The command HomogeneousPart(p,deg) returns the homogeneous part of p of degree deg, that is, the sum of all terms of p with total degree deg.

If deg is greater than the precision of p, calling this function has the side effect of updating the precision of p to be at least deg.

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.

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

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

$\mathrm{Precision}\left(a\right)$

$1$

$\mathrm{HomogeneousPart}\left(a\,3\right)$

$x^3+3x^{2}y+3x^{2}z+3x{y}^2+6xyz+3x{z}^2+y^3+3y^{2}z+3y{z}^2+z^3$

$\mathrm{Precision}\left(a\right)$

$3$

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

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