displaydp(1.05,2)	0.1	1
NumRelative		1000	displaysci(1.05,2,3)	0.1	1
	Options passed
NumRelative		1.05	1	0.1	1
NumRelative		1.05	3	0.1	0
NumRelative		3.14	pi	0.001	1
	Infinity
NumRelative		inf	0		0		Your answer should be a floating point number, but is not.	ATNumerical_SA_not_number.
	Lists
NumRelative		1	[1,2]		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		[1,2]	[1,2,3]		0		Your list should have \(3\) elements, but it actually has \(2\).	ATNumerical_wronglen.
NumRelative		[1,2]	[1,2]		1
NumRelative		[3.141,1.414]	[pi,sqrt(2)]		1
NumRelative		[3,1.414]	[pi,sqrt(2)]	0.01	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		[3,1.414]	{pi,sqrt(2)}	0.01	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		{1.414,3.1}	{significantfigures(pi,6),sqrt (2)}	0.01	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		{1.414,3.1}	{pi,sqrt(2)}	0.1	1

NumAbsolute

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
	Basic tests
NumAbsolute		1/0	0		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATNumAbsolute_STACKERROR_SAns.
NumAbsolute		0	1/0		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATNumAbsolute_STACKERROR_TAns.
NumAbsolute		0	0	1/0	-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATNumAbsolute_STACKERROR_Opt.
NumAbsolute		0	(x		-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.	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		1	0	(x	0
	No option, so 5%
NumAbsolute		1.1	1		0
NumAbsolute		1.05	1		1
	Options passed
NumAbsolute		1.05	1	0.1	1
NumAbsolute		1.05	3	0.1	0
NumAbsolute		3.14	pi	0.001	0
NumAbsolute		1.41e-2	1.41e-2	0.0001	1
NumAbsolute		0.0141	1.41e-2	0.0001	1
NumAbsolute		0.00141	0.00141	0.0001	1
NumAbsolute		0.00141	1.41*10^-3	0.0001	1
NumAbsolute		1.41*10^-3	1.41*10^-3	0.0001	1
NumAbsolute		[3.141,1.414]	[pi,sqrt(2)]	0.01	1
NumAbsolute		[3,1.414]	[pi,sqrt(2)]	0.01	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		[3,1.414]	{pi,sqrt(2)}	0.01	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		{1.414,3.1}	{significantfigures(pi,6),sqrt (2)}	0.01	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		{1,1.414,3.1,2}	{1,2,pi,sqrt(2)}	0.1	1

