&mod - Maple Help

liesymm

 &mod
 reduce a form modulo an exterior ideal

 Calling Sequence f &mod formlist

Parameters

 f - differential form formlist - list or set of differential forms

Description

 • This routine is part of the liesymm package and is loaded via with(liesymm).
 • Reduce the form  f modulo the exterior ideal generated by formlist.  Use a closed formlist to specify a differential ideal.

Examples

 > $\mathrm{with}\left(\mathrm{liesymm}\right):$
 > $\mathrm{setup}\left(t,x,u,\mathrm{w1},\mathrm{w2}\right)$
 $\left[{t}{,}{x}{,}{u}{,}{\mathrm{w1}}{,}{\mathrm{w2}}\right]$ (1)
 > $\mathrm{a1}≔d\left(u\right)-\mathrm{w1}d\left(t\right)-\mathrm{w2}d\left(x\right)$
 ${\mathrm{a1}}{≔}{d}{}\left({u}\right){-}{\mathrm{w1}}{}{d}{}\left({t}\right){-}{\mathrm{w2}}{}{d}{}\left({x}\right)$ (2)
 > $\mathrm{a2}≔\left(\mathrm{w2}+{u}^{2}\right)d\left(x\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&ˆ\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}d\left(t\right)-d\left(\mathrm{w2}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&ˆ\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}d\left(x\right)$
 ${\mathrm{a2}}{≔}{-}\left({{u}}^{{2}}{+}{\mathrm{w2}}\right){}{d}{}\left({t}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&ˆ}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{d}{}\left({x}\right){+}{d}{}\left({x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&ˆ}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{d}{}\left({\mathrm{w2}}\right)$ (3)
 > $\left(d\left(u\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&ˆ\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}d\left(t\right)\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&mod\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left[\mathrm{a1},\mathrm{a2}\right]$
 ${-}{\mathrm{w2}}{}{d}{}\left({t}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&ˆ}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{d}{}\left({x}\right)$ (4)
 > $\left(d\left(u\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&ˆ\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}d\left(t\right)\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&mod\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathrm{close}\left(\left[\mathrm{a1},\mathrm{a2}\right]\right)$
 ${-}{\mathrm{w2}}{}{d}{}\left({t}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&ˆ}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{d}{}\left({x}\right)$ (5)