# Mathematica and differential topology

 P: 4,513 Im not sure what you mean by setting thing up. As one example, $$G = G_{\mu\nu} = G_{[\mu \nu]}[/itex] The brakets indicate that G is antisymmetric. G, in this case is the dual of the electromagnetic field tensor, F. *dG is easy enough to partition into spacelike and timelike parts. [tex](*dG)_i = -\epsilon_{i \lambda \mu\nu}\partial_{[\lambda}G_{\mu\nu]}}$$ $$(*dG)_0 = -\epsilon_{0ijk}\partial_{[i}G_{jk]}}$$ (give or take a factor of 2) 'd' is the exterior derivative, '*' is the Hodge dual (antisymmetric tensor and a scalar factor). It doesn't matter much if your not familiar with the notion, really--just the general idea. Eventually I should recover equations such as these wave equations $$\frac{1}{2}(*d*dF+d*dG)_{0i} = \partial _t(\nabla x B)_{i} + \partial_i (\nabla \cdot E) - \nabla^2 E_i + ...$$ and ½(*d*dF+d*dG)jk = ... This is the sort of partitioning I require. The first is time-space. The second is space-space. I can make the conversions to vector calculus. It's the interim steps that I have to check and rechech and check again that bother me. Some go on for a few pages--and this is in four dimensions. In eight dimensions I don't trust my math skills.