The AdjustDependencies method adjusts dependencies in a LHPDE object. It returns a new LHPDE object with specified dependencies.

The call AdjustDependencies(obj, dep = "least") returns a new LHPDE object whose dependent variables have smallest possible dependencies on the independent variables of obj.

The call AdjustDependencies(obj, dep = "full") returns a new LHPDE object whose dependent variables depend on all the independent variables of obj.

If the optional argument dep =  vars is specified with vars being a list of functions or names then it represents new dependencies that are to be adjusted in a LHPDEs system.

The call AdjustDependencies(S) is equivalent to the call AdjustDependencies(S, dep = "least").

This method is associated with the LHPDE object. For more detail, see Overview of the LHPDE object.

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

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

$S≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\,y\right)=0\,\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,x\right)=0\,\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\right)=-\mathrm{diff}\left(\mathrm{\eta }\left(x\right)\,x\right)\right]\,\mathrm{indep}=\left[x\,y\right]\,\mathrm{dep}=\left[\mathrm{\xi }\left(x\,y\right)\,\mathrm{\eta }\left(x\right)\right]\right)$

$S≔\left[\frac{{\partial }^2}{\partial y^2}\mathrm{\xi }\left(x\,y\right)=0\,\frac{\partial }{\partial x}\mathrm{\xi }\left(x\,y\right)=0\,\frac{\partial }{\partial y}\mathrm{\xi }\left(x\,y\right)=-\frac{\ⅆ}{\ⅆx}\mathrm{\eta }\left(x\right)\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\left(x\,y\right)\,\mathrm{\eta }\left(x\right)\right]$

$\mathrm{S1}≔\mathrm{AdjustDependencies}\left(S\right)$

$\mathrm{S1}≔\left[\frac{{\ⅆ}^2}{\ⅆy^2}\mathrm{\xi }\left(y\right)=0\,\frac{\ⅆ}{\ⅆy}\mathrm{\xi }\left(y\right)=-\frac{\ⅆ}{\ⅆx}\mathrm{\eta }\left(x\right)\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\left(y\right)\,\mathrm{\eta }\left(x\right)\right]$

$\mathrm{AdjustDependencies}\left(S\,\mathrm{dep}=\left[\mathrm{\xi }\left(y\right)\right]\right)$

$\left[\frac{{\ⅆ}^2}{\ⅆy^2}\mathrm{\xi }\left(y\right)=0\,\frac{\ⅆ}{\ⅆy}\mathrm{\xi }\left(y\right)=-\frac{\ⅆ}{\ⅆx}\mathrm{\eta }\left(x\right)\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\left(y\right)\,\mathrm{\eta }\left(x\right)\right]$

$\mathrm{S2}≔\mathrm{AdjustDependencies}\left(S\,\mathrm{dep}=''full''\right)$

$\mathrm{S2}≔\left[\frac{{\partial }^2}{\partial y^2}\mathrm{\xi }\left(x\,y\right)=0\,\frac{\partial }{\partial x}\mathrm{\xi }\left(x\,y\right)=0\,\frac{\partial }{\partial y}\mathrm{\xi }\left(x\,y\right)=-\frac{\partial }{\partial x}\mathrm{\eta }\left(x\,y\right)\,\frac{\partial }{\partial y}\mathrm{\eta }\left(x\,y\right)=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\left(x\,y\right)\,\mathrm{\eta }\left(x\,y\right)\right]$

$\mathrm{S3}≔\mathrm{AdjustDependencies}\left(S\,\mathrm{dep}=\left[\mathrm{\xi }\left(y\right)\,\mathrm{\eta }\left(x\,y\right)\right]\right)$

$\mathrm{S3}≔\left[\frac{{\ⅆ}^2}{\ⅆy^2}\mathrm{\xi }\left(y\right)=0\,\frac{\ⅆ}{\ⅆy}\mathrm{\xi }\left(y\right)=-\frac{\partial }{\partial x}\mathrm{\eta }\left(x\,y\right)\,\frac{\partial }{\partial y}\mathrm{\eta }\left(x\,y\right)=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\left(y\right)\,\mathrm{\eta }\left(x\,y\right)\right]$

$\mathrm{AdjustDependencies}\left(S\,\mathrm{dep}=\left[\mathrm{\xi }\right]\right)$

Error, (in LieAlgebrasOfVectorFields:-LHPDE:-AdjustDependencies) invalid input: dependencies must be at least xi(y)

$\mathrm{AreSame}\left(S\,\mathrm{S1}\right)$

$\mathrm{true}$

$\mathrm{AreSame}\left(\mathrm{S1}\,\mathrm{S2}\right)$

$\mathrm{true}$

$\mathrm{AreSame}\left(\mathrm{S2}\,\mathrm{S3}\right)$

$\mathrm{true}$

The AdjustDependencies command was introduced in Maple 2020.

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