Documentation

# coeffs

Coefficients of polynomial

## Syntax

``C = coeffs(p)``
``C = coeffs(p,var)``
``C = coeffs(p,vars)``
``````[C,T] = coeffs(___)``````
``___ = coeffs(___,'All')``

## Description

example

````C = coeffs(p)` returns coefficients of the polynomial `p` with respect to all variables determined in `p` by `symvar`.```

example

````C = coeffs(p,var)` returns coefficients of the polynomial `p` with respect to the variable `var`.```

example

````C = coeffs(p,vars)` returns coefficients of the multivariate polynomial `p` with respect to the variables `vars`.```

example

``````[C,T] = coeffs(___)``` returns the coefficient `C` and the corresponding terms `T` of the polynomial `p`.```
````___ = 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 3x2.

```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 ax2 + by.

```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

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Polynomial, specified as a symbolic expression or function.

Polynomial variable, specified as a symbolic variable.

Polynomial variables, specified as a vector of symbolic variables.

## Output Arguments

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Coefficients of polynomial, returned as a symbolic number, variable, expression, vector, matrix, or multidimensional array. If there is only one coefficient and one corresponding term, then `C` is returned as a scalar.

Terms of polynomial, returned as a symbolic number, variable, expression, vector, matrix, or multidimensional array. If there is only one coefficient and one corresponding term, then `T` is returned as a scalar.