&^ - Maple Help

difforms

 &^
 wedge product

 Calling Sequence &^(expr1, expr2, ...) expr1 &^ expr2 &^ ...

Parameters

 expr[1], expr[2], ... - Maple expressions

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{difforms}\right):$
 > $\mathrm{defform}\left(a=1,b=1,c=1,d=2,e=2\right)$
 > $\mathrm{&^}\left(a,b,c+d\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&ˆ\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}e\right)$
 ${\mathrm{&^}}{}\left({a}{,}{b}{,}{c}\right){+}{\mathrm{&^}}{}\left({a}{,}{b}{,}{d}{,}{e}\right)$ (1)
 > $\mathrm{&^}\left(a,b,c+\mathrm{&^}\left(d,e,a\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&ˆ\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}d\right)\right)$
 ${\mathrm{&^}}{}\left({a}{,}{b}{,}{c}\right)$ (2)