The AreSame method checks if the two LHPDE objects obj1 and obj2 are the same.

This methods returns true if obj1 and obj2 are the same, in the sense they match the following criteria:

criterion = "sameSystem" -- they are identical meaning that they have same independent variables, same dependent variables (with same dependencies) and same system of DEs.

criterion = "sameOperator" -- they have the same operator. That is, LHPDO(obj1) matches LHPDO(obj2) apart from the ordering of DEs. See examples below.

criterion = "sameSolutions" -- they have the same solutions.

The default criterion is "sameOperator". That is, AreSame(obj1, obj2) is equivalent to AreSame(obj1, obj2, criteria = "sameOperator").

In the second calling sequence, the word criterion is provided as alias for criteria.

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

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

$\mathrm{E2}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\,y\right)=0\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,x\right)=-\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\right)\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,y\right)=0\,\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,x\right)=0\right]\,\mathrm{indep}=\left[x\,y\right]\,\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]\right)$

$\mathrm{E2}≔\left[\frac{{\partial }^2}{\partial y^2}\mathrm{\xi }\left(x\,y\right)=0\,\frac{\partial }{\partial x}\mathrm{\eta }\left(x\,y\right)=-\frac{\partial }{\partial y}\mathrm{\xi }\left(x\,y\right)\,\frac{\partial }{\partial y}\mathrm{\eta }\left(x\,y\right)=0\,\frac{\partial }{\partial x}\mathrm{\xi }\left(x\,y\right)=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\left(x\,y\right)\,\mathrm{\eta }\left(x\,y\right)\right]$

$\mathrm{E2p}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\alpha }\left(x\,y\right)\,y\,y\right)=0\,\mathrm{diff}\left(\mathrm{\beta }\left(x\right)\,x\right)=-\mathrm{diff}\left(\mathrm{\alpha }\left(x\,y\right)\,y\right)\,\mathrm{diff}\left(\mathrm{\alpha }\left(x\,y\right)\,x\right)=0\right]\,\mathrm{indep}=\left[x\,y\right]\,\mathrm{dep}=\left[\mathrm{\alpha }\,\mathrm{\beta }\right]\right)$

$\mathrm{E2p}≔\left[\frac{{\partial }^2}{\partial y^2}\mathrm{\alpha }\left(x\,y\right)=0\,\frac{\ⅆ}{\ⅆx}\mathrm{\beta }\left(x\right)=-\frac{\partial }{\partial y}\mathrm{\alpha }\left(x\,y\right)\,\frac{\partial }{\partial x}\mathrm{\alpha }\left(x\,y\right)=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\alpha }\left(x\,y\right)\,\mathrm{\beta }\left(x\right)\right]$

$\mathrm{AreSame}\left(\mathrm{E2}\,\mathrm{E2p}\right)$

$\mathrm{true}$

$\mathrm{\Delta }≔\mathrm{convert}\left(\mathrm{E2}\,'\mathrm{LHPDO}'\right)$

$\mathrm{\Delta }≔\left(\mathrm{\ξ}\,\mathrm{\η}\right)\→\left[\frac{\partial }{\partial y}\left(\frac{\partial }{\partial y}\mathrm{\ξ}\right)\,\frac{\partial }{\partial x}\mathrm{\η}\+\frac{\partial }{\partial y}\mathrm{\ξ}\,\frac{\partial }{\partial y}\mathrm{\η}\,\frac{\partial }{\partial x}\mathrm{\ξ}\right]$

$\mathrm{\Δ1}≔\mathrm{convert}\left(\mathrm{E2p}\,'\mathrm{LHPDO}'\right)$

$\mathrm{\Δ1}≔\left(\mathrm{\α}\,\mathrm{\β}\right)\→\left[\frac{\partial }{\partial y}\left(\frac{\partial }{\partial y}\mathrm{\α}\right)\,\frac{\partial }{\partial x}\mathrm{\β}\+\frac{\partial }{\partial y}\mathrm{\α}\,\frac{\partial }{\partial x}\mathrm{\α}\right]$

$\mathrm{AreSame}\left(\mathrm{E2}\,\mathrm{E2p}\,\mathrm{criterion}=''sameSystem''\right)$

$\mathrm{false}$

$\mathrm{AreSame}\left(\mathrm{E2}\,\mathrm{E2p}\,\mathrm{criteria}=''sameSolutions''\right)$

$\mathrm{true}$

The AreSame command was introduced in Maple 2020.

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