On Wed, Mar 24, 2021 at 9:11 AM [email protected] <[email protected]> wrote: > > El miércoles, 24 de marzo de 2021 a las 10:01:43 UTC+1, [email protected] > escribió: >> >> I think the author uses "present" to say "generate" >>> >>> > > I suppose you mean the finitely generated Z-module (abelian group) presented > by the matrix, ie. its cokernel. In that case, you can do: > > sage: A=matrix([[1,-3],[-3,4]]) > sage: ZZ^2/A.column_space() > Finitely generated module V/W over Integer Ring with invariants (5)
Or just sage: A.smith_form() ( [1 0] [ 0 1] [-3 -4] [0 5], [ 1 -3], [-2 -3] ) here the 1st entry is the Smith Normal Form of A, and the 2nd and 3rd ones are what one uses to conjugate A to get it. (Yes, in English "present a group" means generators and relations, as opposed to "represent", which means a linear representation. Non-native Englsh speakers sometimes flip the meaning of these, e.g. in Russian the "представление" means "represenation", and ''копредставление'' means "presentation'') > > > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-support/47dcb142-e6af-49e6-81bc-ad8093d00362n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/CAAWYfq00zM0eQD%2B%2BUxRQ2oMRJEGGyEiO3cFKEVjkdF4gnXhhMg%40mail.gmail.com.
