MultivariatePowerSeries/MainVariable - Maple Help

MultivariatePowerSeries

 MainVariable
 Get the polynomial variable of a univariate polynomial over power series

 Calling Sequence MainVariable(u)

Parameters

 u - univariate polynomial over power series generated by this package

Description

 • MainVariable(u) returns the polynomial variable of the univariate polynomial over power series u.
 • If u is considered as an element of $\mathrm{𝕂}⟦{x}_{1},\dots ,{x}_{n}⟧\left[y\right]$, then $y$ is the main variable.
 • 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 construct a univariate polynomial over power series in $\mathrm{𝕂}⟦x⟧\left[z\right]$. Its main variable is $z$.

 > $f≔\mathrm{UnivariatePolynomialOverPowerSeries}\left(\left(z-1\right)\left(z-2\right)\left(z-3\right)+x\left({z}^{2}+z\right),z\right):$
 > $\mathrm{MainVariable}\left(f\right)$
 ${z}$ (1)

We can view the same expression as an element of  $\mathrm{𝕂}⟦z⟧\left[x\right]$. Then its main variable is $x$.

 > $g≔\mathrm{UnivariatePolynomialOverPowerSeries}\left(\left(z-1\right)\left(z-2\right)\left(z-3\right)+x\left({z}^{2}+z\right),x\right):$
 > $\mathrm{MainVariable}\left(g\right)$
 ${x}$ (2)

We construct a univariate polynomial over power series in $\mathrm{𝕂}⟦x,y⟧\left[z\right]$. Its main variable is $z$.

 > $h≔\mathrm{UnivariatePolynomialOverPowerSeries}\left(\left[\mathrm{PowerSeries}\left(z\right),\mathrm{PowerSeries}\left(y\right),\mathrm{GeometricSeries}\left(\left[y,z\right]\right)\right],x\right):$
 > $\mathrm{MainVariable}\left(h\right)$
 ${x}$ (3)

Compatibility

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