As Dima points out, SPLU decomposition is probably more useful in practice,
so it's great to expose it. It should probably be exposed through a
different method than PLU decomposition, though.
For the return format: permutations are much more compact and efficient to
describe permutations than permutation matrices. Also because of the
parent: a permutation matrix is a {0,1}-valued matrix so it can be well
represented over ZZ, rather than floats. So primarily the routine should
expose that scipy exposes. Whether other bells and whistles are required is
another matter.
Is this only for system floats/complex numbers? or will you also be
implementing multiprecision versions?
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