NumSigFigs

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
	Basic tests
NumSigFigs		3.141	3.1415927		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test.	STACKERROR_OPTION.
NumSigFigs		1/0	3	3	-1			ATNumSigFigs_STACKERROR_SAns.
NumSigFigs		0	1/0	3	-1			ATNumSigFigs_STACKERROR_TAns.
NumSigFigs		0	0	1/0	-1			ATNumSigFigs_STACKERROR_Opt.
NumSigFigs		0	1	(	-1	TEST_FAILED	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		(	1	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.	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		1	3	pi	-1		The answer test failed to execute correctly: please alert your teacher.	ATNumSigFigs_STACKERROR_not_integer.
NumSigFigs		1	3	[3,x]	-1		The answer test failed to execute correctly: please alert your teacher.	ATNumSigFigs_STACKERROR_not_integer.
NumSigFigs		1	3	[1,2,3]	-1		The answer test failed to execute correctly: please alert your teacher.	ATNumSigFigs_STACKERROR_list_wrong_length.
NumSigFigs		1	3		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test.	STACKERROR_OPTION.
NumSigFigs		pi	pi	4	0		Your answer should be a decimal number, but is not!	ATNumSigFigs_NotDecimal.
	Edge cases
NumSigFigs		0	0	2	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		0	0	1	1
NumSigFigs		0.0	0	1	1
NumSigFigs		0.0	0	2	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		0	0.0	2	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		0.0	0.0	2	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		0.00	0.00	2	1
	Large numbers
NumSigFigs		5.4e21	5.3e21	2	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		5.3e21	5.3e21	2	1
NumSigFigs		5.3e22	5.3e22	2	1
NumSigFigs		5.3e20	5.3e22	2	0			ATNumSigFigs_VeryInaccurate.
NumSigFigs		6.02214086e23	6.02214086e23	9	1
NumSigFigs		6.0221409e23	6.02214086e23	9	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		6.02214087e23	6.02214086e23	9	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		6.02214085e23	6.02214086e23	9	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		5.3910632e-44	5.3910632e-44	8	1
NumSigFigs		5.391063e-44	5.3910632e-44	8	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		5.3910631e-44	5.3910632e-44	8	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		5.3910633e-44	5.3910632e-44	8	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		1.61622938e-35	1.61622938e-35	9	1
NumSigFigs		1.6162294e-35	1.61622938e-35	9	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		1.61622939e-35	1.61622938e-35	9	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		1.61622937e-35	1.61622938e-35	9	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		1.2345e82	1.2345e82	5	1
NumSigFigs		1.2346e82	1.2345e82	5	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		1.2344e82	1.2345e82	5	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		1.234	4	1	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		3.141	3.1415927	3	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		3.141	3.1415927	4	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		3.146	3.1415927	4	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		3.147	3.1415927	4	0			ATNumSigFigs_VeryInaccurate.
NumSigFigs		3.142	3.1415927	4	1
NumSigFigs		3.142	pi	4	1
NumSigFigs		3141	3.1415927	4	0			ATNumSigFigs_VeryInaccurate.
NumSigFigs		0.00123	0.001234567	3	1
NumSigFigs		1.23e-3	0.001234567	3	1
NumSigFigs		138*10^-3	138*10^-3	3	1
NumSigFigs		-138*10^-3	-138*10^-3	3	1
NumSigFigs		138*10^-3	-138*10^-3	3	0		Your answer has the wrong algebraic sign.	ATNumSigFigs_WrongSign.
NumSigFigs		1.38*10^-1	138*10^-3	3	1
NumSigFigs		1.24e-3	0.001234567	3	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		1.235e-3	0.001234567	4	1
NumSigFigs		1000	999	2	1			ATNumSigFigs_WithinRange.
NumSigFigs		1E3	999	2	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		-100	-149	1	1
NumSigFigs		-0.05	-0.0499	1	1
NumSigFigs		-(0.05)	-0.0499	1	1
NumSigFigs		1170	1174.34	3	1
NumSigFigs		61300	61250	3	1
	Previous tricky case
NumSigFigs		0.1667	0.1667	4	1
NumSigFigs		0.1666	0.1667	4	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		0.1663	0.1667	4	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		0.1662	0.1667	4	0			ATNumSigFigs_VeryInaccurate.
NumSigFigs		0.166	0.1667	4	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATNumSigFigs_VeryInaccurate.
NumSigFigs		0.16667	0.1667	4	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
	Negative numbers
NumSigFigs		-3.141	-3.1415927	4	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		-3.141	-3.1415927	3	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		-3.141	-3.1415927	4	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		-3.142	-3.1415927	4	1
NumSigFigs		3.142	-3.1415927	4	0		Your answer has the wrong algebraic sign.	ATNumSigFigs_WrongSign.
NumSigFigs		-3.142	3.1415927	4	0		Your answer has the wrong algebraic sign.	ATNumSigFigs_WrongSign.
