 hook - Maple Help

liesymm

 hook
 inner product (hook) Calling Sequence hook(f, V) Parameters

 f - expression involving differential forms relative to specific coordinates V - vector (or list) Description

 • This routine is part of the liesymm package and is loaded via with(liesymm).
 • Compute the inner product of f with respect to a vector V.
 • Use setup() to change the underlying coordinate system. Examples

 > $\mathrm{with}\left(\mathrm{liesymm}\right):$
 > $\mathrm{setup}\left(x,y,z\right)$
 $\left[{x}{,}{y}{,}{z}\right]$ (1)
 > $\mathrm{hook}\left(f\left(x,y,z\right),V\right)$
 ${0}$ (2)
 > $\mathrm{hook}\left(d\left(f\left(x,y,z\right)\right),V\right)$
 $\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{f}{}\left({x}{,}{y}{,}{z}\right){}{{V}}_{{1}}{}\left({x}{,}{y}{,}{z}\right){+}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{f}{}\left({x}{,}{y}{,}{z}\right){}{{V}}_{{2}}{}\left({x}{,}{y}{,}{z}\right){+}\frac{{\partial }}{{\partial }{z}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{f}{}\left({x}{,}{y}{,}{z}\right){}{{V}}_{{3}}{}\left({x}{,}{y}{,}{z}\right)$ (3)
 > $\mathrm{hook}\left(d\left(f\left(x,y,z\right)\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&ˆ\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}d\left(z\right),V\right)$
 $\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{f}{}\left({x}{,}{y}{,}{z}\right){}\left({{V}}_{{1}}{}\left({x}{,}{y}{,}{z}\right){}{d}{}\left({z}\right){-}{d}{}\left({x}\right){}{{V}}_{{3}}{}\left({x}{,}{y}{,}{z}\right)\right){+}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{f}{}\left({x}{,}{y}{,}{z}\right){}\left({{V}}_{{2}}{}\left({x}{,}{y}{,}{z}\right){}{d}{}\left({z}\right){-}{d}{}\left({y}\right){}{{V}}_{{3}}{}\left({x}{,}{y}{,}{z}\right)\right)$ (4)