The operator &^ represents the wedge product of differential forms.

Elementary simplifications are done on wedge products. For example, if a is a form of odd degree, then &^(a, a) is simplified to 0.

The operator &^ will distribute over + whenever possible. The preferred representation of &^ is a sum of wedge products. Otherwise, it may be necessary to apply expand, then simpform to an expression to reduce it to simplest form.

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

$\mathrm{defform}\left(a=1\,b=1\,c=1\,d=2\,e=2\right)$

$\mathrm{`\&^`}\left(a\,b\,c+d\&ˆe\right)$

$\mathrm{\&^}\left(a\,b\,c\right)+\mathrm{\&^}\left(a\,b\,d\,e\right)$

$\mathrm{`\&^`}\left(a\,b\,c+\mathrm{`\&^`}\left(d\,e\,a\&ˆd\right)\right)$

$\mathrm{\&^}\left(a\,b\,c\right)$