negate a power series or a Puiseux series or a univariate polynomial over power series or over Puiseux series
power series generated by this package
Puiseux series generated by this package
univariate polynomial over power series or over Puiseux series generated by this package
The commands -p and Negate(p) return the additive inverse of the power series p.
The commands -s and Negate(s) return the additive inverse of the Puiseux series s.
The commands -u and Negate(u) return the additive inverse of the univariate polynomial over power series u.
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 and form its additive inverse in two ways.
a ≔ GeometricSeries⁡x,y,z
a≔PowⅇrSⅇrⅈⅇs of 11−x−y−z : 1+x+y+z+…
b ≔ −a
b≔PowⅇrSⅇrⅈⅇs of −11−x−y−z : −1+…
c ≔ Negate⁡a
c≔PowⅇrSⅇrⅈⅇs of −11−x−y−z : −1−x−y−z+…
We verify that the results are the same up to homogeneous degree 10.
We create a univariate polynomial over power series and form its additive inverse.
f ≔ UnivariatePolynomialOverPowerSeries⁡z3−z2⁢x−2⁢x⁢y,z
g ≔ −f
The additive inverse of g should be equal to f.
Now we define a Puiseux series s and compute its additive inverse.
s ≔ PuiseuxSeries⁡x+y1+x+y,x=x⁢y12,y=x⁢y−1
s≔PuⅈsⅇuxSⅇrⅈⅇs of x⁢y+xy1+x⁢y+xy : 0+…
ns ≔ Negate⁡s
ns≔PuⅈsⅇuxSⅇrⅈⅇs of −x⁢y+xy1+x⁢y+xy : 0+…
Finally, we create a univariate polynomial over power series from a list of Puiseux series.
h ≔ 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
We compute -h.
nh ≔ Negate⁡h
The MultivariatePowerSeries[Negate] command was introduced in Maple 2021.
For more information on Maple 2021 changes, see Updates in Maple 2021.
The MultivariatePowerSeries[Negate] command was updated in Maple 2023.
Download Help Document
What kind of issue would you like to report? (Optional)