The function simpform will simplify an expression involving forms.  Its operations include collecting like terms, simplifying wedge products, and pulling out scalar factors.

The command with(difforms,simpform) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{difforms}\right)\:$$\mathrm{defform}\left(f=\mathrm{scalar}\,g=\mathrm{scalar}\right)$

$\left(fv\right)\&ˆu+u\&ˆ\left(gv\right)$

$fv\&ˆu+gu\&ˆv$

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

$\left(f+{\left(\mathrm{-1}\right)}^{\mathrm{wdegree}\left(u\right)\mathrm{wdegree}\left(v\right)}g\right)v\&ˆu$

$f\left(u\&ˆv+u\&ˆw\right)+gu\&ˆv$

$f\left(u\&ˆv+u\&ˆw\right)+gu\&ˆv$

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

$\left(f+g\right)u\&ˆv+fu\&ˆw$