NumSigFigs		-3.149	3.1415927	4	0		Your answer has the wrong algebraic sign.	ATNumSigFigs_WrongSign. ATNumSigFigs_VeryInaccurate.
NumSigFigs		2.15	75701719/35227192	3	1
	Round teacher answer
NumSigFigs		0.0499	0.04985	3	1
NumSigFigs		0.0498	0.04985	3	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		0.0498	0.04975	3	1
NumSigFigs		0.0497	0.04975	3	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		0.0499	0.0498	3	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		1.5	1.500	3	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		1.50	1.500	3	1
NumSigFigs		1.500	1.500	3	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		245.0	245	3	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
	Too few digits
NumSigFigs		180	178.35	3	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		33	33.1558	3	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		3.142	3.1415927	[4,3]	1
NumSigFigs		3.143	3.1415927	[4,3]	1
NumSigFigs		3.150	3.1415927	[4,3]	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		3.211	3.1415927	[4,3]	0			ATNumSigFigs_VeryInaccurate.
NumSigFigs		3.1416	3.1415927	[4,3]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		0.1666	0.1667	[4,3]	1
NumSigFigs		180	178.35	[3,1]	1			ATNumSigFigs_WithinRange.
NumSigFigs		33	33.1558	[3,1]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		1.500	1.5	[3,1]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		245.0	245	[3,1]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		12345.7	12345.654321	[6,6]	1
NumSigFigs		12345.7	12345.654321	[6,3]	1
NumSigFigs		12300.0	12345.654321	[6,3]	1
NumSigFigs		12400.0	12345.654321	[6,3]	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		13500.0	12345.654321	[6,3]	0			ATNumSigFigs_VeryInaccurate.
NumSigFigs		12000.0	12345.654321	[6,2]	1
NumSigFigs		13000.0	12345.654321	[6,2]	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		11000.0	12345.654321	[6,2]	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		0.0010	0	[1,0]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		0.0010	0	[2,0]	1
NumSigFigs		0.0010	0	[3,0]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		0.001	0	[1,0]	1
NumSigFigs		0.001	0	[2,0]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		0.00100	null	[2,0]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		0.00100	null	[3,0]	1
NumSigFigs		0.00100	null	[4,0]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		5.00	null	[2,0]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		5.00	null	[3,0]	1
NumSigFigs		5.00	null	[4,0]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		100	0	[1,0]	1
NumSigFigs		100	0	[2,0]	1			ATNumSigFigs_WithinRange.
NumSigFigs		100	0	[3,0]	1			ATNumSigFigs_WithinRange.
NumSigFigs		100	0	[4,0]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		10.0	0	[2,0]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		10.0	0	[3,0]	1
NumSigFigs		10.0	0	[4,0]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		0	0	[1,0]	1
NumSigFigs		0	0	[2,0]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		0.00	0	[1,0]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		0.00	0	[2,0]	1
NumSigFigs		0.00	0	[3,0]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		0.00	0	[4,0]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
	Condone too many sfs.
NumSigFigs		8.250	8.250	[4,-1]	1
NumSigFigs		8.25	8.250	[4,-1]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits.
NumSigFigs		8.250000	8.250	[4,-1]	1
NumSigFigs		8.250434	8.250	[4,-1]	1
NumSigFigs		82.4	82	[2,-1]	1
NumSigFigs		82.5	82	[2,-1]	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		83	82	[2,-1]	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		0.1430	1/7	[4,-1]	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		0.1429	1/7	[4,-1]	1
NumSigFigs		0.1428	1/7	[4,-1]	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		0.143	1/7	[4,-1]	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		0.14284	1/7	[4,-1]	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		0.14285	1/7	[4,-1]	1
NumSigFigs		0.14286	1/7	[4,-1]	1
NumSigFigs		0.14291	1/7	[4,-1]	1
NumSigFigs		0.14294	1/7	[4,-1]	1
NumSigFigs		0.14295	1/7	[4,-1]	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		0.142	1/7	[2,-1]	1
NumSigFigs		0.14290907676	1/7	[2,-1]	1
NumSigFigs		0.143	1/7	[2,-1]	1
NumSigFigs		0.1433333	1/7	[2,-1]	1
NumSigFigs		0.144	1/7	[2,-1]	1
NumSigFigs		0.145	1/7	[2,-1]	1
NumSigFigs		0.146	1/7	[2,-1]	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		1.279	ev(lg(19),lg=logbasesimp)	4	1
NumSigFigs		3.14	pi	3	1
NumSigFigs		3.15	pi	3	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		1.73205	sqrt(3)	6	1
	No support for matrices!
NumSigFigs		matrix([0.33,1],[1,1])	matrix([0.333,1],[1,1])	2	-1		Your answer should be a decimal number, but is not!	ATNumSigFigs_NotDecimal.
NumSigFigs		3.1415	matrix([0.333,1],[1,1])	2	-1	TEST_FAILED	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		1.50	dispsf(1.500,3)	3	1
NumSigFigs		1.50	dispdp(1.500,3)	3	1

