wdegree - Maple Help

liesymm

 wdegree
 compute the wedge degree of a form

 Calling Sequence wdegree(expr)

Parameters

 expr - differential form

Description

 • 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, $\mathrm{nops}\left(\mathrm{getform}\left(\mathrm{expr}\right)\right)$).

Examples

 > $\mathrm{with}\left(\mathrm{liesymm}\right):$
 > $\mathrm{setup}\left(x,y,z\right)$
 $\left[{x}{,}{y}{,}{z}\right]$ (1)
 > $\mathrm{wdegree}\left(0\right)$
 ${-1}$ (2)
 > $\mathrm{wdegree}\left(x\right)$
 ${0}$ (3)
 > $\mathrm{wdegree}\left({x}^{2}d\left(x\right)\right)$
 ${1}$ (4)
 > $a≔{x}^{2}\left(d\left(x\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&ˆ\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}d\left(y\right)\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&ˆ\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}d\left(z\right)$
 ${a}{≔}{{x}}^{{2}}{}{\mathrm{&^}}{}\left({d}{}\left({x}\right){,}{d}{}\left({y}\right){,}{d}{}\left({z}\right)\right)$ (5)
 > $\mathrm{wdegree}\left(a\right)$
 ${3}$ (6)