# coeffs

Coefficients of polynomial

## Description

`___ = coeffs(___,'All')`

returns all
coefficients, including coefficients that are 0. For example,
`coeffs(2*x^2,'All')`

returns `[ 2, 0, 0]`

instead of `2`

.

## Examples

### Coefficients of Univariate Polynomial

Find the coefficients of this univariate polynomial. The coefficients are ordered from the lowest degree to the highest degree.

syms x c = coeffs(16*x^2 + 19*x + 11)

c = [ 11, 19, 16]

Reverse the ordering of coefficients by using `fliplr`

.

c = fliplr(c)

c = [ 16, 19, 11]

### Coefficients of Multivariate Polynomial with Respect to Particular Variable

Find the coefficients of this polynomial with respect to
variable `x`

and variable `y`

.

syms x y cx = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, x) cy = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, y)

cx = [ 4*y^3, 3*y^2, 2*y, 1] cy = [ x^3, 2*x^2, 3*x, 4]

### Coefficients of Multivariate Polynomial with Respect to Two Variables

Find the coefficients of this polynomial with respect to both
variables `x`

and `y`

.

syms x y cxy = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, [x y]) cyx = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, [y x])

cxy = [ 4, 3, 2, 1] cyx = [ 1, 2, 3, 4]

### Coefficients and Corresponding Terms of Univariate Polynomial

Find the coefficients and the corresponding terms of this univariate polynomial. When two outputs are provided, the coefficients are ordered from the highest degree to the lowest degree.

syms x [c,t] = coeffs(16*x^2 + 19*x + 11)

c = [ 16, 19, 11] t = [ x^2, x, 1]

### Coefficients and Corresponding Terms of Multivariate Polynomial

Find the coefficients and the corresponding terms of this
polynomial with respect to variable `x`

and variable
`y`

.

syms x y [cx,tx] = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, x) [cy,ty] = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, y)

cx = [ 1, 2*y, 3*y^2, 4*y^3] tx = [ x^3, x^2, x, 1] cy = [ 4, 3*x, 2*x^2, x^3] ty = [ y^3, y^2, y, 1]

Find the coefficients of this polynomial with respect to both variables
`x`

and `y`

.

syms x y [cxy, txy] = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, [x,y]) [cyx, tyx] = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, [y,x])

cxy = [ 1, 2, 3, 4] txy = [ x^3, x^2*y, x*y^2, y^3] cyx = [ 4, 3, 2, 1] tyx = [ y^3, x*y^2, x^2*y, x^3]

### All Coefficients of Polynomial

Find all coefficients of a polynomial, including coefficients
that are `0`

, by specifying the option
`'All'`

. The returned coefficients are ordered from the highest
degree to the lowest degree.

Find all coefficients of 3*x*^{2}.

syms x c = coeffs(3*x^2, 'All')

c = [ 3, 0, 0]

If you find coefficients with respect to multiple variables and specify
`'All'`

, then `coeffs`

returns coefficients
for all combinations of the variables.

Find all coefficients and corresponding terms of *a**x*^{2} + *b**y*.

syms a b y [cxy, txy] = coeffs(a*x^2 + b*y, [y x], 'All')

cxy = [ 0, 0, b] [ a, 0, 0] txy = [ x^2*y, x*y, y] [ x^2, x, 1]

## Input Arguments

## Output Arguments

**Introduced before R2006a**