NumDecPlaces

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
	Basic tests
NumDecPlaces		1/0	3	2	-1			ATNumDecPlaces_STACKERROR_SAns.
NumDecPlaces		0.1	1/0	2	-1			ATNumDecPlaces_STACKERROR_TAns.
NumDecPlaces		0.1	0	1/0	-1			ATNumDecPlaces_STACKERROR_Opt.
NumDecPlaces		0.1	1	x	-1		For ATNumDecPlaces the test option must be a positive integer, in fact "\(x\)" was received.	ATNumDecPlaces_OptNotInt.
NumDecPlaces		0.1	1	-1	-1		For ATNumDecPlaces the test option must be a positive integer, in fact "\(-1\)" was received.	ATNumDecPlaces_OptNotInt.
NumDecPlaces		0.1	1	0	-1		For ATNumDecPlaces the test option must be a positive integer, in fact "\(0\)" was received.	ATNumDecPlaces_OptNotInt.
NumDecPlaces		0.1	1	(	-1	TEST_FAILED	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		(	1	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.	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		x	3.143	2	0		Your answer must be a floating point number, but is not.	ATNumDecPlaces_SA_Not_num.
NumDecPlaces		pi	3.000	3	0		Your answer must be a floating point number, but is not.	ATNumDecPlaces_SA_Not_num.
	Right number of places
NumDecPlaces		3.14	3.143	2	1			ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.
NumDecPlaces		3.14	3.14	2	1			ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.
NumDecPlaces		3.140	3.140	3	1			ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.
NumDecPlaces		3141.5972	3141.5972	4	1			ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.
NumDecPlaces		4.14	3.14	2	0			ATNumDecPlaces_Correct. ATNumDecPlaces_Not_equiv.
NumDecPlaces		3.1416	pi	4	1			ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.
NumDecPlaces		-7.3	-7.3	1	1			ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.
	Wrong number of places
NumDecPlaces		3.14	3.143	1	0		Your answer has been given to the wrong number of decimal places.	ATNumDecPlaces_Wrong_DPs. ATNumDecPlaces_Equiv.
NumDecPlaces		3.14	3.143	1	0		Your answer has been given to the wrong number of decimal places.	ATNumDecPlaces_Wrong_DPs. ATNumDecPlaces_Equiv.
NumDecPlaces		3.14	3.140	3	0		Your answer has been given to the wrong number of decimal places.	ATNumDecPlaces_Wrong_DPs. ATNumDecPlaces_Equiv.
NumDecPlaces		7.000	7	4	0		Your answer has been given to the wrong number of decimal places.	ATNumDecPlaces_Wrong_DPs. ATNumDecPlaces_Equiv.
NumDecPlaces		7.0000	7	4	1			ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.
	Both wrong DPs and inaccurate.
NumDecPlaces		8.0000	7	3	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		4.000	3.99999	3	1			ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.
	Teacher uses displaydp
NumDecPlaces		0.10	displaydp(0.1,2)	2	1			ATNumDecPlaces_Correct. ATNumDecPlaces_Equiv.

