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

It computes the wedge product of differential forms relative to the coordinates defined by setup().

All 1-forms are generated by applying d() to the coordinates.

All wedge products are automatically simplified to a wedge product of n 1-forms by extracting coefficients of wedge degree 0.

All results of a wedge product are reported using an address ordering of the 1-forms to facilitate simplifications.  Thus $d\left(y\right)\&ˆd\left(x\right)$ may simplify to $-d\left(x\right)\&ˆd\left(y\right)$ and if so will do so consistently within a given session.

The ordering used for simplifications of the products of 1-forms is available as $\left\{\mathrm{wedgeset}\left(1\right)\right\}$.

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

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

$\left[x\,y\,z\right]$

$d\left(t\right)\&ˆd\left(x\right)$

$0$

$d\left(x\right)\&ˆd\left(y\right)$

$-d\left(y\right)\&ˆd\left(x\right)$

$\left(\left(5d\left(x\right)\right)\&ˆd\left(y\right)\right)\&ˆ\left(3d\left(z\right)\right)$

$-15\mathrm{\&^}\left(d\left(z\right)\,d\left(y\right)\,d\left(x\right)\right)$

$\mathrm{`\&^`}\left(ad\left(x\right)\,bd\left(y\right)\,cd\left(z\right)\right)$

$-abc\mathrm{\&^}\left(d\left(z\right)\,d\left(y\right)\,d\left(x\right)\right)$