Overview - Maple Help

Overview of the RationalNormalForms Package

 Calling Sequence RationalNormalForms[command](arguments) command(arguments)

Description

 • The RationalNormalForms package is used to solve the following problems:
 1 Construct the polynomial normal form of a rational function.
 2 Construct the rational canonical forms of a rational function.
 3 Construct a minimal representation of a hypergeometric term.
 • Each command in the RationalNormalForms package can be accessed by using either the long form or the short form of the command name in the command calling sequence.
 As the underlying implementation of the RationalNormalForms package is a module, it is also possible to use the form RationalNormalForms:-command to access a command from the package. For more information,  see Module Members.

List of RationalNormalForms Package Commands

 The following is a list of available commands.

 To display the help page for a particular RationalNormalForms command, see Getting Help with a Command in a Package.

Examples

 > $\mathrm{with}\left(\mathrm{RationalNormalForms}\right):$
 > $F≔\frac{\left({n}^{2}-1\right)\left(3n+1\right)!}{\left(n+3\right)!\left(2n+7\right)!}$
 ${F}{≔}\frac{\left({{n}}^{{2}}{-}{1}\right){}\left({3}{}{n}{+}{1}\right){!}}{\left({n}{+}{3}\right){!}{}\left({2}{}{n}{+}{7}\right){!}}$ (1)
 > $\mathrm{IsHypergeometricTerm}\left(F,n,'\mathrm{certificate}'\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{certificate}$
 $\frac{{3}{}\left({3}{}{n}{+}{2}\right){}\left({3}{}{n}{+}{4}\right){}{n}{}\left({n}{+}{2}\right)}{{2}{}\left({2}{}{n}{+}{9}\right){}{\left({n}{+}{4}\right)}^{{2}}{}\left({n}{-}{1}\right)}$ (3)
 > $z,r,s,u,v≔\mathrm{RationalCanonicalForm}\left[1\right]\left(\mathrm{certificate},n\right)$
 ${z}{,}{r}{,}{s}{,}{u}{,}{v}{≔}\frac{{27}}{{4}}{,}\left({n}{+}\frac{{2}}{{3}}\right){}\left({n}{+}\frac{{4}}{{3}}\right){,}\left({n}{+}\frac{{9}}{{2}}\right){}\left({n}{+}{4}\right){,}{n}{-}{1}{,}\left({n}{+}{3}\right){}\left({n}{+}{2}\right)$ (4)
 > $\mathrm{MinimalRepresentation}\left[1\right]\left(F,n,k\right)$
 $\frac{{\left(\frac{{27}}{{4}}\right)}^{{n}}{}\left({n}{-}{1}\right){}\left({\prod }_{{k}{=}{2}}^{{n}{-}{1}}{}\frac{\left({k}{+}\frac{{2}}{{3}}\right){}\left({k}{+}\frac{{4}}{{3}}\right)}{\left({k}{+}{4}\right){}\left({k}{+}\frac{{9}}{{2}}\right)}\right)}{{721710}{}\left({n}{+}{3}\right){}\left({n}{+}{2}\right)}$ (5)

References

 Abramov, S., and Petkovsek, M. "Canonical Representations of Hypergeometric Terms." FPSAC. 2000.