Mathematics
# Algebra

solve a polynomial equation

solve x^2 + 4x + 6 = 0
solve a system of linear equations

x+y=10, x-y=4
solve an equation with parameters

solve a x^2 + b x + c = 0 for x
compute properties of a polynomial in several variables

x^3 + x^2 y + x y^2 + y^3
factor a polynomial

factor 2x^5 - 19x^4 + 58x^3 - 67x^2 + 56x - 48
compute properties of a rational function

(x^2-1)/(x^2+1)
compute a partial fraction decomposition

partial fractions (x^2-4)/(x^4-x)
simplify an expression

1/(1+sqrt(2))
simplify x^5-20x^4+163x^3-676x^2+1424x-1209
simplify cos(arcsin(x)/2)
compute properties of a vector

vector {2, -5, 4}
compute a cross product

{1/4, -1/2, 1} cross {1/3, 1, -2/3}
do basic arithmetic on matrices

{{0,-1},{1,0}}.{{1,2},{3,4}}+{{2,-1},{-1,2}}
compute eigenvalues and eigenvectors of a matrix

eigenvalues {{4,1},{2,-1}}
get information about a quaternion

quaternion: 0+2i-j-3k
do calculations with quaternions

quaternion -Sin[Pi]+3i+4j+3k multiplied by -1j+3.9i+4-3k
get information about a finite group

alternating group A_5
ask about a property of a group

order of the monster group
do algebra with permutations

perm (1 2 3 4)^3(1 2 3)^-1
compute properties of a finite field

Z/7Z
compute a specific property

number of primitive polynomials of GF(3125)
compute the domain of a function

domain of f(x) = x/(x^2-1)
compute the range of a function

range of e^(-x^2)