On Mon, Sep 28, 2015 at 04:56:47PM -0600, Alexander Hulpke wrote: > > Now, classically, I can define s = > > Sum(SL(2,5),g->g^rep*TransposedMat(ComplexConjugate(g^rep))), which is the > > Gram matrix of a positive-definite invariant sesquilinear form; but I don't > > know how to factor s as t*TransposedMat(ComplexConjugate(t)) so as to > > conjugate rep by t. > > This is a Cholesky decomposition, which (Wikipedia be thanked) seems to be a > standard operation in the numerical world, and this is exactly what GAP uses. > > However in your concrete example this fails yet — the reason is that the > Cholesky decomposition requires square roots, and the existing code for > CholeskyDecomp in GAP cannot deal with square roots for irrationals. (It > would have to construct a larger field etc. which makes the code far more > complicated.)
Do you mean the code in pkg/HAPcryst/examples/orbitcoloring.gap ? In the numerical world people avoid doing the classical Cholesky decomposition; they do LDL* decomposition (same Wikipedia article), which does not need square roots, but leaves you with a diagonal sesqulinear form with positive coefficients. I imagine in some cases it'd just give you a scalar that you can cancel... Best, Dima _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
