Hi jack
"vector" package is broken,but if you may delete these words,
cross&&,grad&&,div&&,curl&&,laplacian&&,dotdel&&,christoffel&&,
from vector.mac (share/vector/vector.mac),
you can load it,such that load("vector.mac"),
and use finely.
Gosei furuya
if you will use differential forms,Iam testing new cartan package
now,so send you it. this is rewrited version of the cartan.lisp.
for example orthogonal basis [Dx,Dy,Dz]
scalar a <---> a
vector v=(a,b,c)<---> 1form U=a*Dx+b*Dy+c*Dz
|(a,b,c)|^2 <---> (a*Dx+b*Dy+c*Dz)&(a*Dx+b*Dy+c*Dz) (& is clifford product)
(a,b,c).(f,g,h)<---> 1/2((a*Dx+b*Dy+c*Dz)&(f*Dx+g*Dy+h*Dz)+
(f*Dx+g*Dy+h*Dz)&(a*Dx+b*Dy+c*Dz))
(a,b,c)X(f,g,h)<--->h_st((a*Dx+b*Dy+c*Dz)@(f*Dx+g*Dy+h*Dz))
or -J((a*Dx+b*Dy+c*Dz)@(f*Dx+g*Dy+h*Dz))
grad(a) <---> D(a)
rot(V) <---> h_st(D(U)) or nest2([h_st,D],U)
div(V) <---> h_st(D(h_st(U))) or nest2([h_st,D,h_st],U)
laplacian(a) <---> D(h_st(D(a))) or nest2([D,h_st,D],a)
many equations <---> D(D(...))=0 ,poincare's lennma
almost every thing <--- differntial form calculation with hodge star
operator h_st(or pseudo scalar J in clifford algebra)