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 | 5/4*%e^(%i*%pi/6) |
5*sqrt(3)/8+5/8*%i |
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 | 'root(x) |
x^(1/2) |
1 | ||||
| AlgEquiv | 'root(x,m) |
x^(1/m) |
1 | ||||
| AlgEquiv | x |
'root(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 | 1-root(2) |
1-2^(1/2) |
1 | ||||
| AlgEquiv | 1-root(2) |
1-sqrt(2) |
1 | ||||
| AlgEquiv | root(2,2)+1 |
1+sqrt(2) |
1 | ||||
| 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 | ||||
| AlgEquiv | log((x+1)/(1-x)) |
-log((1-x)/(x+1)) |
0 | ||||
| AlgEquiv | ratsimp(logcontract(log((x+1)/ (1-x)))) |
ratsimp(logcontract(-log((1-x) /(x+1)))) |
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 | ! | {5/4*%e^(%i*%pi/6)} |
{5*sqrt(3)/8+5/8*%i} |
-3 | ATSet_wrongentries. | ||
| The following entries are incorrect, although they may appear in a simplified form from that which you actually entered. \[\left \{\frac{5\cdot \mathrm{i}+5\cdot \sqrt{3}}{8} \right \}\] | |||||||
| AlgEquiv | map(expand,{5/4*%e^(%i*%pi/6)}
) |
{5*sqrt(3)/8+5/8*%i} |
1 | ||||
| AlgEquiv | ratsimp({5/4*%e^(%i*%pi/6)}) |
ratsimp({5*sqrt(3)/8+5/8*%i}) |
1 | ||||
| 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 | ||||
| AlgEquiv | stack_units_nums(stackunits_ma ke(m/s)) |
1 |
0 | ||||
| AlgEquiv | stack_units_nums(stackunits_ma ke(m/s)) |
NULLNUM |
1 | ||||
| AlgEquiv | ev(stack_units_nums(stackunits _make(m/s)),NULLNUM=1) |
1 |
1 | ||||
| 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. | |||||||