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.

$\mathrm{with}\left(\mathrm{liesymm}\right)\:$

$\mathrm{setup}\left(x\,y\,z\right)$

$\left[x\,y\,z\right]$

$\mathrm{hook}\left(f\left(x\,y\,z\right)\,V\right)$

$0$

$\mathrm{hook}\left(d\left(f\left(x\,y\,z\right)\right)\,V\right)$

$\left(\frac{\partial }{\partial x}f\left(x\,y\,z\right)\right)V_1\left(x\,y\,z\right)+\left(\frac{\partial }{\partial y}f\left(x\,y\,z\right)\right)V_2\left(x\,y\,z\right)+\left(\frac{\partial }{\partial z}f\left(x\,y\,z\right)\right)V_3\left(x\,y\,z\right)$

$\mathrm{hook}\left(d\left(f\left(x\,y\,z\right)\right)\&ˆd\left(z\right)\,V\right)$

$\left(\frac{\partial }{\partial x}f\left(x\,y\,z\right)\right)\left(V_1\left(x\,y\,z\right)d\left(z\right)-d\left(x\right)V_3\left(x\,y\,z\right)\right)+\left(\frac{\partial }{\partial y}f\left(x\,y\,z\right)\right)\left(V_2\left(x\,y\,z\right)d\left(z\right)-d\left(y\right)V_3\left(x\,y\,z\right)\right)$