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DifferentialAlgebra[Tools]

 SortByRank
 sorts a list of differential polynomials

 Calling Sequence SortByRank(L,criterion,R,opts)

Parameters

 L - a list or a set of differential polynomials criterion - one of the keywords ascending or descending R - a differential polynomial ring or ideal 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 SortByRank(L,criterion,R) returns the list of the elements of L, sorted according to criterion. The leading ranks of the elements of L are compared. Leading ranks are taken with respect to the ranking of R, or its embedding ring, if R is an ideal.
 • This command is part of the DifferentialAlgebra:-Tools package. It can be called using the form SortByRank(...) after executing the command with(DifferentialAlgebra:-Tools). It can also be directly called using the form DifferentialAlgebra[Tools][SortByRank](...).

Examples

 > $\mathrm{with}\left(\mathrm{DifferentialAlgebra}\right):$$\mathrm{with}\left(\mathrm{Tools}\right):$
 > $R≔\mathrm{DifferentialRing}\left(\mathrm{derivations}=\left[t\right],\mathrm{blocks}=\left[u,v\right]\right)$
 ${R}{≔}{\mathrm{differential_ring}}$ (1)
 > $\mathrm{SortByRank}\left(\left[{u}_{t},3,{v}_{t,t},0,{t}^{2}+1\right],\mathrm{ascending},R\right)$
 $\left[{0}{,}{3}{,}{{t}}^{{2}}{+}{1}{,}{{v}}_{{t}{,}{t}}{,}{{u}}_{{t}}\right]$ (2)
 > $\mathrm{SortByRank}\left(\left[{u}_{t},3,{v}_{t,t},0,{t}^{2}+1\right],\mathrm{descending},R\right)$
 $\left[{{u}}_{{t}}{,}{{v}}_{{t}{,}{t}}{,}{{t}}^{{2}}{+}{1}{,}{3}{,}{0}\right]$ (3)