# coefficients

coefficients is used to extract coefficients in a polynomial.

### Syntax

```
[c,v] = coefficients(p,x)
```

### Examples

Define a polynomial in variables **x** and **y**, with coefficients parameterized by **s** and **t**.

```
sdpvar x y s t
p = x^2+x*y*(s+t)+s^2+t^2;
```

The coefficients are easily recovered

```
c = coefficients(p,[x y]);
sdisplay(c)
ans =
's^2+t^2'
's+t'
'1'
```

By adding a second output, the monomial basis is returned also.

```
[c,v] = coefficients(p,[x y]);
sdisplay([c v])
ans =
's^2+t^2' '1'
's+t' 'xy'
'1' 'x^2'
p-c'*v
ans =
0
```

Of course, we might just as well consider this to be a polynomial in s and t with coefficients parameterized by x and y.

```
[c,v] = coefficients(p,[s t]);
sdisplay([c v])
ans =
'x^2' '1'
'x*y' 't'
'1' 't^2'
'x*y' 's'
'1' 's^2'
```

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