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Collect

Collect

Collect[expr,x]

collects together terms involving the same powers of objects matching x.

Collect[expr,{x₁,x₂,…}]

successively collects together terms that involve the same powers of objects matching x₁, then x₂, ….

Collect[expr,var,h]

applies h to the expression that forms the coefficient of each term obtained.

Details and Options

Collect[expr,x] effectively writes expr as a polynomial in x or a fractional power of x.
Collect[expr,x,Simplify] can be used to simplify each coefficient separately.
Collect automatically threads over lists in expr, as well as equations, inequalities and logic functions.

Examples

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Basic Examples (4)

Combine like terms involving :

Collect terms involving :

Collect terms involving :

Collect each power of :

Simplify each coefficient:

Scope (6)

Basic Uses (3)

A polynomial:

A Puiseux polynomial:

Collect with respect to first, then collect with respect to :

Advanced Uses (3)

Collect with respect to a pattern:

Collect derivative terms:

Factor each coefficient after collection of terms:

Collect terms over the integers modulo :

Options (1)

Modulus (1)

Collect over the integers modulo 2:

Applications (1)

When a polynomial has many variables, it can be put into many different forms. Here is a polynomial in three variables:

Collect reorganizes the polynomial so that is the dominant variable:

If is specified as the parameter, the terms are organized with as the leading variable:

When two variables are specified, the function will collect with respect to first, then collect with respect to :

Or collect with respect to first, then collect with respect to :

Properties & Relations (3)

Expand is effectively the inverse of Collect:

The order of variables matters:

Use NonCommutativeCollect to collect terms in a noncommutative polynomial:

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