Copy - Maple Programming Help

Home : Support : Online Help : Mathematics : Differential Equations : Lie Symmetry Method : Commands for PDEs (and ODEs) : LieAlgebrasOfVectorFields : LHPDE : LieAlgebrasOfVectorFields/LHPDE/Copy

Copy

clone a LHPDE or a IDBasis object to have different dependent variable names

 Calling Sequence Copy( obj, vars) Copy( obj)

Parameters

 obj - a LHPDE or IDBasis object vars - a list of names as new dependent variable names

Description

 • The Copy method clones a LHPDE or a IDBasis object to have new dependent variable names. It returns a new LHPDE (respectively IDBasis) object.
 • The new dependent variable names vars will replace the ones from the object. The number of entries in vars must  be the same as the number of dependent variables from obj (see GetDependents).
 • In the second calling sequence, the method clones the object obj without changing the dependent variable names.
 • This method is associated with the LHPDE and IDBasis object. For more detail, see Overview of the LHPDE object and Overview of the IDBasis object.

Examples

 > $\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right):$
 > $S≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(y\right),y,y\right)=0,\mathrm{diff}\left(\mathrm{\eta }\left(x\right),x\right)=-\mathrm{diff}\left(\mathrm{\xi }\left(y\right),y\right)\right],\mathrm{indep}=\left[x,y\right],\mathrm{dep}=\left[\mathrm{\xi },\mathrm{\eta }\right]\right)$
 ${S}{≔}\left[\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{y}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({y}\right){=}{0}{,}\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\eta }}{}\left({x}\right){=}{-}\frac{{ⅆ}}{{ⅆ}{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({y}\right)\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\xi }}{}\left({y}\right){,}{\mathrm{\eta }}{}\left({x}\right)\right]$ (1)
 > $\mathrm{Copy}\left(S,\left[\mathrm{\alpha },\mathrm{\beta }\right]\right)$
 $\left[\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{y}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\alpha }}{}\left({y}\right){=}{0}{,}\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\beta }}{}\left({x}\right){=}{-}\frac{{ⅆ}}{{ⅆ}{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\alpha }}{}\left({y}\right)\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\alpha }}{}\left({y}\right){,}{\mathrm{\beta }}{}\left({x}\right)\right]$ (2)
 > $\mathrm{ParametricDerivatives}\left(S\right)$
 $\left[{\mathrm{\xi }}{}\left({y}\right){,}\frac{{ⅆ}}{{ⅆ}{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({y}\right){,}{\mathrm{\eta }}{}\left({x}\right)\right]$ (3)
 > $B≔\mathrm{IDBasis}\left(S,\left[⟨1,0,-1⟩,⟨0,1,1⟩,⟨0,1,0⟩\right]\right)$
 ${B}{≔}\left[{\mathrm{\xi }}{}\left({y}\right){,}\frac{{ⅆ}}{{ⅆ}{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({y}\right){+}{\mathrm{\eta }}{}\left({x}\right){,}{-}{\mathrm{\xi }}{}\left({y}\right){+}\frac{{ⅆ}}{{ⅆ}{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({y}\right)\right]$ (4)
 > $\mathrm{Copy}\left(B,\left[\mathrm{\alpha },\mathrm{\beta }\right]\right)$
 $\left[{\mathrm{\alpha }}{}\left({y}\right){,}\frac{{ⅆ}}{{ⅆ}{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\alpha }}{}\left({y}\right){+}{\mathrm{\beta }}{}\left({x}\right){,}{-}{\mathrm{\alpha }}{}\left({y}\right){+}\frac{{ⅆ}}{{ⅆ}{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\alpha }}{}\left({y}\right)\right]$ (5)

Compatibility

 • The Copy command was introduced in Maple 2020.