# collect

Collect coefficients

## Description

## Examples

### Collect Coefficients of Powers of Default Variable

Collect the coefficients of a symbolic expression.

syms x coeffs = collect((exp(x) + x)*(x + 2))

coeffs = x^2 + (exp(x) + 2)*x + 2*exp(x)

Because you did not specify the variable, `collect`

uses the default variable defined by `symvar`

.
For this expression, the default variable is
`x`

.

symvar((exp(x) + x)*(x + 2),1)

ans = x

### Collect Coefficients of Powers of a Particular Variable

Collect coefficients of a particular variable
by specifying the variable as the second argument to
`collect`

.

Collect coefficients of an expression in powers of
`x`

, and then in powers of
`y`

.

syms x y coeffs_x = collect(x^2*y + y*x - x^2 - 2*x,x) coeffs_y = collect(x^2*y + y*x - x^2 - 2*x,y)

coeffs_x = (y - 1)*x^2 + (y - 2)*x coeffs_y = (x^2 + x)*y - x^2 - 2*x

Collect coefficients in powers of both `x`

and
`y`

by specifying the second argument as a
vector of variables.

syms a b coeffs_xy = collect(a^2*x*y + a*b*x^2 + a*x*y + x^2,[x y])

coeffs_xy = (a*b + 1)*x^2 + (a^2 + a)*x*y

### Collect Coefficients in Terms of `i`

and `pi`

Collect coefficients of an expression in terms of
`i`

, and then in terms of
`pi`

.

syms x y coeffs_i = collect(2*x*i - 3*i*y,i) coeffs_pi = collect(x*pi*(pi - y) + x*(pi + i) + 3*pi*y,pi)

coeffs_i = (2*x - 3*y)*1i coeffs_pi = x*pi^2 + (x + 3*y - x*y)*pi + x*1i

### Collect Coefficients of Symbolic Expressions and Functions

Collect coefficients of expressions and functions by specifying the second argument as an expression or function. Collect coefficients of multiple expressions or functions by using vector input.

Expand `sin(x + 3*y)`

and collect coefficients of
`cos(y)`

, and then of both
`sin(x)`

and
`sin(y)`

.

syms x y f = expand(sin(x + 3*y)); coeffs_cosy = collect(f,cos(y))

coeffs_cosy = 4*sin(x)*cos(y)^3 + 4*cos(x)*sin(y)*cos(y)^2 + (-3*sin(x))*cos(y) - cos(x)*sin(y)

coeffs_sinxsiny = collect(f,[sin(x) sin(y)])

coeffs_sinxsiny = (4*cos(y)^3 - 3*cos(y))*sin(x) + (4*cos(x)*cos(y)^2 - cos(x))*sin(y)

Collect coefficients of the symbolic function `y(x)`

in a symbolic expression.

syms y(x) f = y^2*x + y*x^2 + y*sin(x) + x*y; coeffs_y = collect(f,y)

coeffs_y(x) = x*y(x)^2 + (x + sin(x) + x^2)*y(x)

### Collect Coefficients for Each Element of Matrix

Call `collect`

on a matrix.
`collect`

acts element-wise on the
matrix.

syms x y collect([(x + 1)*(y + 1), x^2 + x*(x -y); 2*x*y - x, x*y + x/y], x)

ans = [ (y + 1)*x + y + 1, 2*x^2 - y*x] [ (2*y - 1)*x, (y + 1/y)*x]

### Collect Coefficients of Function Calls

Collect coefficients of calls to a particular function by specifying the function name as the second argument. Collect coefficients of function calls with respect to multiple functions by specifying the multiple functions as a cell array of character vectors.

Collect coefficients of calls to the `sin`

function
in `F`

, where `F`

contains
multiple calls to different functions.

syms a b c d e f x F = a*sin(2*x) + b*sin(2*x) + c*cos(x) + d*cos(x) + e*sin(3*x) + f*sin(3*x); collect(F,'sin')

ans = (a + b)*sin(2*x) + (e + f)*sin(3*x) + c*cos(x) + d*cos(x)

Collect coefficients of calls to both the `sin`

and
`cos`

functions in
`F`

.

collect(F,{'sin' 'cos'})

ans = (a + b)*sin(2*x) + (e + f)*sin(3*x) + (c + d)*cos(x)

## Input Arguments

## Tips

`collect`

returns an output that is syntactically different from the input expression (although the input and output expressions might look the same). For this reason, functions like`isequal`

might not return`true`

when checking for equality. Instead, use`isAlways`

to prove equivalence between the input and output expressions.

## Version History

**Introduced before R2006a**