Hi all
if you will use differential forms,Iam testing new cartan package
now,so send you it. this is rewrited version of the cartan.lisp.
please tell me.
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)
Gosei Furuya