Lrank - Maple Help

liesymm

 Lrank
 the Lie Rank of a set of forms

 Calling Sequence Lrank(form)

Parameters

 form - list or set of differential forms

Description

 • This routine is part of the liesymm package and is loaded via with(liesymm) .
 • It removes forms which are redundant with respect to the generation of the determining equations.

Examples

 > $\mathrm{with}\left(\mathrm{liesymm}\right):$
 > $\mathrm{setup}\left(\right)$
 $\left[\right]$ (1)
 > $\mathrm{eq}≔\mathrm{Diff}\left(u\left(x,t\right),x,t\right)+\mathrm{Diff}\left(u\left(x,t\right),x\right)+{u\left(x,t\right)}^{2}=0$
 ${\mathrm{eq}}{≔}\frac{{{\partial }}^{{2}}}{{\partial }{x}{\partial }{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{u}{}\left({x}{,}{t}\right){+}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{u}{}\left({x}{,}{t}\right){+}{{u}{}\left({x}{,}{t}\right)}^{{2}}{=}{0}$ (2)
 > $\mathrm{forms}≔\mathrm{makeforms}\left(\mathrm{eq},u\left(x,t\right),w\right)$
 ${\mathrm{forms}}{≔}\left[{d}{}\left({u}\right){-}{\mathrm{w1}}{}{d}{}\left({x}\right){-}{\mathrm{w2}}{}{d}{}\left({t}\right){,}{d}{}\left({\mathrm{w2}}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&ˆ}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{d}{}\left({t}\right){+}\left({{u}}^{{2}}{+}{\mathrm{w1}}\right){}{d}{}\left({x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&ˆ}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{d}{}\left({t}\right)\right]$ (3)
 > $\mathrm{forms}≔\mathrm{close}\left(\mathrm{forms}\right)$
 ${\mathrm{forms}}{≔}\left[{d}{}\left({u}\right){-}{\mathrm{w1}}{}{d}{}\left({x}\right){-}{\mathrm{w2}}{}{d}{}\left({t}\right){,}{d}{}\left({\mathrm{w2}}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&ˆ}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{d}{}\left({t}\right){+}\left({{u}}^{{2}}{+}{\mathrm{w1}}\right){}{d}{}\left({x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&ˆ}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{d}{}\left({t}\right){,}{-}{d}{}\left({\mathrm{w1}}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&ˆ}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{d}{}\left({x}\right){-}{d}{}\left({\mathrm{w2}}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&ˆ}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{d}{}\left({t}\right)\right]$ (4)
 > $\mathrm{Lrank}\left(\mathrm{forms}\right)$
 $\left[{d}{}\left({u}\right){-}{\mathrm{w1}}{}{d}{}\left({x}\right){-}{\mathrm{w2}}{}{d}{}\left({t}\right){,}{d}{}\left({\mathrm{w2}}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&ˆ}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{d}{}\left({t}\right){+}\left({{u}}^{{2}}{+}{\mathrm{w1}}\right){}{d}{}\left({x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&ˆ}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{d}{}\left({t}\right)\right]$ (5)