Copy(p), Copy(s), and Copy(u) return copies of p, s, and u, respectively. If the original object is subsequently modified (for example, by computing extra coefficients, or modifying the display style), these changes are not reflected in the copy, and vice versa. Note that the original object and its copy may share ancestors, such as power series or Puiseux series objects from which they were computed.

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.

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

$a≔\mathrm{Inverse}\left(\mathrm{PowerSeries}\left(1+x-y\right)\right)\:$

$b≔\mathrm{Inverse}\left(\mathrm{PowerSeries}\left(y^2-x+1\right)\right)\:$

$c≔a+b$

$c≔\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs\; of}\frac{1}{1+x-y}+\frac{1}{y^2-x+1}\mathrm{:}2+\mathrm{\dots }\right]$

$d≔\mathrm{Copy}\left(c\right)$

$d≔\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs\; of}\frac{1}{1+x-y}+\frac{1}{y^2-x+1}\mathrm{:}2+\mathrm{\dots }\right]$

$\mathrm{SetDisplayStyle}\left(c\,\left['\mathrm{precision}'=7\right]\right)$

$\left[\mathrm{precision}=7\right]$

$\mathrm{SetDisplayStyle}\left(d\,\left['\mathrm{precision}'=4\right]\right)$

$\left[\mathrm{precision}=4\right]$

$\mathrm{UpdatePrecision}\left(c\,7\right)\:$$\mathrm{UpdatePrecision}\left(d\,7\right)\:$

$c$

$\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs\; of}\frac{1}{1+x-y}+\frac{1}{y^2-x+1}\mathrm{:}2+y+2x^2-2xy+3x^{2}y-5y^{2}x+y^3+2x^4-4x^{3}y+3x^2{y}^2-4x{y}^3+2y^4+5x^{4}y-14x^3{y}^2+10x^2{y}^3-2x{y}^4+y^5+2x^6-6x^{5}y+10x^4{y}^2-20x^3{y}^3+21x^2{y}^4-6x{y}^5+7x^{6}y-27x^5{y}^2+35x^4{y}^3-25x^3{y}^4+21x^2{y}^5-11x{y}^6+y^7+\mathrm{\dots }\right]$

$d$

$\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs\; of}\frac{1}{1+x-y}+\frac{1}{y^2-x+1}\mathrm{:}2+y+2x^2-2xy+3x^{2}y-5y^{2}x+y^3+2x^4-4x^{3}y+3x^2{y}^2-4x{y}^3+2y^4+\mathrm{\dots }\right]$

$\mathrm{gc}\left(\right)\:$

$\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{HomogeneousPart}\left(c\,500\right)\right)\:$

memory used=143.59MiB, alloc change=108.62MiB, cpu time=1.60s, real time=1.52s, gc time=216.32ms

$\mathrm{Precision}\left(a\right)$

$500$

$\mathrm{Precision}\left(b\right)$

$500$

$\mathrm{Precision}\left(c\right)$

$500$

$\mathrm{Precision}\left(d\right)$

$7$

$\mathrm{gc}\left(\right)\:$

$\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{HomogeneousPart}\left(d\,500\right)\right)\:$

memory used=6.70MiB, alloc change=0 bytes, cpu time=22.00ms, real time=23.00ms, gc time=0ns

$\mathrm{Precision}\left(d\right)$

$500$

Monforte, A.A., & Kauers, M. "Formal Laurent series in several variables." Expositiones Mathematicae. Vol. 31 No. 4 (2013): 350-367.

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

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

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