Try mat.kernel_on(V). Also, if v is a vector in the ambient space which happens to lie in V then V.coordinates(v) will give its coordinates w.r.t. the basis of V.
John Cremona On Monday, December 3, 2012 1:38:38 AM UTC, Andrew Mathas wrote: > > Hi All, > > I have been playing with some code where I want to find a submodule of a > module V which is annihilated by a bunch of maps. What I want to do > something like the following: > > V= some free submodule of rank v inside a space of rank d\ge v. > mat=[[0 for col in range(w)] for row in range(v)] # fairly sparse matrix > which describes the map f on bases of V and W > ...compute non-zero entries of the matrix ``mat`` > V = V.intersection( matrix(mat).kernel() ) > > where v=dim V, w=dim W where f is a map from V to W. Of course, this > doesn't quite work because matrix(mat).kernel() returns a submodule of ZZ^v > with respect to its standard basis whereas the space V has a very different > basis in general. To get around this I found myself writing > > kernel=V.submodule_with_basis([V.linear_combination_of_basis(b.list()) > for b in matrix(pmat).kernel().basis()]) > V=V.intersection(kernel) > > This strikes me as being a very convoluted way of writing something is > presumably quite common: writing the standard basis elements as linear > combinations of another basis. My question is: is there a better way to > do this? > > For a little while, I tried defining W=FreeModule(ZZ,w) and then > constructing the map f explicitly as a homomorphism from V to W. Doing it > this way does make f.kernel() into a submodule of V, but this approach just > seems to create a lot of extra overhead with very little benefit as I > essentially still had to construct the matrix ``mat`` above and used it to > define ``f`` with respect to the bases of ``V`` and ``W``. In fact, all > this really did was shift my problem above of writing the basis of the > kernel in terms of the basis of V to the problem of writing the images of f > in terms of the standard basis of W. (Even though I imagine that this > second approach is much slower I really should have checked by doing some > profiling before rewriting as above, but I didn't...) > > Any thoughts? > > Cheers, > Andrew > > > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
