The commands -p and Negate(p) return the additive inverse of the power series p.

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 and univariate polynomials over power series. If you do, you may see invalid results.

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

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

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

$b≔-a$

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

$c≔\mathrm{Negate}\left(a\right)$

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

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

$\mathrm{true}$

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

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

$g≔-f$

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

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

$\mathrm{true}$

The MultivariatePowerSeries[Negate] command was introduced in Maple 2021.

For more information on Maple 2021 changes, see Updates in Maple 2021.