liesymm - Maple Programming Help

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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)
 > $\mathrm{hook}\left(d\left(f\left(x,y,z\right)\right),V\right)$
 $\left(\frac{{\partial }}{{\partial }{x}}{}{f}{}\left({x}{,}{y}{,}{z}\right)\right){}{V}{[}{1}{]}{}\left({x}{,}{y}{,}{z}\right){+}\left(\frac{{\partial }}{{\partial }{y}}{}{f}{}\left({x}{,}{y}{,}{z}\right)\right){}{V}{[}{2}{]}{}\left({x}{,}{y}{,}{z}\right){+}\left(\frac{{\partial }}{{\partial }{z}}{}{f}{}\left({x}{,}{y}{,}{z}\right)\right){}{V}{[}{3}{]}{}\left({x}{,}{y}{,}{z}\right)$ (3)
 > $\mathrm{hook}\left(\left(d\left(f\left(x,y,z\right)\right)\right)&^\left(d\left(z\right)\right),V\right)$
 $\left(\frac{{\partial }}{{\partial }{x}}{}{f}{}\left({x}{,}{y}{,}{z}\right)\right){}\left({V}{[}{1}{]}{}\left({x}{,}{y}{,}{z}\right){}{d}{}\left({z}\right){-}{d}{}\left({x}\right){}{V}{[}{3}{]}{}\left({x}{,}{y}{,}{z}\right)\right){+}\left(\frac{{\partial }}{{\partial }{y}}{}{f}{}\left({x}{,}{y}{,}{z}\right)\right){}\left({V}{[}{2}{]}{}\left({x}{,}{y}{,}{z}\right){}{d}{}\left({z}\right){-}{d}{}\left({y}\right){}{V}{[}{3}{]}{}\left({x}{,}{y}{,}{z}\right)\right)$ (4)

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