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).

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](...).

$\mathrm{with}\left(\mathrm{DifferentialAlgebra}\right)\:$$\mathrm{with}\left(\mathrm{Tools}\right)\:$

$R≔\mathrm{DifferentialRing}\left(\mathrm{derivations}=\left[t\right]\,\mathrm{blocks}=\left[u\,v\right]\right)$

$R≔\mathrm{differential\_ring}$

$\mathrm{SortByRank}\left(\left[u\left[t\right]\,3\,v\left[t,t\right]\,0\,t^2+1\right]\,\mathrm{ascending}\,R\right)$

$\left[0\,3\,t^2+1\,v_{t,t}\,u_t\right]$

$\mathrm{SortByRank}\left(\left[u\left[t\right]\,3\,v\left[t,t\right]\,0\,t^2+1\right]\,\mathrm{descending}\,R\right)$

$\left[u_t\,v_{t,t}\,t^2+1\,3\,0\right]$