The coeff function extracts the coefficient of x^n in the polynomial p.

If the third argument is omitted, it is determined by looking at the second argument. Thus coeff(p, x^n) is equivalent to coeff(p, x, n) for n <> 0.

The cases of the second argument being a number or a product are disallowed since they do not make sense.

The related functions lcoeff, tcoeff, and coeffs extract the leading coefficient, trailing coefficient and all the coefficients of p in x respectively.

The coeff command is thread-safe as of Maple 15.

For more information on thread safety, see index/threadsafe.

$p≔2x^2+3y^3-5\&colon;$

$\mathrm{coeff}\left(p\&comma;x\&comma;2\right)$

$2$

$\mathrm{coeff}\left(p\&comma;x^2\right)$

$2$

$\mathrm{coeff}\left(p\&comma;x\&comma;0\right)$

$3y^3-5$

$\mathrm{coeff}\left(p\&comma;y^3\right)$

$3$

$r≔x^2+4x-6xy+9$

$r≔x^2-6xy+4x+9$

$\mathrm{coeff}\left(r\&comma;xy\right)$

Error, invalid input: coeff received x*y, which is not valid for its 2nd argument, x

$q≔3a{\left(x+1\right)}^2+\sin \left(a\right)x^{2}y-y^{2}x+x-a$

$q≔3a{\left(x+1\right)}^2+\sin \left(a\right)x^{2}y-y^{2}x+x-a$

$\mathrm{coeff}\left(q\&comma;x\right)$

$-y^2+6a+1$

$\mathrm{expand}\left(q\right)$

$3a{x}^2+6ax+2a+\sin \left(a\right)x^{2}y-y^{2}x+x$