NumDecPlacesWrong

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

SigFigsStrict

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
	Basic tests
SigFigsStrict		3.141	null		-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test.	STACKERROR_OPTION.
SigFigsStrict		3.141	null	x^2	-1			STACKERROR_OPTION.
SigFigsStrict		3.141	null	-2	-1			STACKERROR_OPTION.
SigFigsStrict		3.141	null	0	-1			STACKERROR_OPTION.
SigFigsStrict		0.0010	null	1	0
SigFigsStrict		0.0010	null	2	1
SigFigsStrict		0.0010	null	3	0
SigFigsStrict		0.00100	null	2	0
SigFigsStrict		0.00100	null	3	1
SigFigsStrict		0.00100	null	4	0
SigFigsStrict		0.001	null	1	1
SigFigsStrict		0.001	null	2	0
SigFigsStrict		100	null	1	1
SigFigsStrict		100	null	2	0			ATSigFigsStrict_WithinRange.
SigFigsStrict		100	null	3	0			ATSigFigsStrict_WithinRange.
SigFigsStrict		100	null	4	0
SigFigsStrict		100.	null	1	0
SigFigsStrict		100.	null	2	0
SigFigsStrict		100.	null	3	1
SigFigsStrict		100.	null	4	0
SigFigsStrict		123.	null	1	0
SigFigsStrict		123.	null	2	0
SigFigsStrict		123.	null	3	1
SigFigsStrict		123.	null	4	0
SigFigsStrict		1.00e2	null	1	0
SigFigsStrict		1.00e2	null	2	0
SigFigsStrict		1.00e2	null	3	1
SigFigsStrict		1.00e2	null	4	0
SigFigsStrict		10.0	null	2	0
SigFigsStrict		10.0	null	3	1
SigFigsStrict		10.0	null	4	0
SigFigsStrict		0	null	1	1
SigFigsStrict		0	null	2	0
SigFigsStrict		0.0	null	1	1
SigFigsStrict		0.0	null	2	0
SigFigsStrict		.0	null	1	1
SigFigsStrict		.0	null	2	0
SigFigsStrict		.001030	null	4	1
SigFigsStrict		0.00	null	1	0
SigFigsStrict		0.00	null	2	1
SigFigsStrict		0.00	null	3	0
SigFigsStrict		25.00e1	null	1	0
SigFigsStrict		25.00e1	null	3	0
SigFigsStrict		25.00e1	null	4	1
SigFigsStrict		25.00e1	null	5	0
SigFigsStrict		15.1	15.1	3	1
SigFigsStrict		15.10	15.1	3	0
SigFigsStrict		15.100	15.1	3	0
	Units are ignored
SigFigsStrict		9.81*m/s^2	null	3	1

