Examples for

Algebra

Algebra is one of the core subjects of mathematics. Algebra consists of the study of variables within number systems, along with operations that act on numbers and symbols. Wolfram|Alpha is a tremendous resource for solving equations; exploring polynomials; and studying fields, groups, vectors and matrices.

Equation Solving

Solve equations in one or more variables both symbolically and numerically.

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
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Rational Functions

Compute discontinuities and other properties of 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)
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Quaternions

Perform computations with the quaternion number system.

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
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Domain & Range

Find the domain and range of mathematical functions.

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)
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Polynomials

Solve, plot and find alternate forms of polynomial expressions in one or more variables.

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
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Simplification

Simplify algebraic functions and expressions.

Simplify an expression:

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

Discover properties of groups containing a finite number of elements.

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
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Step-by-Step Solutions for Algebra

Algebra Web App

RELATED EXAMPLES

  • Arithmetic
  • Calculus & Analysis
  • Geometry
  • Linear Algebra
    • Matrices

    Find properties and perform computations on matrices.

    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}}
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    Finite Fields

    Discover properties of fields containing a finite number of elements.

    Compute properties of a finite field:

    Z/7Z

    Compute a specific property:

    number of primitive polynomials of GF(3125)
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