divide two power series
power series generated by this package
The commands a/b and Divide(a,b) return the product of a by the inverse of b. The power series b is required to be invertible, that is, b must have a nonzero constant term.
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 define two power series in the variables x, y, and z.
a ≔ GeometricSeries⁡x,y
a≔PowⅇrSⅇrⅈⅇs of 11−x−y : 1+x+y+…
b ≔ PowerSeries⁡1+x+y+z
We define the quotient of a by b in two equivalent ways.
c ≔ ab
c≔PowⅇrSⅇrⅈⅇs of 11−x−y⁢1+x+y+z : 1+…
d ≔ Divide⁡a,b
d≔PowⅇrSⅇrⅈⅇs of 11−x−y⁢1+x+y+z : 1+…
We verify that the homogeneous parts of degree at most 20 of c and d are equal.
The MultivariatePowerSeries[Divide] command was introduced in Maple 2021.
For more information on Maple 2021 changes, see Updates in Maple 2021.
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