Units

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
Units		1/0	1	2	-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATUnits_STACKERROR_SAns.
Units		1	1/0	2	-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATUnits_STACKERROR_TAns.
Units		1	1	1/0	-1	TEST_FAILED	The answer test failed to execute correctly: please alert your teacher. Division by zero.	ATUnits_STACKERROR_Opt.
Units		x-1)^2	(x-1)^2	2	-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.	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		12.3*m*s^(-1)	3*m	[3,x]	-1		The answer test failed to execute correctly: please alert your teacher.	ATNumSigFigs_STACKERROR_not_integer.
Units		3*m*s^(-1)	3*m	[1,2,3]	-1		The answer test failed to execute correctly: please alert your teacher.	ATNumSigFigs_STACKERROR_list_wrong_length.
Units		12.3*m*s^(-1)	{12.3*m*s^(-1)}	3	-1		The answer test failed to execute correctly: please alert your teacher.	ATUnits_TA_not_expression.
Units		x=12.3*m*s^(-1)	12.3*m*s^(-1)	3	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		12.3	12.3*m	3	0		Your answer must have units.	ATUnits_SA_no_units.
Units		12	12.3*m	3	0		Your answer must have units.	ATUnits_SA_no_units.
Units		1/2	12.3*m	3	0		Your answer must have units.	ATUnits_SA_no_units.
Units		e^(1/2)	12.3*m	3	0		Your answer must have units.	ATUnits_SA_no_units.
Units		9.81*m	12.3	3	-1		The answer test failed to execute correctly: please alert your teacher.	ATUnits_SB_no_units.
	Only units
Units		m/s	12.3*m/s	3	0		Your answer needs to be a number together with units. Your answer only has units.	ATUnits_SA_only_units.
Units		m	12.3*m/s	3	0		Your answer needs to be a number together with units. Your answer only has units.	ATUnits_SA_only_units.
	Bad units
Units		9.81+m/s	9.81*m/s	3	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		12.3*m/s	12.3*m/s	3	1			ATUnits_units_match.
Units		12.4*m/s	12.3*m/s	3	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		12.4*m/s	12.3*m/s	[3,2]	1			ATUnits_units_match.
Units		12.45*m/s	12.3*m/s	[3,2]	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATUnits_units_match.
Units		13.45*m/s	12.3*m/s	[3,2]	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		7.54E-5*(s*M)^-1	5.625E-5*s^-1	[3,2]	0		Your units are incompatible with those used by the teacher.	ATNumSigFigs_VeryInaccurate. ATUnits_incompatible_units.
Units		7.54E-5*(s*M)^-1	stackunits(5.625E-5,1/s)	[3,2]	0		Your units are incompatible with those used by the teacher.	ATNumSigFigs_VeryInaccurate. ATUnits_incompatible_units.
Units		12*m/s	12.3*m/s	3	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		-9.81*m/s^2	-9.81*m/s^2	3	1			ATUnits_units_match.
Units		-9.82*m/s^2	-9.815*m/s^2	3	1			ATUnits_units_match.
Units		-9.81*m/s^2	-9.815*m/s^2	3	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		-9.81*m*s^(-2)	-9.81*m/s^2	3	1			ATUnits_units_match.
Units		-9.82*m/s^2	-9.81*m/s^2	3	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		-9.81*m*s^(-2)	-9.81*m/s^2	3	1			ATUnits_units_match.
Units		-9.81*m/s/s	-9.81*m/s^2	3	1			ATUnits_units_match.
Units		-9.81*m/s	-9.81*m/s^2	3	0		Your units are incompatible with those used by the teacher. Please check your units carefully.	ATUnits_incompatible_units. ATUnits_correct_numerical.
Units		-9.81*m/s	-9.81*m/s^2	3	0		Your units are incompatible with those used by the teacher. Please check your units carefully.	ATUnits_incompatible_units. ATUnits_correct_numerical.
Units		(-9.81)*m/s^2	-9.81*m/s^2	3	1			ATUnits_units_match.
Units		520*amu	520*amu	3	1			ATNumSigFigs_WithinRange. ATUnits_units_match.
Units		520*amu	521*amu	3	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		(-9.81)	-9.81*m/s^2	3	0		Your answer must have units.	ATUnits_SA_no_units.
Units		9.81*m/s	-9.81*m/s^2	3	0		Your answer has the wrong algebraic sign. Your units are incompatible with those used by the teacher.	ATNumSigFigs_WrongSign. ATUnits_incompatible_units.
Units		8.81*m/s	-9.81*m/s^2	3	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		8.1*m/s	-9.81*m/s^2	3	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		m/4	0.25*m	3	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATUnits_units_match.
	Student is too exact
Units		pi*s	3.14*s	3	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATUnits_units_match.
Units		sqrt(2)*m	1.41*m	3	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATUnits_units_match.
	Different units
Units		25*g	0.025*kg	2	1			ATUnits_compatible_units kg.
Units		26*g	0.025*kg	2	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		100*g	10*kg	2	0			ATNumSigFigs_WithinRange. ATNumSigFigs_VeryInaccurate. ATUnits_compatible_units kg.
Units		0.025*g	0.025*kg	2	0		Please check your units carefully.	ATUnits_compatible_units kg. ATUnits_correct_numerical.
Units		1000*m	1*km	2	1			ATNumSigFigs_WithinRange. ATUnits_compatible_units m.
Units		1*Mg/10^6	1*N*s^2/(km)	1	1			ATUnits_compatible_units kg.
Units		1*Mg/10^6	1*kN*ns/(mm*Hz)	1	1			ATUnits_compatible_units kg.
Units		3.14*Mg/10^6	%pi*kN*ns/(mm*Hz)	3	1			ATUnits_compatible_units kg.
Units		3.141*Mg/10^6	%pi*kN*ns/(mm*Hz)	3	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATUnits_compatible_units kg.
Units		4.141*Mg/10^6	%pi*kN*ns/(mm*Hz)	3	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATNumSigFigs_VeryInaccurate. ATUnits_compatible_units kg.
Units		400*cc	0.4*l	2	1			ATNumSigFigs_WithinRange. ATUnits_compatible_units m^3.
Units		400*cm^3	0.4*l	2	1			ATNumSigFigs_WithinRange. ATUnits_compatible_units m^3.
Units		400*ml	0.4*l	2	1			ATNumSigFigs_WithinRange. ATUnits_compatible_units m^3.
Units		18*kJ	18000.0*J	2	1			ATUnits_compatible_units (kg*m^2)/s^2.
Units		18.1*kJ	18000.0*J	2	0		Your answer contains the wrong number of significant digits.	ATNumSigFigs_WrongDigits. ATUnits_compatible_units (kg*m^2)/s^2.
Units		120*kWh	0.12*MWh	2	1			ATUnits_compatible_units (kg*m^2)/s^2.
Units		2.0*hh	720000*s	2	1			ATUnits_compatible_units s.
Units		723*kVA	0.723*MVA	3	1			ATUnits_compatible_units VA.
	Edge case
Units		0*m/s	0*m/s	1	1			ATUnits_units_match.
Units		0.0*m/s	0*m/s	1	1			ATUnits_units_match.
Units		0*m/s	0.0*m/s	1	1			ATUnits_units_match.
Units		0.00*m/s	0.0*m/s	2	1			ATUnits_units_match.
Units		0.0*km/s	0.0*m/s	1	1			ATUnits_compatible_units m/s.
Units		0.0*m	0.0*m/s	1	0		Your units are incompatible with those used by the teacher. Please check your units carefully.	ATUnits_incompatible_units. ATUnits_correct_numerical.
Units		0.0	0.0*m/s	1	0		Your answer must have units.	ATUnits_SA_no_units.
	Imperial
Units		7*in	7*in	1	1			ATUnits_units_match.
Units		6*in	0.5*ft	1	1			ATUnits_compatible_units in.
Units		2640*ft	0.5*mi	4	1			ATNumSigFigs_WithinRange. ATUnits_compatible_units in.
Units		2650*ft	0.5*mi	4	0			ATNumSigFigs_WithinRange. ATNumSigFigs_VeryInaccurate. ATUnits_compatible_units in.
	TODO
Units	!	142.8*C	415.9*K	4	-3		Your units are incompatible with those used by the teacher.	ATNumSigFigs_VeryInaccurate. ATUnits_incompatible_units.
Units	!	520*mamu	520*mamu	3	-3		The answer test failed to execute correctly: please alert your teacher.	ATUnits_SB_no_units.

