liesymm - Maple Programming 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)
 > $\mathrm{eq}≔\frac{{{\partial }}^{2}}{{\partial }t{\partial }x}u\left(x,t\right)+\frac{{\partial }}{{\partial }x}u\left(x,t\right)+{u\left(x,t\right)}^{2}=0$
 ${\mathrm{eq}}{≔}\frac{{{\partial }}^{{2}}}{{\partial }{t}{}{\partial }{x}}{}{u}{}\left({x}{,}{t}\right){+}\frac{{\partial }}{{\partial }{x}}{}{u}{}\left({x}{,}{t}\right){+}{{u}{}\left({x}{,}{t}\right)}^{{2}}{=}{0}$ (2)
 > $\mathrm{forms}≔\mathrm{makeforms}\left(\mathrm{eq},u\left(x,t\right),w\right)$
 ${\mathrm{forms}}{≔}\left[{d}{}\left({u}\right){-}{\mathrm{w1}}{}{d}{}\left({x}\right){-}{\mathrm{w2}}{}{d}{}\left({t}\right){,}\left({d}{}\left({\mathrm{w2}}\right)\right){&^}\left({d}{}\left({t}\right)\right){+}\left({{u}}^{{2}}{+}{\mathrm{w1}}\right){}\left({d}{}\left({x}\right)\right){&^}\left({d}{}\left({t}\right)\right)\right]$ (3)
 > $\mathrm{forms}≔\mathrm{close}\left(\mathrm{forms}\right)$
 ${\mathrm{forms}}{≔}\left[{d}{}\left({u}\right){-}{\mathrm{w1}}{}{d}{}\left({x}\right){-}{\mathrm{w2}}{}{d}{}\left({t}\right){,}\left({d}{}\left({\mathrm{w2}}\right)\right){&^}\left({d}{}\left({t}\right)\right){+}\left({{u}}^{{2}}{+}{\mathrm{w1}}\right){}\left({d}{}\left({x}\right)\right){&^}\left({d}{}\left({t}\right)\right){,}{-}\left({d}{}\left({\mathrm{w1}}\right)\right){&^}\left({d}{}\left({x}\right)\right){-}\left({d}{}\left({\mathrm{w2}}\right)\right){&^}\left({d}{}\left({t}\right)\right)\right]$ (4)
 > $\mathrm{Lrank}\left(\mathrm{forms}\right)$
 $\left[{d}{}\left({u}\right){-}{\mathrm{w1}}{}{d}{}\left({x}\right){-}{\mathrm{w2}}{}{d}{}\left({t}\right){,}\left({d}{}\left({\mathrm{w2}}\right)\right){&^}\left({d}{}\left({t}\right)\right){+}\left({{u}}^{{2}}{+}{\mathrm{w1}}\right){}\left({d}{}\left({x}\right)\right){&^}\left({d}{}\left({t}\right)\right)\right]$ (5)