MultivariatePowerSeries/HomogeneousPart - Maple Help

MultivariatePowerSeries

 HomogeneousPart
 Compute the homogeneous part of a power series for a particular degree

 Calling Sequence HomogeneousPart(p, deg)

Parameters

 p - power series generated by this package deg - the degree of the requested homogeneous part

Description

 • 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 and univariate polynomials over power series. If you do, you may see invalid results.

Examples

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

We define a power series, $a$.

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

It is initially known to precision 1.

 > $\mathrm{Precision}\left(a\right)$
 ${1}$ (1)

We compute its homogeneous part of degree 3.

 > $\mathrm{HomogeneousPart}\left(a,3\right)$
 ${{x}}^{{3}}{+}{3}{}{{x}}^{{2}}{}{y}{+}{3}{}{{x}}^{{2}}{}{z}{+}{3}{}{x}{}{{y}}^{{2}}{+}{6}{}{x}{}{y}{}{z}{+}{3}{}{x}{}{{z}}^{{2}}{+}{{y}}^{{3}}{+}{3}{}{{y}}^{{2}}{}{z}{+}{3}{}{y}{}{{z}}^{{2}}{+}{{z}}^{{3}}$ (2)

The precision is now 3.

 > $\mathrm{Precision}\left(a\right)$
 ${3}$ (3)

Compatibility

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