The EliminationSystem command finds a LHPDE object that only contain some specific variables from a given LHPDEs system.

The command returns a LHPDE object that is in rif-reduced form (see IsRifReduced), and with varsToKeep as the dependent variables.

The command computes a differentially reduced form for the elimination module with respect to some specific variables, this is achieved by performing rif-reduce on a LHPDE object (see RifReduce) with a block ranking.

In the first sequence, the command is part of the LieAlgebrasOfVectorFields package. For more detail, see Overview of the LieAlgebrasOfVectorFields package.

This command can be used in the form LHPDE(...) only after executing the command with(LieAlgebrasOfVectorFields), but can always be used by executing LieAlgebrasOfVectorFields:-LHPDE(...).

The second calling sequence is an extension of the first, so that the command works for a LHPDE object. That is, a call EliminationSystem(obj, varsToKeep) is equivalent to EliminationSystem(GetSystem(obj), GetDependents(obj), varsToKeep, indep = GetIndependents(obj)).

In the second calling sequence, the method is associated with the LHPDE object. For more detail, see Overview of the LHPDE object.

$\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right)\:$

$\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{userep}=\mathrm{true}\right)\:$

$\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left\{\mathrm{\eta }\,\mathrm{\xi }\right\}\left(x\,y\right)\right)\:$

$\mathrm{DEs}≔\left[\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,x\right)=0\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,y\right)=0\,\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\right)+\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,x\right)=0\,\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\,y\right)=0\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,x\,x\right)=0\right]$

$\mathrm{DEs}≔\left[{\mathrm{\xi }}_x=0\,{\mathrm{\eta }}_y=0\,{\mathrm{\xi }}_y+{\mathrm{\eta }}_x=0\,{\mathrm{\xi }}_{y,y}=0\,{\mathrm{\eta }}_{x,x}=0\right]$

$\mathrm{EliminationSystem}\left(\mathrm{DEs}\,\left[\mathrm{\xi }\left(x\,y\right)\,\mathrm{\eta }\left(x\,y\right)\right]\,\left[\mathrm{\xi }\right]\right)$

$\left[{\mathrm{\xi }}_{y,y}=0\,{\mathrm{\xi }}_x=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\right]$

$S≔\mathrm{LHPDE}\left(\mathrm{DEs}\,\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]\,\mathrm{indep}=\left[x\,y\right]\right)$

$S≔\left[{\mathrm{\xi }}_x=0\,{\mathrm{\eta }}_y=0\,{\mathrm{\xi }}_y+{\mathrm{\eta }}_x=0\,{\mathrm{\xi }}_{y,y}=0\,{\mathrm{\eta }}_{x,x}=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]$

$\mathrm{EliminationSystem}\left(S\,\left[\mathrm{\xi }\right]\right)$

$\left[{\mathrm{\xi }}_{y,y}=0\,{\mathrm{\xi }}_x=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\right]$

The LieAlgebrasOfVectorFields[EliminationSystem] and EliminationSystem commands were introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.