The command Variables(p), where p is a power series object created by the MultivariatePowerSeries package, returns the variables occurring in p.

The command Variables(s), where s is a Puiseux series object created by the MultivariatePowerSeries package, returns the variables occurring in s.

The command Variables(u), where p is a univariate polynomial over power series or over Puiseux series created by the MultivariatePowerSeries package, returns the variables occurring in u (its main variable and the variables occurring in all coefficients).

Not every variable name returned by the Variables command needs to actually occur in p or u, however, every variable that occurs in p or u is returned by the Variables command.

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.

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

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

$a≔\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs:}1+x+x^2+xy\right]$

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

$\left\{x\,y\right\}$

bproc := proc(d) local s; s := 2*x + y; return expand(s^d); end proc:

$b≔\mathrm{PowerSeries}\left(\mathrm{bproc}\,\mathrm{variables}=\left\{x\,y\right\}\right)$

$b≔\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs:}1+\mathrm{\dots }\right]$

$\mathrm{Variables}\left(b\right)$

$\left\{x\,y\right\}$

$c≔\mathrm{PowerSeries}\left(d\mapsto \frac{x^d}{d!}\,\mathrm{analytic}=\exp \left(x\right)\right)$

$c≔\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs\; of}{\ⅇ}^x\mathrm{:}1+\mathrm{\dots }\right]$

$\mathrm{Variables}\left(c\right)$

$\left\{x\right\}$

$d≔c\mathrm{Inverse}\left(c\right)$

$d≔\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs:}1\right]$

$\mathrm{Variables}\left(d\right)$

$\left\{x\right\}$

$u≔\mathrm{UnivariatePolynomialOverPowerSeries}\left(\left[a\,b\,c\right]\,z\right)$

$u≔\left[\mathrm{Univariat\ⅇPolynomialOv\ⅇrPow\ⅇrS\ⅇri\ⅇs:}\left(1+x+x^2+xy\right)\mathrm{+}\left(1+\mathrm{\dots }\right)z\mathrm{+}\left(1+\mathrm{\dots }\right)z^2\right]$

$\mathrm{Variables}\left(u\right)$

$\left\{x\,y\,z\right\}$

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

$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]$

$\mathrm{Variables}\left(g\right)$

$\left\{x\,y\,z\right\}$

$s≔\mathrm{PuiseuxSeries}\left(\frac{x+y}{1+x+y}\,\left[x=x{y}^{\frac{1}{2}}\,y=x{y}^{-1}\right]\right)$

$s≔\left[\mathrm{Puis\ⅇuxS\ⅇri\ⅇs\; of}\frac{x\sqrt{y}+\frac{x}{y}}{1+x\sqrt{y}+\frac{x}{y}}\mathrm{:}0+\mathrm{\dots }\right]$

$\mathrm{Variables}\left(s\right)$

$\left\{x\,y\right\}$

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

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

The MultivariatePowerSeries[Variables] command was updated in Maple 2023.