On Thursday, April 3, 2014 9:28:41 AM UTC-5, John Cremona wrote: > > > Or one could give the Gram matrix G (A^t * A (in the real case), which > is real and positive definite. You definitely need to be able to > define a lattice just by its Gram matrix; theoretically one can go > from such a G via a factorization G=A^t * A to a basis representation > (not unique). > > There are situations where it is very useful to allow Gram matrices which are *not* positive definite. In particular, both the negative definite and indefinite cases arise when doing computations in algebraic geometry involving K3 surfaces. There are some nice results of Nikulin on existence and uniqueness of lattice embeddings that only apply to the indefinite case.
Anyone want to team up with me and spend a week in July (the first month I realistically have time, sigh) implementing some of this? --Ursula. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
