get the power series representing the sum of all monomials over a set of variables
list of variables
The command SumOfAllMonomials(x) returns the power series containing each monomial in the variables x with coefficient 1; that is, its homogeneous part of degree d is the sum of all monomials of degree d.
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 that is the sum of all monomials in x, and compute its homogeneous part of degree 2 and its truncation at precision 4.
a ≔ SumOfAllMonomials⁡x
a≔PowⅇrSⅇrⅈⅇs of 11−x : 1+x+…
We create a power series that is the sum of all monomials in x, y, and/or z. We compute its homogeneous part of degree 2 and its truncation at precision 3.
b ≔ SumOfAllMonomials⁡x,y,z
b≔PowⅇrSⅇrⅈⅇs of 11−x⁢1−y⁢1−z : 1+x+y+z+…
The MultivariatePowerSeries[SumOfAllMonomials] command was introduced in Maple 2021.
For more information on Maple 2021 changes, see Updates in Maple 2021.
Download Help Document