Wolfram|Alpha Mathematics

Algebra

Equation Solving ››

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

Polynomials ››

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

Rational Functions ››

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)

Simplification ››

simplify an expression
1/(1+sqrt(2)) simplify x^5-20x^4+163x^3-676x^2+1424x-1209 simplify cos(arcsin(x)/2)

Vectors ››

compute properties of a vector
vector {2, -5, 4}
compute a cross product
{1/4, -1/2, 1} cross {1/3, 1, -2/3}

Matrices & Linear Algebra ››

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}}

Quaternions ››

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

Finite Groups ››

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

Finite Fields ››

compute properties of a finite field
Z/7Z
compute a specific property
number of primitive polynomials of GF(3125)

Domain & Range ››

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)