get a coefficient of a power series or a univariate polynomial over power series or over Puiseux series
power series generated by this package
univariate polynomial over power series or over Puiseux series generated by this package
The command GetCoefficient(p,m) returns the coefficient of p with respect to the multivariate monomial m. This coefficient is a complex number.
The command GetCoefficient(u,d) returns the coefficient of z^d in u, where z is the main variable of u. This coefficient is a power series.
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.
We create a power series corresponding to a polynomial and find a few of its coefficients.
a ≔ PowerSeries⁡1+3⁢x+7⁢x⁢y+4⁢x2:
We create a univariate polynomial over power series with z as its main variable, corresponding to the expression x+y⁢z+z21−x−y.
f ≔ UnivariatePolynomialOverPowerSeries⁡PowerSeries⁡x,PowerSeries⁡y,GeometricSeries⁡x,y,z:
The coefficient of z0 is the power series corresponding to x.
The coefficient of z0 is the power series corresponding to 11−x−y.
PowⅇrSⅇrⅈⅇs of 11−x−y : 1+x+y+…
Create a univariate polynomial over power series from a list of Puiseux series.
g ≔ UnivariatePolynomialOverPuiseuxSeries⁡PuiseuxSeries⁡1,PuiseuxSeries⁡0,PuiseuxSeries⁡x,x=x13,PuiseuxSeries⁡y,y=y12,PuiseuxSeries⁡x+y1+x+y,x=x⁢y12,y=x⁢y−1,z
The MultivariatePowerSeries[GetCoefficient] command was introduced in Maple 2021.
For more information on Maple 2021 changes, see Updates in Maple 2021.
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