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AlgEquiv: 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
Answer note
AlgEquiv
1/0
1
-1 ATAlgEquiv_STACKERROR_SAns.
TEST_FAILED
The answer test failed to execute correctly: please alert your teacher. Division by zero.
AlgEquiv
1
1/0
-1 ATAlgEquiv_STACKERROR_TAns.
TEST_FAILED
The answer test failed to execute correctly: please alert your teacher. Division by zero.
AlgEquiv
(x-1)^2
-1 ATAlgEquivTEST_FAILED-Empty SA.
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.
AlgEquiv
x^2
-1 ATAlgEquivTEST_FAILED-Empty TA.
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.
AlgEquiv
x-1)^2
(x-1)^2
-1 ATAlgEquivTEST_FAILED-Empty SA.
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.
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
1/(R-r)
1
0
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
AlgEquiv
0.333333333333333*x^2
x^2/3
0
AlgEquiv
0.1*(2.0*s^2+6.0*s-25.0)/s
(2*s^2+6*s-25)/(10*s)
1
AlgEquiv
0.1*(2.0*s^2+6.0*s-25.00001)/s
(2*s^2+6*s-25)/(10*s)
0
AlgEquiv
100.4-80.0
20.4
0
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
AlgEquiv
exp(-%i)
inf
0
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
1/(a-b)-1/(b-a)
1/(a-b)+1/(b-a)
0
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
4*x*cos(x^12/%pi)
x*cos(x^12/%pi)
0
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 (ATList_wrongentries 1).
The entries underlined in red below are those that are incorrect. \[\left[ {\color{red}{\underline{\sin \left( \frac{\pi}{8} \right)}}} , \frac{1}{2} , \frac{1}{\sqrt{2}} , \frac{\sqrt{3}}{2} , 1 , 0 \right] \]
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 ATAlgEquiv_SA_not_list.
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.
AlgEquiv
[1,2]
[1,2,3]
0 ATList_wronglen.
Your list should have \(3\) elements, but it actually has \(2\).
AlgEquiv
[1,2,4]
[1,2,3]
0 (ATList_wrongentries 3).
The entries underlined in red below are those that are incorrect. \[\left[ 1 , 2 , {\color{red}{\underline{4}}} \right] \]
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 (ATList_wrongentries 3: (ATList_wrongentries 2: ATSet_wrongsz)).
The entries underlined in red below are those that are incorrect. \[\left[ 1 , 2 , \left[ 2-x < 0 , \left \{1 , 2 , 3 \right \} \right] \right] \]
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 ATAlgEquiv_SA_not_expression.
Your answer should be an expression, not an equation, inequality, list, set or matrix.
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 ATAlgEquiv_SA_not_set.
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.
AlgEquiv
co(1,2)
{1,2,3}
0 ATAlgEquiv_SA_not_set.
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.
AlgEquiv
{1,2}
{1,2,3}
0 ATSet_wrongsz.
Your set should have \(3\) different elements, but it actually has \(2\).
AlgEquiv
{2/4, 1/3}
{1/2, 1/3}
1
AlgEquiv
{A[1],A[2],A[4]}
{A[1],A[2],A[3]}
0 ATSet_wrongentries.
The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{A_{4} \right \}\]
AlgEquiv
{A[1],A[2],A[3]}
{A[1],A[2],A[3]}
1
AlgEquiv
{1,2,4}
{1,2,3}
0 ATSet_wrongentries.
The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{4 \right \}\]
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 ATSet_wrongentries.
The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{x-1=0 \right \}\]
AlgEquiv
{x-1=0,x>1 and 5>x}
{x>1 and x<3,x=1}
0 ATSet_wrongentries.
The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{5-x > 0\,{\text{ and }}\, x-1 > 0 \right \}\]
Equivalence for elements of sets is different from expressions: see docs.
AlgEquiv !
{-sqrt(2)/sqrt(3)}
{-2/sqrt(6)}
-3 ATSet_wrongentries.
The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{-\frac{\sqrt{2}}{\sqrt{3}} \right \}\]
AlgEquiv !
{[-sqrt(2)/sqrt(3),0],[2/sqrt(
6),0]}
{[2/sqrt(6),0],[-2/sqrt(6),0]}
-3 ATSet_wrongentries.
