On Wed, Sep 12, 2012 at 01:44:26AM -0700, Andrew Mathas wrote:
> I worked out what is causing my code to take so long to invert these
> maps: it is because the inverse map is defined as a linear morphism on
> the basis of the codomain (=domain of the inverse) rather than by
> recursively stripping off the leading terms.
Ah right: there is even a comment about it in the file ``This should
be removed and optimized (the inverse should not be computed on the
basis''. That's because, at this point, __invert__ insists on
constructing the inverse morphism as a triangular morphism (it's good
to keep that mathematical information), and TriangularModuleMorphism
inherits from ModuleMorphismByLinearity (for which there are no
compelling reasons).
We really need to introduce an option in __invert__, as both
approaches (calculating on the basis or recursively stripping) can
have their advantage depending on the context. It's like when solving
linear equations: does one prefer to compute the inverse once for all,
or rather use an LU decomposition.
Note that for the moment you can compute inverse images by recursively
stripping using phi.preimage. And you can build the inverse morphism
by hand using what's done in the non invertible case for __invert__:
SetMorphism(Hom(self.codomain(), self.domain(),
ModulesWithBasis(self.domain().base_ring())),
self.preimage)
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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