MultivariatePowerSeries/Precision - Maple Help

MultivariatePowerSeries

 Precision
 Get the current precision to which a power series is known

 Calling Sequence Precision(p)

Parameters

 p - power series generated by this package

Description

 • The command Precision(p) returns the precision of the power series p, that is, the degree up to which all the homogeneous parts of p have currently been computed.
 • The precision of a power series is updated as needed by calls to commands such as HomogeneousPart, Truncate, or UpdatePrecision.
 • 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.

Examples

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

We create a power series representing $\frac{1}{yz+2x+1}$. Its precision is initially low: Maple is lazy about computing the homogeneous components.

 > $a≔\frac{1}{\mathrm{PowerSeries}\left(1+2x+yz\right)}$
 ${a}{≔}\left[{PowⅇrSⅇriⅇs of}\frac{{1}}{{y}{}{z}{+}{2}{}{x}{+}{1}}{:}{1}{+}{\dots }\right]$ (1)
 > $\mathrm{Precision}\left(a\right)$
 ${0}$ (2)

Commands such as UpdatePrecision and HomogeneousPart change the precision of $a$.

 > $\mathrm{HomogeneousPart}\left(a,5\right)$
 ${-}{32}{}{{x}}^{{5}}{+}{32}{}{{x}}^{{3}}{}{y}{}{z}{-}{6}{}{x}{}{{y}}^{{2}}{}{{z}}^{{2}}$ (3)
 > $\mathrm{Precision}\left(a\right)$
 ${5}$ (4)
 > $\mathrm{UpdatePrecision}\left(a,10\right):$
 > $\mathrm{Precision}\left(a\right)$
 ${10}$ (5)

The precision of a power series is never lowered.

 > $\mathrm{UpdatePrecision}\left(a,5\right)$
 $\left[{PowⅇrSⅇriⅇs of}\frac{{1}}{{y}{}{z}{+}{2}{}{x}{+}{1}}{:}{1}{-}{2}{}{x}{+}{4}{}{{x}}^{{2}}{-}{y}{}{z}{-}{8}{}{{x}}^{{3}}{+}{4}{}{y}{}{z}{}{x}{+}{16}{}{{x}}^{{4}}{-}{12}{}{{x}}^{{2}}{}{y}{}{z}{+}{{y}}^{{2}}{}{{z}}^{{2}}{-}{32}{}{{x}}^{{5}}{+}{32}{}{{x}}^{{3}}{}{y}{}{z}{-}{6}{}{x}{}{{y}}^{{2}}{}{{z}}^{{2}}{+}{64}{}{{x}}^{{6}}{-}{80}{}{{x}}^{{4}}{}{y}{}{z}{+}{24}{}{{x}}^{{2}}{}{{y}}^{{2}}{}{{z}}^{{2}}{-}{{y}}^{{3}}{}{{z}}^{{3}}{-}{128}{}{{x}}^{{7}}{+}{192}{}{{x}}^{{5}}{}{y}{}{z}{-}{80}{}{{x}}^{{3}}{}{{y}}^{{2}}{}{{z}}^{{2}}{+}{8}{}{x}{}{{y}}^{{3}}{}{{z}}^{{3}}{+}{256}{}{{x}}^{{8}}{-}{448}{}{{x}}^{{6}}{}{y}{}{z}{+}{240}{}{{x}}^{{4}}{}{{y}}^{{2}}{}{{z}}^{{2}}{-}{40}{}{{x}}^{{2}}{}{{y}}^{{3}}{}{{z}}^{{3}}{+}{{y}}^{{4}}{}{{z}}^{{4}}{-}{512}{}{{x}}^{{9}}{+}{1024}{}{{x}}^{{7}}{}{y}{}{z}{-}{672}{}{{x}}^{{5}}{}{{y}}^{{2}}{}{{z}}^{{2}}{+}{160}{}{{x}}^{{3}}{}{{y}}^{{3}}{}{{z}}^{{3}}{-}{10}{}{x}{}{{y}}^{{4}}{}{{z}}^{{4}}{+}{1024}{}{{x}}^{{10}}{-}{2304}{}{{x}}^{{8}}{}{y}{}{z}{+}{1792}{}{{x}}^{{6}}{}{{y}}^{{2}}{}{{z}}^{{2}}{-}{560}{}{{x}}^{{4}}{}{{y}}^{{3}}{}{{z}}^{{3}}{+}{60}{}{{x}}^{{2}}{}{{y}}^{{4}}{}{{z}}^{{4}}{-}{{y}}^{{5}}{}{{z}}^{{5}}{+}{\dots }\right]$ (6)
 > $\mathrm{Precision}\left(a\right)$
 ${10}$ (7)

Compatibility

 • The MultivariatePowerSeries[Precision] command was introduced in Maple 2021.