This routine is part of the liesymm package and is loaded via with(liesymm).

A set of differential forms is closed with respect to the exterior derivative d() by adding additional forms to the original set.

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

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

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

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

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

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

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

$\mathrm{hasclosure}\left(\left[\mathrm{a1}\,\mathrm{a2}\right]\right)$

$\mathrm{false}$

$\mathrm{close}\left(\left[\mathrm{a1}\,\mathrm{a2}\right]\right)$

$\left[d\left(u\right)-\mathrm{w1}d\left(t\right)-\mathrm{w2}d\left(x\right)\,-\left(u^2+\mathrm{w2}\right)d\left(t\right)\&ˆd\left(x\right)+d\left(x\right)\&ˆd\left(\mathrm{w2}\right)\,d\left(t\right)\&ˆd\left(\mathrm{w1}\right)+d\left(x\right)\&ˆd\left(\mathrm{w2}\right)\right]$

$\mathrm{hasclosure}\left(\right)$

$\mathrm{true}$