The commands p - q and Subtract(p, q) return the difference of p and q.

The commands r - s and Subtract(r, s) return the difference of r and s. This can only be computed if the orders of r and s are compatible. See the Add help page for an explanation.

The commands u - v and Subtract(u, v) return the difference of u and v.

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.

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

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

$b≔\mathrm{PowerSeries}\left(1+x+y+z\right)\:$

$c≔a-b$

$c≔\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs\; of}\frac{1}{1-x-y}-1-x-y-z\mathrm{:}0+\mathrm{\dots }\right]$

$d≔\mathrm{Subtract}\left(a\,b\right)$

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

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

$\mathrm{true}$

$f≔\mathrm{UnivariatePolynomialOverPowerSeries}\left(xz+y{z}^2+xy{z}^3\,z\right)\:$

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

$h≔\mathrm{Subtract}\left(f\,g\right)$

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

$\mathrm{s1}≔\mathrm{PuiseuxSeries}\left(\mathrm{PowerSeries}\left(\frac{1}{1+u}\right)\,\left[u=x^{-\frac{1}{3}}{y}^2\right]\,\left[x=3\,y=-4\right]\right)$

$\mathrm{s1}≔\left[\mathrm{Puis\ⅇuxS\ⅇri\ⅇs\; of}\frac{x^3}{\left(1+\frac{y^2}{x^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}\right)y^4}\mathrm{:}\frac{x^3}{y^4}+\mathrm{\dots }\right]$

$\mathrm{s2}≔\mathrm{PuiseuxSeries}\left(2+2\left(u+v\right)\,\left[u=x^{-\frac{1}{2}}y\,v=y\right]\,\left[x=3\,y=2\right]\right)$

$\mathrm{s2}≔\left[\mathrm{Puis\ⅇuxS\ⅇri\ⅇs\; of}\left(2+\frac{2y}{\sqrt{x}}+2y\right)x^3{y}^2\mathrm{:}2x^3{y}^2+2x^{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{y}^3+2y^3{x}^3\right]$

$\mathrm{s3}≔\mathrm{PuiseuxSeries}\left(\mathrm{PowerSeries}\left(\frac{1}{1+uv}\right)\,\left[y\,x\right]\,\left[u\,v\right]\,\left[\left[1\,0\right]\,\left[1\,-\frac{1}{2}\right]\right]\right)$

$\mathrm{s3}≔\left[\mathrm{Puis\ⅇuxS\ⅇri\ⅇs\; of}\frac{1}{\frac{y^2}{\sqrt{x}}+1}\mathrm{:}1+\mathrm{\dots }\right]$

$\mathrm{Subtract}\left(\mathrm{s1}\,\mathrm{s2}\right)$

$\left[\mathrm{Puis\ⅇuxS\ⅇri\ⅇs\; of}\frac{\left(\frac{1}{1+\frac{y^2}{x^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}}+\left(-2\mathrm{\dots }-\mathrm{\dots }-2\right)y^6\right)x^3}{y^4}\mathrm{:}\frac{x^3}{y^4}+\mathrm{\dots }\right]$

$\mathrm{Subtract}\left(\mathrm{s1}\,\mathrm{s3}\right)$

Error, (in MultivariatePowerSeries:-Subtract) the order of Puiseux series [x, y] and [y, x] are not compatible

$\mathrm{GetPuiseuxSeriesOrder}\left(\mathrm{s1}\right)$

$\left[x\,y\right]$

$\mathrm{GetPuiseuxSeriesOrder}\left(\mathrm{s3}\right)$

$\left[y\,x\right]$

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

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

The MultivariatePowerSeries[Subtract] command was updated in Maple 2023.