On Tuesday, September 6, 2016 at 9:20:55 AM UTC, Simon Brandhorst wrote: > > Dear all, > > I have written some code (toy implementation) in sage. It could be useful > for other people as well. > So now I am wondering whether I should make an effort to implement it > meeting the sage-devel standards. > How good are the chances for such a project to be included in the sage > source code? > > > So here is the project: LatticeWithIsometry > where a lattice L is a free abelian group equipped with a non-degenerate > symmetric bilinear form (ZZ or QQ valued). An isometry f is a ZZ-Module > automorphism preserving the bilinear form. > So we want to model (L,f) > > Functionality: > - constructor for ideal lattices - that is lattices (+isometries) cooked > up from irreducible reciprocal polynomials (think of the cyclotomic > polynomials) and their trace forms > - gluing of lattices. That is taking a direct sum > (L,f) + (N,g) and getting integral overlattices compatible with (f,g). > - describing the action of the isometry on sub/super lattices such as the > dual lattice L' or quotients such as the discriminant group L'/L > - a method to decide whether a given isometry of a hyperbolic lattice > preserves a chamber of the positive cone cut out by the root hyperplanes > (this relates to Weyl groups) > > A possible reference for this is: > http://www.math.harvard.edu/~ctm/papers/home/text/papers/pos/pos.pdf > > My personal aim in this is to model integral hodge isometries of K3 > surfaces or IHSMs. >
Sounds like a lot of fun; my latest personal foray into this was doing some computations in http://arxiv.org/abs/1604.05836 (with Lemma 2.11 attributed to me :-)) and I'm still trying to understand whether I can publish anything meaningful out of it. It would be interesting to what extent your package can do computations in that paper. Just in case, Dima > > > I also wonder how this would fit into the sage world. Should this inherit > from quadratic forms ? (feels wrong) or is there some lattice class out > there? > Since I am new in sage, writing a whole lattice class seems to be too much > work for me (and well above my level of experience). > > There seem to have been previous discussions about lattices e.g. > > Discussion in Sage devel: > > > https://groups.google.com/forum/#!searchin/sage-devel/lattice|sort:relevance/sage-devel/OO0ADcuraqE/mUG5_UrYFD4J > and > > https://groups.google.com/forum/#!searchin/sage-devel/lattice$20-poset|sort:relevance/sage-devel/KTmqIcav9e4/wWdiQ71PWVYJ > > There also seem to have been previous attempts for implementing lattices > such as > https://trac.sagemath.org/ticket/11940 > https://trac.sagemath.org/ticket/15976 > > > What has happened to them? > > Or the rather incomplete FreeQuadraticModule > > http://doc.sagemath.org/html/en/reference/modules/sage/modules/free_quadratic_module.html > which claims to have non trivial functionality over ZZ - I couldn't find > any. > > > > Simon > -- 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 https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
