The command GetCoefficient(p,m) returns the coefficient of p with respect to the multivariate monomial m. This coefficient is a complex number.

The command GetCoefficient(u,d) returns the coefficient of z^d in u, where z is the main variable of u. This coefficient is a power series.

When using the MultivariatePowerSeries package, do not assign anything to the variables occurring in the power series, Puiseux series, and univariate polynomials over these series. If you do, you may see invalid results.

$\mathrm{with}\left(\mathrm{MultivariatePowerSeries}\right)\:$

$a≔\mathrm{PowerSeries}\left(1+3x+7xy+4x^2\right)\:$

$\mathrm{GetCoefficient}\left(a\,x\right)$

$3$

$\mathrm{GetCoefficient}\left(a\,xy\right)$

$7$

$\mathrm{GetCoefficient}\left(a\,x{y}^2\right)$

$0$

$f≔\mathrm{UnivariatePolynomialOverPowerSeries}\left(\left[\mathrm{PowerSeries}\left(x\right)\,\mathrm{PowerSeries}\left(y\right)\,\mathrm{GeometricSeries}\left(\left[x\,y\right]\right)\right]\,z\right)\:$

$\mathrm{GetCoefficient}\left(f\,0\right)$

$\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs:}x\right]$

$\mathrm{GetCoefficient}\left(f\,2\right)$

$\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs\; of}\frac{1}{1-x-y}\mathrm{:}1+x+y+\mathrm{\dots }\right]$

$g≔\mathrm{UnivariatePolynomialOverPuiseuxSeries}\left(\left[\mathrm{PuiseuxSeries}\left(1\right)\,\mathrm{PuiseuxSeries}\left(0\right)\,\mathrm{PuiseuxSeries}\left(x\,\left[x=x^{\frac{1}{3}}\right]\right)\,\mathrm{PuiseuxSeries}\left(y\,\left[y=y^{\frac{1}{2}}\right]\right)\,\mathrm{PuiseuxSeries}\left(\frac{x+y}{1+x+y}\,\left[x=x{y}^{\frac{1}{2}}\,y=x{y}^{-1}\right]\right)\right]\,z\right)$

$g≔\left[\mathrm{Univariat\ⅇPolynomialOv\ⅇrPuis\ⅇuxS\ⅇri\ⅇs:}\left(1\right)\mathrm{+}\left(0\right)z\mathrm{+}\left(x^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)z^2\mathrm{+}\left(\sqrt{y}\right)z^3\mathrm{+}\left(0+\mathrm{\dots }\right)z^4\right]$

$\mathrm{GetCoefficient}\left(f\,2\right)$

$\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs\; of}\frac{1}{1-x-y}\mathrm{:}1+x+y+\mathrm{\dots }\right]$

The MultivariatePowerSeries[GetCoefficient] command was introduced in Maple 2021.

For more information on Maple 2021 changes, see Updates in Maple 2021.