GetIDBasis - Maple Help

GetIDBasis

get initial data basis as an IDBasis object from a LHPDE object

SetIDBasis

set initial data basis as an IDBasis object in a LHPDE object

 Calling Sequence GetIDBasis( obj) SetIDBasis( obj, B)

Parameters

 obj - a LHPDE object. B - a IDBasis object.

Description

 • The GetIDBasis method returns the initial data basis as an IDBasis object for a LHPDE object.
 • The SetIDBasis method sets the IDBasis object in a LHPDE object.
 • To set an initial data basis in a LHPDE object, constructing an IDBasis object is required. See LieAlgebrasOfVectorFields[IDBasis] for more detail.
 • For an IDBasis object to be eligible to be set in a LHPDE object, their parametric derivatives must be the same. See example below.
 • These methods are associated with the LHPDE and IDBasis objects. For more detail, see Overview of the LHPDE object and Overview of the IDBasis object.

Examples

 > $\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right):$
 > $\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{userep}=\mathrm{true}\right):$
 > $\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left[\mathrm{ξ}\left(x,y\right),\mathrm{η}\left(x,y\right)\right]\right):$
 > $\mathrm{E2}≔\mathrm{LHPDE}\left(\left[\frac{{\partial }^{2}}{\partial {y}^{2}}\mathrm{ξ}\left(x,y\right)=0,\frac{\partial }{\partial x}\mathrm{η}\left(x,y\right)=-\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right),\frac{\partial }{\partial y}\mathrm{η}\left(x,y\right)=0,\frac{\partial }{\partial x}\mathrm{ξ}\left(x,y\right)=0\right],\mathrm{indep}=\left[x,y\right],\mathrm{dep}=\left[\mathrm{ξ},\mathrm{η}\right]\right)$
 ${\mathrm{E2}}{≔}\left[{{\mathrm{\xi }}}_{{y}{,}{y}}{=}{0}{,}{{\mathrm{\eta }}}_{{x}}{=}{-}{{\mathrm{\xi }}}_{{y}}{,}{{\mathrm{\eta }}}_{{y}}{=}{0}{,}{{\mathrm{\xi }}}_{{x}}{=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\xi }}{,}{\mathrm{\eta }}\right]$ (1)
 > $B≔\mathrm{IDBasis}\left(\mathrm{E2},\left[\mathrm{ξ}\left(x,y\right)-y\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right),\mathrm{η}\left(x,y\right)-x\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right),-\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right)\right]\right)$
 ${B}{≔}\left[{\mathrm{\xi }}{-}{y}{}\left({{\mathrm{\xi }}}_{{y}}\right){,}{\mathrm{\eta }}{-}{x}{}\left({{\mathrm{\xi }}}_{{y}}\right){,}{-}{{\mathrm{\xi }}}_{{y}}\right]$ (2)

No initial data basis is set in E2 yet.

 > $\mathrm{GetIDBasis}\left(\mathrm{E2}\right)$
 ${\mathrm{FAIL}}$ (3)

Their parametric derivatives must be the same,

 > $\mathrm{GetParametricDerivatives}\left(B\right)$
 $\left[{\mathrm{\xi }}{,}{{\mathrm{\xi }}}_{{y}}{,}{\mathrm{\eta }}\right]$ (4)
 > $\mathrm{ParametricDerivatives}\left(\mathrm{E2}\right)$
 $\left[{\mathrm{\xi }}{,}{{\mathrm{\xi }}}_{{y}}{,}{\mathrm{\eta }}\right]$ (5)
 > $\mathrm{SetIDBasis}\left(\mathrm{E2},B\right)$
 $\left[{\mathrm{\xi }}{-}{y}{}\left({{\mathrm{\xi }}}_{{y}}\right){,}{\mathrm{\eta }}{-}{x}{}\left({{\mathrm{\xi }}}_{{y}}\right){,}{-}{{\mathrm{\xi }}}_{{y}}\right]$ (6)
 > $\mathrm{B1}≔\mathrm{GetIDBasis}\left(\mathrm{E2}\right)$
 ${\mathrm{B1}}{≔}\left[{\mathrm{\xi }}{-}{y}{}\left({{\mathrm{\xi }}}_{{y}}\right){,}{\mathrm{\eta }}{-}{x}{}\left({{\mathrm{\xi }}}_{{y}}\right){,}{-}{{\mathrm{\xi }}}_{{y}}\right]$ (7)
 > $\mathrm{type}\left(\mathrm{B1},'\mathrm{IDBasis}'\right)$
 ${\mathrm{true}}$ (8)

Compatibility

 • The GetIDBasis and SetIDBasis commands were introduced in Maple 2020.