UnitsStrict

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

UnitsRelative

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
UnitsRelative		12.3*m/s	12.3*m/s	0.01	1			ATUnits_units_match.
UnitsRelative		12*m/s	12.3*m/s	0.01	0			ATUnits_units_match.
UnitsRelative		1.1*Mg/10^6	1.2*kN*ns/(mm*Hz)	0.15	1			ATUnits_compatible_units kg.
UnitsRelative		1.1*Mg/10^6	1.2*kN*ns/(mm*Hz)	0.05	0			ATUnits_compatible_units kg.
	Edge case
UnitsRelative		0*m/s	0*m/s	0.01	1			ATUnits_units_match.
UnitsRelative		0.0*m/s	0*m/s	0.01	1			ATUnits_units_match.
UnitsRelative		0*m/s	0.0*m/s	0.01	1			ATUnits_units_match.
UnitsRelative		0.0*m/s	0.0*m/s	0.01	1			ATUnits_units_match.
UnitsRelative		0.0*km/s	0.0*m/s	0.01	1			ATUnits_compatible_units m/s.
UnitsRelative		0.0*m	0.0*m/s	0.01	0		Your units are incompatible with those used by the teacher. Please check your units carefully.	ATUnits_incompatible_units. ATUnits_correct_numerical.
UnitsRelative		0.0	0.0*m/s	0.01	0		Your answer must have units.	ATUnits_SA_no_units.
UnitsRelative		0.0*kVA	0.0*kVA	0.002	1			ATUnits_units_match.

UnitsStrictRelative

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
UnitsStrictRelative		12.3*m/s	12.3*m/s	0.01	1			ATUnits_units_match.
UnitsStrictRelative		12*m/s	12.3*m/s	0.01	0			ATUnits_units_match.
UnitsStrictRelative		1.1*Mg/10^6	1.2*kN*ns/(mm*Hz)	0.15	0			ATUnits_compatible_units kg.
UnitsStrictRelative		1.1*Mg/10^6	1.2*kN*ns/(mm*Hz)	0.05	0			ATUnits_compatible_units kg.
	Edge case
UnitsStrictRelative		0*m/s	0*m/s	0.01	1			ATUnits_units_match.
UnitsStrictRelative		0.0*m/s	0*m/s	0.01	1			ATUnits_units_match.
UnitsStrictRelative		0*m/s	0.0*m/s	0.01	1			ATUnits_units_match.
UnitsStrictRelative		0.0*m/s	0.0*m/s	0.01	1			ATUnits_units_match.
UnitsStrictRelative		0.0*km/s	0.0*m/s	0.01	0			ATUnits_compatible_units m/s.
UnitsStrictRelative		0.0*m	0.0*m/s	0.01	0			ATUnits_incompatible_units. ATUnits_correct_numerical.
UnitsStrictRelative		0.0	0.0*m/s	0.01	0		Your answer must have units.	ATUnits_SA_no_units.
UnitsStrictRelative		0*J	0.0*J	0.01	1			ATUnits_units_match.

