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.

$\mathrm{with}\left(\mathrm{liesymm}\right)\:$

$\mathrm{setup}\left(t\,x\,u\,\mathrm{w1}\,\mathrm{w2}\right)$

$\left[t\,x\,u\,\mathrm{w1}\,\mathrm{w2}\right]$

$\mathrm{a1}≔d\left(u\right)-\mathrm{w1}d\left(t\right)-\mathrm{w2}d\left(x\right)$

$\mathrm{a1}≔d\left(u\right)-\mathrm{w1}d\left(t\right)-\mathrm{w2}d\left(x\right)$

$\mathrm{a2}≔\left(\mathrm{w2}+u^2\right)d\left(x\right)\&ˆd\left(t\right)-d\left(\mathrm{w2}\right)\&ˆd\left(x\right)$

$\mathrm{a2}≔-\left(u^2+\mathrm{w2}\right)d\left(t\right)\&ˆd\left(x\right)+d\left(x\right)\&ˆd\left(\mathrm{w2}\right)$

$\left(d\left(u\right)\&ˆd\left(t\right)\right)\&mod\left[\mathrm{a1}\,\mathrm{a2}\right]$

$-\mathrm{w2}d\left(t\right)\&ˆd\left(x\right)$

$\left(d\left(u\right)\&ˆd\left(t\right)\right)\&mod\mathrm{close}\left(\left[\mathrm{a1}\,\mathrm{a2}\right]\right)$

$-\mathrm{w2}d\left(t\right)\&ˆd\left(x\right)$