On 2014-04-03, Ursula Whitcher <whitc...@uwec.edu> wrote: > > > 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. I suppose you mean to say that one allows non-Euclidean scalar products. (for many people here a Gram matrix is a matrix of form VV^T, and may sound confusing...)
> 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. they also arise in the theory of reflection groups, cf e.g. http://en.wikipedia.org/wiki/II25,1 This brings up yet another suggestion for the name of the class: "InnerProductSpaceLattice" :-) > > 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.
