 MultivariatePowerSeries/Divide - Maple Help

MultivariatePowerSeries

 Divide
 Divide two power series Calling Sequence a/b Divide(a, b) Parameters

 a - power series generated by this package b - power series generated by this package Description

 • The commands a/b and Divide(a,b) return the product of a by the inverse of b. The power series b is required to be  invertible, that is, b must have a non-zero constant term.
 • 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 two power series in the variables $x$, $y$, and $z$.

 > $a≔\mathrm{GeometricSeries}\left(\left[x,y\right]\right)$
 ${a}{≔}\left[{PowⅇrSⅇriⅇs of}\frac{{1}}{{1}{-}{x}{-}{y}}{:}{1}{+}{x}{+}{y}{+}{\dots }\right]$ (1)
 > $b≔\mathrm{PowerSeries}\left(1+x+y+z\right)$
 ${b}{≔}\left[{PowⅇrSⅇriⅇs:}{1}{+}{x}{+}{y}{+}{z}\right]$ (2)

We define the quotient of $a$ by $b$ in two equivalent ways.

 > $c≔\frac{a}{b}$
 ${c}{≔}\left[{PowⅇrSⅇriⅇs of}\frac{{1}}{\left({1}{-}{x}{-}{y}\right){}\left({1}{+}{x}{+}{y}{+}{z}\right)}{:}{1}{+}{\dots }\right]$ (3)
 > $d≔\mathrm{Divide}\left(a,b\right)$
 ${d}{≔}\left[{PowⅇrSⅇriⅇs of}\frac{{1}}{\left({1}{-}{x}{-}{y}\right){}\left({1}{+}{x}{+}{y}{+}{z}\right)}{:}{1}{+}{\dots }\right]$ (4)

We verify that the homogeneous parts of degree at most 20 of $c$ and $d$ are equal.

 > $\mathrm{ApproximatelyEqual}\left(c,d,20\right)$
 ${\mathrm{true}}$ (5) Compatibility

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