MultivariatePowerSeries/Degree - Maple Help

MultivariatePowerSeries

 Degree
 Degree a univariate polynomial over power series

 Calling Sequence Degree(u)

Parameters

 u - univariate polynomial over power series generated by this package

Description

 • Degree(u) returns the syntactic degree of the univariate polynomial over power series u with respect to its main variable. That is, it doesn't test whether the highest degree coefficient is nonzero (because this cannot be done in general); it just returns the highest degree coefficient of the main variable that is specified.
 • 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

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

This univariate polynomial over power series is quadratic in its main variable, $z$.

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

This univariate polynomial over power series is syntactically cubic in its main variable, $u$, but the coefficient of ${u}^{3}$ is 0.

 > $g≔\mathrm{UnivariatePolynomialOverPowerSeries}\left(\left[\mathrm{PowerSeries}\left(x\right),\mathrm{PowerSeries}\left(y\right),\mathrm{GeometricSeries}\left(\left[x\right]\right),\mathrm{PowerSeries}\left(0\right)\right],u\right):$
 > $\mathrm{Degree}\left(g\right)$
 ${3}$ (2)

Compatibility

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