# coefficients

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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'