The command DisplayStructure(...) displays the structure constants of a LAVF object L as with respect to L's current initial data basis, formatted as a commutator table with the second input argument u as the printed name(s).

The second calling sequence gives alternative way to display the structure constants from the input argument C directly, without needed to know which LAVF object is C from. The structure constants of a LAVF object L can be got by calling StructureConstants(L).

If the second input argument u is a name,then the basis of solution vector fields are printed as $X_1\,X_2\,\dots \,X_r$ where $r$ is the dimension of the Lie algebra. If $u$ is provided as list of names $\left[A\,B\,C\,\dots \right]$ then these will be taken as names of basis elements. The number of entries in the list must be equivalent to $r$.

By specifying the option format = "commutatorList" or "cartan", the structure constants cijk can be displayed as commutator lists or cartan format respectively,

This command is part of the LieAlgebrasOfVectorFields package. For more detail, see Overview of the LieAlgebrasOfVectorFields package.

This command can be used in the form DisplayStructure(...) only after executing the command with(LieAlgebrasOfVectorFields), but can always be used in the form :-LieAlgebrasOfVectorFields:-DisplayStructure(...).

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

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

$\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left[\mathrm{\xi }\left(x\,y\right)\,\mathrm{\eta }\left(x\,y\right)\right]\right)\:$

$V≔\mathrm{VectorField}\left(\mathrm{\xi }\left(x\,y\right)\mathrm{D}\left[x\right]+\mathrm{\eta }\left(x\,y\right)\mathrm{D}\left[y\right]\,\mathrm{space}=\left[x\,y\right]\right)$

$V≔\mathrm{\xi }\left(\frac{\ⅆ}{\ⅆx}\right)+\mathrm{\eta }\left(\frac{\ⅆ}{\ⅆy}\right)$

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

$\mathrm{E2}≔\left[{\mathrm{\xi }}_{y,y}=0\,{\mathrm{\eta }}_x=-{\mathrm{\xi }}_y\,{\mathrm{\eta }}_y=0\,{\mathrm{\xi }}_x=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]$

$L≔\mathrm{LAVF}\left(V\,\mathrm{E2}\right)$

$L≔\left[\mathrm{\xi }\left(\frac{\ⅆ}{\ⅆx}\right)+\mathrm{\eta }\left(\frac{\ⅆ}{\ⅆy}\right)\right]\&where\left\{\left[{\mathrm{\xi }}_{y,y}=0\,{\mathrm{\xi }}_x=0\,{\mathrm{\eta }}_x=-{\mathrm{\xi }}_y\,{\mathrm{\eta }}_y=0\right]\right\}$

$\mathrm{DisplayStructure}\left(L\,'X'\right)$

$\left[\begin{array}{ccc}0& 0& X_2\\ 0& 0& -X_1\\ -X_2& X_1& 0\end{array}\right]$

$\mathrm{Cijk}≔\mathrm{StructureConstants}\left(L\right)$

$\mathrm{DisplayStructure}\left(\mathrm{Cijk}\,'X'\right)$

$\left[\begin{array}{ccc}0& 0& X_2\\ 0& 0& -X_1\\ -X_2& X_1& 0\end{array}\right]$

$\mathrm{DisplayStructure}\left(\mathrm{Cijk}\,'X'\,\mathrm{format}=''commutatorList''\right)$

$\left[\left[X_1\,X_3\right]=X_2\,\left[X_2\,X_3\right]=-X_1\right]$

The LieAlgebrasOfVectorFields[DisplayStructure] command was introduced in Maple 2020.

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