depvars - Maple Help

liesymm

 depvars
 depvars a set of differential forms

 Calling Sequence depvars(x1,..., xn)

Parameters

 x1, ..., xn - (optional) sequence of names of the dependent variables for the system of PDEs currently under investigation

Description

 • A system of PDEs is defined with respect to an underlying coordinate system. This command reports on the current setting of this coordinate system or allows it to be specified.  This information is automatically set by commands like makeforms() and subsequently used by commands such as annul(), TD{}, and Eta().
 • If the function is called with no argument then the current setting for independent variables is reported.
 • If the function is called with one or more arguments then these become the independent variables.
 • This routine is ordinarily loaded via with(liesymm) but can be used in the package style'' as liesymm[depvars]()

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)
 > $\mathrm{indepvars}\left(\right)$
 $\left[{t}{,}{x}\right]$ (3)
 > $\mathrm{depvars}\left(\right)$
 $\left[{h}\right]$ (4)

The dependencies can also be explicitly set.

 > $\mathrm{setup}\left(\right)$
 $\left[\right]$ (5)
 > $\mathrm{indepvars}\left(x,y\right)$
 $\left[{x}{,}{y}\right]$ (6)
 > $\mathrm{depvars}\left(g,h\right)$
 $\left[{g}{,}{h}\right]$ (7)
 > $\mathrm{TD}\left(F,x\right)$
 $\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{F}{+}{\mathrm{w1}}{}\frac{{\partial }}{{\partial }{g}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{F}{+}{\mathrm{w3}}{}\frac{{\partial }}{{\partial }{h}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{F}$ (8)
 > $\mathrm{Η}\left(g,x\right)$
 $\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{V3}}{+}{\mathrm{w1}}{}\frac{{\partial }}{{\partial }{g}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{V3}}{+}{\mathrm{w3}}{}\frac{{\partial }}{{\partial }{h}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{V3}}{-}{\mathrm{w1}}{}\left(\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{V1}}{+}{\mathrm{w1}}{}\frac{{\partial }}{{\partial }{g}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{V1}}{+}{\mathrm{w3}}{}\frac{{\partial }}{{\partial }{h}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{V1}}\right){-}{\mathrm{w2}}{}\left(\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{V2}}{+}{\mathrm{w1}}{}\frac{{\partial }}{{\partial }{g}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{V2}}{+}{\mathrm{w3}}{}\frac{{\partial }}{{\partial }{h}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{V2}}\right)$ (9)