extvars - Maple Help

liesymm

 extvars
 extvars a set of differential forms

 Calling Sequence extvars() extvars(f, x) extvars(f, x, y)

Parameters

 f - name of a dependent variable x, y - names of the independent variables with respect to the system of PDEs currently under investigation

Description

 • During the investigation a particular system of PDEs names are dynamically created for the partials involving some of the and dependent and independent variables. This command reports on the names used for those partials.
 • If the function is called with no argument then a table indicating all the name mappings is returned.
 • In all other cases the first argument is the dependent variable and the remaining arguments are the independent variables defining the partial of interest.    The result is the name used for the specified partial.
 • If there is no such table entry then extvars() returns unevaluated.
 • This routine is ordinarily loaded via with(liesymm) but can be used in the package style'' as liesymm[extvars]()

Examples

 > $\mathrm{with}\left(\mathrm{liesymm}\right):$
 > $\mathrm{eq1}≔\mathrm{Diff}\left(h\left(t,x\right),x,x\right)=\mathrm{Diff}\left(h\left(t,x\right),t\right)$
 ${\mathrm{eq1}}{≔}\frac{{{\partial }}^{{2}}}{{\partial }{{x}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{h}{}\left({t}{,}{x}\right){=}\frac{{\partial }}{{\partial }{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{h}{}\left({t}{,}{x}\right)$ (1)
 > $\mathrm{forms}≔\mathrm{makeforms}\left(\mathrm{eq1},h\left(t,x\right),k\right)$
 ${\mathrm{forms}}{≔}\left[{d}{}\left({h}\right){-}{\mathrm{k1}}{}{d}{}\left({t}\right){-}{\mathrm{k2}}{}{d}{}\left({x}\right){,}{-}{d}{}\left({\mathrm{k2}}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&ˆ}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{d}{}\left({t}\right){-}{\mathrm{k1}}{}{d}{}\left({t}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&ˆ}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{d}{}\left({x}\right)\right]$ (2)
 > $\mathrm{translate}\left(\mathrm{k2}\right)$
 ${h}{,}{x}$ (3)
 > $\mathrm{extvars}\left(\right)$
 ${\mathrm{k2}}$ (4)
 > $\mathrm{extvars}\left(h,y\right)$
 ${\mathrm{extvars}}{}\left({h}{,}{y}\right)$ (5)
 > $\mathrm{extvars}\left(\right)$
 ${table}{}\left(\left[\left({h}{,}{x}\right){=}{\mathrm{k2}}{,}{x}{=}{x}{,}\left({h}{,}{t}\right){=}{\mathrm{k1}}{,}{t}{=}{t}{,}{h}{=}{h}\right]\right)$ (6)