SolutionDimension
calculate the solution dimension of a LHPDE object.
IsFiniteType
check if a LHPDE object is of finite type
IsTrivial
check if a LHPDE object has only the trivial solution
Calling Sequence
Parameters
Description
Examples
Compatibility
SolutionDimension( obj)
IsFiniteType( obj)
IsTrivial( obj)
obj
-
a LHPDE object that is in rif-Reduced from.
The SolutionDimension method calculates the solution dimension of a LHPDE object. It returns ∞ if the solution dimension is not finite.
Let S be a LHPDE object. Then IsFiniteType(S) returns true if and only if SolutionDimension(S) ≠∞.
Let S be a LHPDE object. Then IsTrivial(S) returns true if and only if SolutionDimension(S) =0.
These methods are associated with the LHPDE object. For more detail, see Overview of the LHPDE object.
withLieAlgebrasOfVectorFields:
S≔LHPDEdiffξx,y,y,y=0,diffηx,y,x=−diffξx,y,y,diffηx,y,y=0,diffξx,y,x=0,indep=x,y,dep=ξx,y,ηx,y,inRifReducedForm=true
S≔∂2∂y2ξx,y=0,∂∂xηx,y=−∂∂yξx,y,∂∂yηx,y=0,∂∂xξx,y=0,indep=x,y,dep=ξx,y,ηx,y
SolutionDimensionS
3
The system S is of finite type but not trivial:
IsFiniteTypeS
true
IsTrivialS
false
The SolutionDimension, IsFiniteType and IsTrivial commands were introduced in Maple 2020.
For more information on Maple 2020 changes, see Updates in Maple 2020.
See Also
LHPDE (Object overview)
LieAlgebrasOfVectorFields[LHPDE]
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