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 RankElement(<min, max>, 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](...).

$\mathrm{with}\left(\mathrm{DifferentialAlgebra}\right)\&colon;$$\mathrm{with}\left(\mathrm{Tools}\right)\&colon;$

$R≔\mathrm{DifferentialRing}\left(\mathrm{derivations}=\left[x\&comma;y\right]\&comma;\mathrm{blocks}=\left[\left[v\&comma;u\right]\&comma;p\right]\&comma;\mathrm{parameters}=\left[p\right]\right)$

$R≔\mathrm{differential\_ring}$

$L≔\left[{u\left[x\right]}^2-4u\&comma;u\left[x,y\right]v\left[y\right]-u+p\&comma;v\left[x,x\right]-u\left[x\right]\right]\&colon;$

$\mathrm{RankElement}\left(\min \&comma;L\&comma;R\&comma;'\mathrm{pos}'\right)$

$u_x^2-4u$

$L\left[\mathrm{pos}\right]$

$u_x^2-4u$

$\mathrm{RankElement}\left(\max \&comma;L\&comma;R\&comma;'\mathrm{pos}'\right)$

$v_{x,x}-u_x$

$L\left[\mathrm{pos}\right]$

$v_{x,x}-u_x$

$\mathrm{RankElement}\left(\min \&comma;\mathrm{Get}\left(\mathrm{derivatives}\&comma;R\right)\&comma;R\right)$

$p$

$\mathrm{RankElement}\left(\max \&comma;\mathrm{Get}\left(\mathrm{derivatives}\&comma;R\right)\&comma;R\right)$

$v\left(x\&comma;y\right)$