Let L be a LAVF object with $n$; infinitesimal variables and $k$; (or maybe none) constants of integration variables. Then the Copy method clones L and returns a new LAVF object with new infinitesimals and constants of integration variable names as given in vars. The new variable names vars will replace the ones from the object.

If vars is given as a list of names, then the number of entries in vars must be $n\+k$; (i.e. same as the number of dependent variables from the determining system of L) (see GetDependents).

If vars is given as one single name $\mathrm{\xi }$, then the new variables names will be ${\mathrm{\xi }}_1\,{\mathrm{\xi }}_2\,\dots \,{\mathrm{\xi }}_{n\+k}$.

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

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

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

$\mathrm{false}$

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

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

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

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

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

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

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

$\mathrm{Copy}\left(L\,\left[\mathrm{\alpha }\,\mathrm{\beta }\right]\right)$

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

$\mathrm{Lsol}≔\mathrm{LAVFSolve}\left(L\,\mathrm{output}=''lavf''\right)$

$\mathrm{Lsol}≔\left[\mathrm{\xi }\left(\frac{\ⅆ}{\ⅆx}\right)+\mathrm{\eta }\left(\frac{\ⅆ}{\ⅆy}\right)\right]\&where\left\{\left[\mathrm{\xi }=-\mathrm{c\_\_1}y+\mathrm{c\_\_3}\,\mathrm{\eta }=\mathrm{c\_\_1}x+\mathrm{c\_\_2}\right]\right\}$

$\mathrm{DQ}≔\mathrm{GetDeterminingSystem}\left(\mathrm{Lsol}\right)$

$\mathrm{DQ}≔\left[\mathrm{\xi }=-\mathrm{c\_\_1}y+\mathrm{c\_\_3}\,\mathrm{\eta }=\mathrm{c\_\_1}x+\mathrm{c\_\_2}\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\,\mathrm{c\_\_1}\,\mathrm{c\_\_2}\,\mathrm{c\_\_3}\right]$

$\mathrm{Copy}\left(\mathrm{Lsol}\,\left[\mathrm{\alpha }\,\mathrm{\beta }\,a\,b\,c\right]\right)$

$\left[\mathrm{\alpha }\left(\frac{\ⅆ}{\ⅆx}\right)+\mathrm{\beta }\left(\frac{\ⅆ}{\ⅆy}\right)\right]\&where\left\{\left[\mathrm{\alpha }=-ay+c\,\mathrm{\beta }=ax+b\right]\right\}$

$\mathrm{Copy}\left(\mathrm{Lsol}\,\mathrm{\phi }\right)$

$\left[{\mathrm{\phi }}_1\left(x\,y\right)\left(\frac{\ⅆ}{\ⅆx}\right)+{\mathrm{\phi }}_2\left(x\,y\right)\left(\frac{\ⅆ}{\ⅆy}\right)\right]\&where\left\{\left[{\mathrm{\phi }}_1\left(x\,y\right)=-y{\mathrm{\phi }}_3+{\mathrm{\phi }}_5\,{\mathrm{\phi }}_2\left(x\,y\right)=x{\mathrm{\phi }}_3+{\mathrm{\phi }}_4\right]\right\}$

The Copy command was introduced in Maple 2020.

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