LieAlgebrasOfVectorFields[EliminationSystem]
construct a LHPDE object that only contain some specific variables from a given DEs system.
EliminationSystem
construct a LHPDE object that only contain some specific variables from a given LHPDE object
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Calling Sequence
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EliminationSystem(system, dvars, varsToKeep, indep = ivars)
EliminationSystem(obj, varsToKeep)
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Parameters
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system
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a list or set of linear homogeneous PDEs or ODEs
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dvars
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a list of dependent variables from the system, as functions or names
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varsToKeep
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a list of dependent variable names that are to be kept after elimination in the system
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ivars
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(optional) a list of independent variables from the system
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obj
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a LHPDE object
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Description
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The EliminationSystem command finds a LHPDE object that only contain some specific variables from a given LHPDEs system.
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The command returns a LHPDE object that is in rif-reduced form (see IsRifReduced), and with varsToKeep as the dependent variables.
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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.
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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(...).
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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)).
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Examples
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The variable eta is eliminated from the system. The system only contains xi.
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Similar output, but the input argument is now a LHPDE object.
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Compatibility
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The LieAlgebrasOfVectorFields[EliminationSystem] and EliminationSystem commands were introduced in Maple 2020.
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