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.

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

$a≔\mathrm{GeometricSeries}\left(\left[x\,y\,z\right]\right)$

$a≔\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs\; of}\frac{1}{1-x-y-z}\mathrm{:}1+x+y+z+\mathrm{\dots }\right]$

$b≔-a$

$b≔\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs\; of}-\frac{1}{1-x-y-z}\mathrm{:}\mathrm{-1}+\mathrm{\dots }\right]$

$c≔\mathrm{Negate}\left(a\right)$

$c≔\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs\; of}-\frac{1}{1-x-y-z}\mathrm{:}\mathrm{-1}-x-y-z+\mathrm{\dots }\right]$

$\mathrm{ApproximatelyEqual}\left(b\,c\,10\right)$

$\mathrm{true}$

$f≔\mathrm{UnivariatePolynomialOverPowerSeries}\left(z^3-z^{2}x-2xy\,z\right)$

$f≔\left[\mathrm{Univariat\ⅇPolynomialOv\ⅇrPow\ⅇrS\ⅇri\ⅇs:}\left(-2xy\right)\mathrm{+}\left(0\right)z\mathrm{+}\left(-x\right)z^2\mathrm{+}\left(1\right)z^3\right]$

$g≔-f$

$g≔\left[\mathrm{Univariat\ⅇPolynomialOv\ⅇrPow\ⅇrS\ⅇri\ⅇs:}\left(0+\mathrm{\dots }\right)\mathrm{+}\left(0\right)z\mathrm{+}\left(0+\mathrm{\dots }\right)z^2\mathrm{+}\left(\mathrm{-1}\right)z^3\right]$

$\mathrm{ApproximatelyEqual}\left(f\,\mathrm{Negate}\left(g\right)\,10\right)$

$\mathrm{true}$

$s≔\mathrm{PuiseuxSeries}\left(\frac{x+y}{1+x+y}\,\left[x=x{y}^{\frac{1}{2}}\,y=x{y}^{-1}\right]\right)$

$s≔\left[\mathrm{Puis\ⅇuxS\ⅇri\ⅇs\; of}\frac{x\sqrt{y}+\frac{x}{y}}{1+x\sqrt{y}+\frac{x}{y}}\mathrm{:}0+\mathrm{\dots }\right]$

$\mathrm{ns}≔\mathrm{Negate}\left(s\right)$

$\mathrm{ns}≔\left[\mathrm{Puis\ⅇuxS\ⅇri\ⅇs\; of}-\frac{x\sqrt{y}+\frac{x}{y}}{1+x\sqrt{y}+\frac{x}{y}}\mathrm{:}0+\mathrm{\dots }\right]$

$\mathrm{Truncate}\left(s+\mathrm{ns}\,20\right)$

$0$

$h≔\mathrm{UnivariatePolynomialOverPuiseuxSeries}\left(\left[\mathrm{PuiseuxSeries}\left(1\right)\,\mathrm{PuiseuxSeries}\left(0\right)\,\mathrm{PuiseuxSeries}\left(x\,\left[x=x^{\frac{1}{3}}\right]\right)\,\mathrm{PuiseuxSeries}\left(y\,\left[y=y^{\frac{1}{2}}\right]\right)\,\mathrm{PuiseuxSeries}\left(\frac{x+y}{1+x+y}\,\left[x=x{y}^{\frac{1}{2}}\,y=x{y}^{-1}\right]\right)\right]\,z\right)$

$h≔\left[\mathrm{Univariat\ⅇPolynomialOv\ⅇrPuis\ⅇuxS\ⅇri\ⅇs:}\left(1\right)\mathrm{+}\left(0\right)z\mathrm{+}\left(x^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)z^2\mathrm{+}\left(\sqrt{y}\right)z^3\mathrm{+}\left(0+\mathrm{\dots }\right)z^4\right]$

$\mathrm{nh}≔\mathrm{Negate}\left(h\right)$

$\mathrm{nh}≔\left[\mathrm{Univariat\ⅇPolynomialOv\ⅇrPuis\ⅇuxS\ⅇri\ⅇs:}\left(\mathrm{-1}\right)\mathrm{+}\left(0\right)z\mathrm{+}\left(-x^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)z^2\mathrm{+}\left(-\sqrt{y}\right)z^3\mathrm{+}\left(0+\mathrm{\dots }\right)z^4\right]$

$\mathrm{Truncate}\left(h+\mathrm{nh}\,20\right)$

$0$

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.