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

It returns the wedge degree of a differential form.

It is defined relative to a given coordinate system, so use of setup() may change its value.

As the list of coordinates fully defines the one-forms, the value of this routine is just the number of terms in the basic wedge product (that is, $\mathrm{nops}\left(\mathrm{getform}\left(\mathrm{expr}\right)\right)$).

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

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

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

$\mathrm{wdegree}\left(0\right)$

$\mathrm{-1}$

$\mathrm{wdegree}\left(x\right)$

$0$

$\mathrm{wdegree}\left(x^{2}d\left(x\right)\right)$

$1$

$a≔x^2\left(d\left(x\right)\&ˆd\left(y\right)\right)\&ˆd\left(z\right)$

$a≔x^2\mathrm{\&^}\left(d\left(z\right)\,d\left(x\right)\,d\left(y\right)\right)$

$\mathrm{wdegree}\left(a\right)$

$3$