chain and cochain

[luiswirth]

A k-chain is a linear combination of k-simplicies. Chains will be relevant in our library. For instance the boundary of a simplex is a chain. So this is a useful tool.

A k-cochain is linear form on the simplicial k-skeleton. Cochains will be relevant to our library because our PDE solutions will be represented as cochains. A differential k-form is represented as a cochain on our mesh, and the coefficents in the cochain are the basis coefficents. The cochain is the disretized representation of a differential form. Once can interpolate a cochain to get a differential form. A cochain are the coefficents of the diff form in the whitney basis.