d - Maple Help

liesymm

 d
 the exterior derivative

 Calling Sequence d(form)

Parameters

 form - expression involving differential forms relative to specific coordinates

Description

 • This routine is part of the liesymm package and is loaded via with(liesymm) .
 • It computes the exterior derivative of the differential form form with respect to the coordinates defined by setup() .
 • For coordinate x, $d\left(x\right)$ is a 1-form, and $d\left(d\left(x\right)\right)=0$.
 • Expressions not involving the coordinates are treated as constants. The coordinate list is given by wedgeset(0).

Examples

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