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

The expression is rewritten in a sum of products form with each distinct wedge product or 1-form occurring exactly once. As the arguments to a wedge product are sorted into ``address'' order and coefficients are automatically extracted,  $d\left(x\right)\&ˆd\left(t\right)$ is recognized as being the same as $-d\left(t\right)\&ˆd\left(x\right)$.

$\mathrm{with}\left(\mathrm{liesymm}\right)\:$$\mathrm{setup}\left(x\,y\,z\right)\:$

$\mathrm{wcollect}\left(ad\left(x\right)\&ˆd\left(y\right)+bd\left(x\right)\&ˆd\left(y\right)\right)$

$\left(-a-b\right)d\left(y\right)\&ˆd\left(x\right)$

$\mathrm{wcollect}\left(ad\left(x\right)\&ˆd\left(y\right)+bd\left(y\right)\&ˆd\left(x\right)\right)$

$\left(-a+b\right)d\left(y\right)\&ˆd\left(x\right)$