 RankElement - Maple Help

DifferentialAlgebra[Tools]

 RankElement
 returns the element of minimal (or maximal) rank in a list Calling Sequence RankElement(minmax, L, R, pos, opts) Parameters

 minmax - the keyword min or max L - a non-empty list or a set of differential polynomials R - a differential polynomial ring or ideal pos(optional) - a name opts(optional) - a sequence of options Options

 • The opts arguments may contain one or more of the options below.
 • notation = jet, tjet, diff or Diff. Specifies the notation used for the result of the function call. If not specified, the notation of L is used.
 • memout = nonnegative. Specifies a memory limit, in MB, for the computation. Default is zero(no memory out). Description

 • The function call RankElement(, L, R, pos) returns the element of minimal or maximal rank  occurring in the list L. Ranks are compared with respect to the ranking of R, or its embedding polynomial ring, if R is an ideal. If pos is present, it is assigned the index of the element in L.
 • This command is part of the DifferentialAlgebra:-Tools package. It can be called using the form MinRankElement(...) after executing the command with(DifferentialAlgebra:-Tools). It can also be directly called using the form DifferentialAlgebra[MinRankElement](...). Examples

 > $\mathrm{with}\left(\mathrm{DifferentialAlgebra}\right):$$\mathrm{with}\left(\mathrm{Tools}\right):$
 > $R≔\mathrm{DifferentialRing}\left(\mathrm{derivations}=\left[x,y\right],\mathrm{blocks}=\left[\left[v,u\right],p\right],\mathrm{parameters}=\left[p\right]\right)$
 ${R}{≔}{\mathrm{differential_ring}}$ (1)
 > $L≔\left[{u\left[x\right]}^{2}-4u,u\left[x,y\right]v\left[y\right]-u+p,v\left[x,x\right]-u\left[x\right]\right]:$
 > $\mathrm{RankElement}\left(\mathrm{min},L,R,'\mathrm{pos}'\right)$
 ${{u}}_{{x}}^{{2}}{-}{4}{}{u}$ (2)
 > $L\left[\mathrm{pos}\right]$
 ${{u}}_{{x}}^{{2}}{-}{4}{}{u}$ (3)
 > $\mathrm{RankElement}\left(\mathrm{max},L,R,'\mathrm{pos}'\right)$
 ${{v}}_{{x}{,}{x}}{-}{{u}}_{{x}}$ (4)
 > $L\left[\mathrm{pos}\right]$
 ${{v}}_{{x}{,}{x}}{-}{{u}}_{{x}}$ (5)

The following command returns the lowest dependent variable of $R$,

 > $\mathrm{RankElement}\left(\mathrm{min},\mathrm{Get}\left(\mathrm{derivatives},R\right),R\right)$
 ${p}$ (6)

The following command returns the highest dependent variable of $R$,

 > $\mathrm{RankElement}\left(\mathrm{max},\mathrm{Get}\left(\mathrm{derivatives},R\right),R\right)$
 ${v}{}\left({x}{,}{y}\right)$ (7)