Dear Dima, sorry for taking such a long time to answer your question. I'd say it could do a lot of stuff involving over and sublattices. But then it seems like Alex is counting orbits. You'd have to build on top of my code to achieve that. For my purposes it sufficed to consider a single isometry at a time.
Best --Simon On Tuesday, September 6, 2016 at 3:08:56 PM UTC+2, Dima Pasechnik wrote: > > > > 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.
