1. How can I compute the cokernel of a matrix? For example: sage: mat = matrix(ZZ, 2, 2, [[1, 0], [0, 2]]) sage: M = FreeModule(ZZ, rank=2)
Then I would like to use M / mat.image() or M / mat.column_module(), but those give errors. (It works if M and mat are defined over QQ, and perhaps over any field?) Is there an easy way to do this? If not, are quotients of free modules (e.g., over PIDs) defined in Sage, and if so, how do I get at them? 2. Another question about free modules: what does == mean, mathematically, for them? For example: sage: id = matrix(ZZ, 2, 2, [[1, 0], [0, 1]]) sage: id.right_kernel() == FreeModule(ZZ, rank=0) False I guess if I want to test isomorphism, I should just check that the ranks are equal? Oh, wait, I just found the method nonembedded_free_module, which looks like what I want: sage: id.right_kernel().nonembedded_free_module() == FreeModule(ZZ, 0) True 3. One more thing: is the following a bug? sage: id = matrix(ZZ, 2, 2, [[1, 0], [0, 1]]) Then id.right_kernel() works, as does id.kernel() (which gives the left kernel), but id.left_kernel() gives an error: "TypeError: Argument K (= Integer Ring) must be a field." John --~--~---------~--~----~------------~-------~--~----~ 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 For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