The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{\left[ -\frac{\sqrt{2}}{\sqrt{3}} , 0 \right] \right \}\]
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
(a^b)^c
a^(b*c)
0
AlgEquiv
ev(radcan((a^b)^c),radexpand:a
ll,simp)
a^(b*c)
1
AlgEquiv
(n+1)^((n+2)/(n+1))/(n+2)
1/(n+2)*((n+1)^(1/(n+1)))^(n+2
)
0
AlgEquiv
ev(radcan((n+1)^((n+2)/(n+1))/
(n+2)),radexpand:all,simp)
ev(radcan(1/(n+2)*((n+1)^(1/(n
+1)))^(n+2)),radexpand:all,sim
p)
1
AlgEquiv
{(2-2^(5/2))/2,(2^(5/2)+2)/2}
{1-2^(3/2),2^(3/2)+1}
0 ATSet_wrongentries.
The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{\frac{2-2^{\frac{5}{2}}}{2} , \frac{2^{\frac{5}{2}}+2}{2} \right \}\]
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 ATSet_wrongentries.
The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{{\left(x-a\right)}^{6000} \right \}\]
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 ATMatrix_wrongsz_columns.
Your matrix should be \(2\) by \(3\), but it is actually \(2\) by \(2\).
AlgEquiv
matrix([1,2],[2,3])
matrix([1,2],[2,5])
0 ATMatrix_wrongentries.
The entries underlined in red below are those that are incorrect. \[ \left[\begin{array}{cc} 1 & 2 \\ 2 & {\color{red}{\underline{3}}} \end{array}\right]\]
AlgEquiv
matrix([0.33,1],[1,1])
matrix([0.333,1],[1,1])
0 ATMatrix_wrongentries.
The entries underlined in red below are those that are incorrect. \[ \left[\begin{array}{cc} {\color{red}{\underline{0.33}}} & 1 \\ 1 & 1 \end{array}\right]\]
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 ATMatrix_wrongentries.
The entries underlined in red below are those that are incorrect. \[ \left[\begin{array}{cc} {\color{red}{\underline{\varepsilon_{2}}}} & 2 \\ 2 & {\color{red}{\underline{x^2}}} \end{array}\right]\]
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 ATMatrix_wrongentries.
The entries underlined in red below are those that are incorrect. \[ \left[\begin{array}{cc} x > 4 & \left \{1 , x^2 \right \} \\ \left[ 1 , 2 \right] & \left[ 1 , {\color{red}{\underline{3}}} \right] \end{array}\right]\]
Vectors
AlgEquiv
a
stackvector(a)
0
Equations
AlgEquiv
1
x=1
0 ATAlgEquiv_SA_not_equation.
Your answer should be an equation, but is not.
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
x^2=4
x=2 nounor x=-2
1 ATEquation_ratio
AlgEquiv
x^2-5*x+6=0
x=2 nounor x=3
1 ATEquation_sides
AlgEquiv
x^2-5*x+6=0
x=(5 #pm# sqrt(25-24))/2
1 ATEquation_sides
AlgEquiv
x^2-5*x+6=0
x=(5 #pm# sqrt(25-23))/2
0 ATEquation_default
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
2=3
2=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 ATAlgEquiv_SA_not_equation.
Your answer should be an equation, but is not.
AlgEquiv
[]
1=2
0 ATAlgEquiv_SA_not_equation.
Your answer should be an equation, but is not.
AlgEquiv
{}
none
0 ATAlgEquiv_SA_not_logic.
Your answer should be an equation, inequality or a logical combination of many of these, but is not.
Sets of real numbers
AlgEquiv
x^2
cc(1,3)
0 ATAlgEquiv_SA_not_realset.
Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals.
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 ATAlgEquiv_SA_not_logic.
Your answer should be an equation, inequality or a logical combination of many of these, but is not.
AlgEquiv
1 <= x nounand x<2
co(1,2)
0 ATAlgEquiv_SA_not_realset.
Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals.
AlgEquiv
minf <= x
co(minf,inf)
0 ATAlgEquiv_SA_not_realset.
Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals.
AlgEquiv
-inf <= x
co(minf,inf)
0 ATAlgEquiv_SA_not_realset.
Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals.
