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.

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

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

$\mathrm{MainVariable}\left(f\right)$

$z$

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

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

$x$

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

$\mathrm{MainVariable}\left(h\right)$

$x$

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

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