SolutionDimension - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

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 SolutionDimension( obj) IsFiniteType( obj) IsTrivial( obj)

Parameters

 obj - a LHPDE object that is in rif-Reduced from.

Description

 • The SolutionDimension method calculates the solution dimension of a LHPDE object. It returns $\mathrm{\infty }$ if the solution dimension is not finite.
 • Let S be a LHPDE object. Then IsFiniteType(S) returns true if and only if SolutionDimension(S) $\ne \mathrm{\infty }$.
 • 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.

Examples

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

 > $S≔\mathrm{LHPDE}\left(\left[\frac{{\partial }^{2}}{\partial {y}^{2}}\mathrm{ξ}\left(x,y\right)=0,\frac{\partial }{\partial x}\mathrm{η}\left(x,y\right)=-\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right),\frac{\partial }{\partial y}\mathrm{η}\left(x,y\right)=0,\frac{\partial }{\partial x}\mathrm{ξ}\left(x,y\right)=0\right],\mathrm{indep}=\left[x,y\right],\mathrm{dep}=\left[\mathrm{ξ}\left(x,y\right),\mathrm{η}\left(x,y\right)\right],\mathrm{inRifReducedForm}=\mathrm{true}\right)$
 ${S}{≔}\left[\frac{{{\partial }}^{{2}}}{{\partial }{{y}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\eta }}{}\left({x}{,}{y}\right){=}{-}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({x}{,}{y}\right){,}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\eta }}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({x}{,}{y}\right){=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\xi }}{}\left({x}{,}{y}\right){,}{\mathrm{\eta }}{}\left({x}{,}{y}\right)\right]$ (1)
 > $\mathrm{SolutionDimension}\left(S\right)$
 ${3}$ (2)

The system S is of finite type but not trivial:

 > $\mathrm{IsFiniteType}\left(S\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{IsTrivial}\left(S\right)$
 ${\mathrm{false}}$ (4)

Compatibility

 • The SolutionDimension, IsFiniteType and IsTrivial commands were introduced in Maple 2020.
 • For more information on Maple 2020 changes, see Updates in Maple 2020.