UnitsAbsolute

Test	?	Student response	Teacher answer	Opt	Mark	CAS errors	Feedback	Answer note
UnitsAbsolute		-123000*J	-123*kJ	5*J	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		12.3*m/s	12.3*m/s	0.01	1			ATUnits_units_match.
UnitsAbsolute		12*m/s	12.3*m/s	0.01	0			ATUnits_units_match.
UnitsAbsolute		1.1*Mg/10^6	1.2*kN*ns/(mm*Hz)	0.15	1			ATUnits_compatible_units kg.
	The following illustrates that we convert to base units to compare.
UnitsAbsolute		1.1*Mg/10^6	1.2*kN*ns/(mm*Hz)	0.1	1			ATUnits_compatible_units kg.
UnitsAbsolute		1.1*Mg/10^6	1.2*kN*ns/(mm*Hz)	0.09	0			ATUnits_compatible_units kg.
	Units in the options
UnitsAbsolute		-123000*J	-123*kJ	5*kJ	1			ATUnits_compatible_units (kg*m^2)/s^2.
UnitsAbsolute		-123006*J	-123*kJ	5*kJ	1			ATUnits_compatible_units (kg*m^2)/s^2.
UnitsAbsolute		-129006*J	-123*kJ	5*kJ	0			ATUnits_compatible_units (kg*m^2)/s^2.
UnitsAbsolute		1.1*Mg/10^6	1.2*kN*ns/(mm*Hz)	0.1*kN*ns/(mm*H z)	1			ATUnits_compatible_units kg.
UnitsAbsolute		1.1*Mg/10^6	1.2*kN*ns/(mm*Hz)	0.09*kN*ns/(mm* Hz)	0			ATUnits_compatible_units kg.
	Edge case
UnitsAbsolute		0*m/s	0*m/s	0.01	1			ATUnits_units_match.
UnitsAbsolute		0.0*m/s	0*m/s	0.01	1			ATUnits_units_match.
UnitsAbsolute		0*m/s	0.0*m/s	0.01	1			ATUnits_units_match.
UnitsAbsolute		0.0*m/s	0.0*m/s	0.01	1			ATUnits_units_match.
UnitsAbsolute		0.0*km/s	0.0*m/s	0.01	1			ATUnits_compatible_units m/s.
UnitsAbsolute		0.0*m	0.0*m/s	0.01	0		Your units are incompatible with those used by the teacher. Please check your units carefully.	ATUnits_incompatible_units. ATUnits_correct_numerical.
UnitsAbsolute		0.0	0.0*m/s	0.01	0		Your answer must have units.	ATUnits_SA_no_units.
UnitsAbsolute		1.0*m/s	m/s	0.01	1			ATUnits_units_match.
UnitsAbsolute		15/pi*kN/mm^2	15/pi*kN/mm^2	0.01	1			ATUnits_units_match.
UnitsAbsolute		(15*kN)/(pi*mm^2)	(15*kN)/(pi*mm^2)	0.01	1			ATUnits_units_match.
UnitsAbsolute		(15/pi)*(kN/mm^2)	(15/pi)*(kN/mm^2)	0.01	1			ATUnits_units_match.
UnitsAbsolute		(600*N)/(%pi*mm^2)	(600*N)/(%pi*mm^2)	0.01	1			ATUnits_units_match.
UnitsAbsolute		(600/pi)*kN/m^2	(600/pi)*kN/m^2	0.01	1			ATUnits_units_match.
UnitsAbsolute		(600/pi)*kN/mm^2	(600/pi)*kN/mm^2	0.01	1			ATUnits_units_match.