AlgEquiv
x <= inf
oc(minf,inf)
0 ATAlgEquiv_SA_not_realset.
Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals.
AlgEquiv
minf <= x
oo(minf,inf)
0 ATAlgEquiv_SA_not_realset.
Your answer should be a subset of the real numbers. This could be a set of numbers, or a collection of intervals.
AlgEquiv
stack_single_variable_solver(m
inf <= x)
co(minf,inf)
1 ATRealSet_true.
AlgEquiv
stack_single_variable_solver(-
inf <= x)
co(minf,inf)
1 ATRealSet_true.
AlgEquiv
stack_single_variable_solver(x
 <= inf)
oc(minf,inf)
1 ATRealSet_true.
AlgEquiv
stack_single_variable_solver(m
inf <= 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
TEST_FAILED
The answer test failed to execute correctly: please alert your teacher. Division by zero.
AlgEquiv
1
f(x):=x^2
0 ATAlgEquiv_SA_not_function.
Your answer should be a function, defined using the operator :=, but is not.
AlgEquiv
f(x)=x^2
f(x):=x^2
0 ATAlgEquiv_SA_not_function.
Your answer should be a function, defined using the operator :=, but is not.
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 ATAlgEquiv_SA_not_equation.
Your answer should be an equation, but is not.
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 ATAlgEquiv_SA_not_inequality.
Your answer should be an inequality, but is not.
AlgEquiv
x=1
x>1 and x<5
0 ATAlgEquiv_TA_not_equation.
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".
AlgEquiv
x<1
x>1
0 ATInequality_backwards.
Your inequality appears to be 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 ATInequality_strict. ATInequality_backwards.
Your inequality should not be strict! Your inequality appears to be backwards.
AlgEquiv
x>=2
x<2
0 ATInequality_nonstrict. ATInequality_backwards.
Your inequality should be strict, but is not! Your inequality appears to be backwards.
AlgEquiv
x>=1
x>2
0 ATInequality_nonstrict.
Your inequality should be strict, but is not!
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
sigma>1
x>1
1 ATInequality_solver.
AlgEquiv
a>1
x>1
1 ATInequality_solver.
AlgEquiv
sigma>1
x>2
0
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 ATAlgEquiv_SA_not_logic.
Your answer should be an equation, inequality or a logical combination of many of these, but is not.
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 ATInequality_backwards.
Your inequality appears to be 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 ATInequality_strict.
Your inequality should not be 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
a#b
b#a
1
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-1)!*(n-k+1)!)
n!*k/(k!*(n-k+1)!)
1
AlgEquiv
n!/(k!*(n-k)!)
n!*(n-k+1)/(k!*(n-k+1)!)
1
AlgEquiv
n!/(k!*(n-k)!)
binomial(n,k)
1
AlgEquiv
binomial(n,k)+binomial(n,k+1)
binomial(n+1,k+1)
1
AlgEquiv
n!/((k-1)!*(n-k+1)!)+n!/(k!*(n
-k)!)
n!*k/(k!*(n-k+1)!)+n!*(n-k+1)/
(k!*(n-k+1)!)
1
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
AlgEquiv
binomial(58,[9,15,20,14])
binomial(58,[15,9,20,14])
1
AlgEquiv
binomial(x,[a,b,c])
binomial(x,[b,c,a])
1
Unevaluated derviatives
AlgEquiv
3*s*diff(q(s),s)
3*s*diff(q(s),s)
1
AlgEquiv
3*t*diff(q(s),s)
3*diff(t*q(s),s)
1
AlgEquiv
diff(diff(q(s),s),s)
diff(q(s),s,2)
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 ATEquation_sides
AlgEquiv
x=b#pm#c^2
x=c^2-b or x=-c^2-b
0 ATEquation_default
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 ATSet_wrongentries.
The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{{\rm not}\left( A \right)\,{\text{ or }}\, B \right \}\]
AlgEquiv
{A implies B,A and B}
{not(A) and B,A and B}
0 ATSet_wrongentries.
The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{A\,{\text{ implies }}\, B \right \}\]
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 ATAlgEquiv_SA_not_string.
Your answer should be a string, but is not.
AlgEquiv
"Hello"
x^2
0 ATAlgEquiv_SA_not_expression.
Your answer should be an expression, not an equation, inequality, list, set or matrix.