The coeffs function returns an expression sequence of all the coefficients of the polynomial p with respect to the indeterminate(s) x.

If x is not specified, coeffs computes the coefficients with respect to all the indeterminates of p (see the indets function).  If a third argument t is specified (call by name), it is assigned an expression sequence of the terms of p.  There is a one-to-one correspondence between the coefficients and the terms of p.

Note that p must be collected (collect) with respect to the appropriate indeterminates.  For multivariate polynomials, you may need to use collect with `distributed`.

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

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

$s≔3v^2{y}^2+2v{y}^3$

$s≔3v^2{y}^2+2v{y}^3$

$\mathrm{coeffs}\left(s\right)$

$3,2$

$\mathrm{coeffs}\left(s\,v\,'t'\right)$

$3y^2,2y^3$

$t$

$v^2,v$

$r≔-6x+3y+23x^2-4xyz+7z^2$

$r≔-4xyz+23x^2+7z^2-6x+3y$

$\mathrm{coeffs}\left(r\right)$

$\mathrm{-4},23,7,\mathrm{-6},3$

$\mathrm{coeffs}\left(r\,x\,'k'\right)$

$23,-4yz-6,7z^2+3y$

$k$

$x^2,x,1$

$u≔\left[\mathrm{coeffs}\left(x^2-y^2-1\,\left[x\,y\right]\,'l'\right)\right]$

$u≔\left[1\,\mathrm{-1}\,\mathrm{-1}\right]$

$\left[l\left[3\right]\,u\left[3\right]\right]$

$\left[1\,\mathrm{-1}\right]$

$p≔\left(c+a\right)x^2+\left(d+bx\right)y+ey+f\:$

$\mathrm{coeffs}\left(p\,\left[x\,y\right]\right)$

Error, invalid arguments to coeffs

$\mathrm{coeffs}\left(\mathrm{collect}\left(p\,\left[x\,y\right]\,'\mathrm{distributed}'\right)\,\left[x\,y\right]\right)$

$f,b,c+a,d+e$