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.

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

#### Solve a polynomial equation:

#### Solve a system of linear equations:

#### Solve an equation with parameters:

Compute discontinuities and other properties of rational functions.

#### Compute properties of a rational function:

#### Compute a partial fraction decomposition:

Perform computations with the quaternion number system.

#### Get information about a quaternion:

#### Do calculations with quaternions:

Find the domain and range of mathematical functions.

#### Compute the domain of a function:

#### Compute the range of a function:

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

#### Compute properties of a polynomial in several variables:

#### Factor a polynomial:

Simplify algebraic functions and expressions.

#### Simplify an expression:

Discover properties of groups containing a finite number of elements.

#### Get information about a finite group:

#### Ask about a property of a group:

#### Do algebra with permutations:

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Find properties and perform computations on matrices.

#### Do basic arithmetic on matrices:

#### Compute eigenvalues and eigenvectors of a matrix:

Discover properties of fields containing a finite number of elements.