[sage-devel] Re: Project: LatticeWithIsometry
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.
[sage-devel] Re: Project: LatticeWithIsometry
On Tuesday, September 6, 2016 at 11:20:55 AM UTC+2, Simon Brandhorst wrote: > > Dear all, > Dear Simon, > > I have written some code (toy implementation) in sage. It could be useful > for other people as well. > That is nice! I am sure it could be useful to other. > So now I am wondering whether I should make an effort to implement it > meeting the sage-devel standards. > Of course you should. The main reason being that your research will benefit from having doctested and documented code: you will trust your code. > How good are the chances for such a project to be included in the sage > source code? > I have seen so many times modules trying to get into Sage with difficulty for bad and also for good reasons. Good reasons being that for a module to get into Sage, it needs to be mature (changing its interface requires deprecation warnings after it gets into sage...) What I would strongly suggest you to do is to create your own pip installable package and share its existence to sage-devel. This will make it easy for people to try your code, easy for you to change its interface if you want, including backward incompatible changes... The question of merging the code into sage will come by itself later once your code and its interface becomes stable, once your code meets the sage-devel standards (if it happens that you have time to do so: the best thing being to write code directly meeting the sage standards that being said) and more importantly once the community has decided that your code must live longer than yourself working on this project. Cheers! Sébastien Labbé -- 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.
[sage-devel] Re: Project: LatticeWithIsometry
O.K. It seems there is some functionality for positive definite lattices in https://trac.sagemath.org/ticket/15976 and it hides in the sage source :). However I could not find anything for Indefinite "lattices". On Tuesday, September 6, 2016 at 11:20:55 AM UTC+2, 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. > > > 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.
[sage-devel] Re: Project: LatticeWithIsometry
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.
