Hi, well, Sage's functionality for modules over polynomial rings is quite limited. It assumes that a submodule of a free module is free. We discussed this at length at a recent Sage/Macaulay2 coding sprint at IMA, and concluded that it would be quite a bit of work to do.
While this is not improved, your solution is a good one. Dima On Fri, Oct 18, 2019 at 1:32 PM Mao Zeng <[email protected]> wrote: > > I've come up with a rather awkward workaround using the Sage interface to > libSingular. Still I'd be interested to learn about any simpler solution. > Below is the Singular code, followed by Sage code which performs the same > task. > > Singular input: > > ring R=73, (a,b), dp; > module module1 = [a,a^3], [1,a]; > print(groebner(module1)); > > Singular output: > > 1,a2-a, > a,0 > > Sage input: > > import sage.libs.singular.function_factory > groebner = sage.libs.singular.function_factory.ff.groebner > from sage.modules.free_module_element import FreeModuleElement_generic_dense > as module_elem > P.<a,b> = PolynomialRing(GF(73)) > M=P^2 > module1=Sequence( > [module_elem(M, [a,a^3]), > module_elem(M, [1, a]) > ]) > groebner(module1) > > Sage output: > [(1, a), (a^2 - a, 0)] > > On Friday, October 18, 2019 at 9:43:53 AM UTC+2, Mao Zeng wrote: >> >> As I understand, groebner_basis() in Sage uses Singular as a backend to >> compute the groebner basis of ideals in polynomial rings. However, Singular >> can also compute the groebner basis of modules. Is this functionality >> available in Sage? Similarly, in Singular the "syz" function can compute the >> syzygy module of either an ideal or a module, but the syzygy_module() >> function in Sage seems to work for ideals only. I would like to use Sage >> instead of using Singular directly. Is there an easy workaround? >> >> Thank you! > > -- > 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 [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/d5973687-a902-476b-97fa-c3f2cfbe7a81%40googlegroups.com. -- 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAAWYfq19RvTZvGwNh48gP9xRKCaU3GmW6KCuUBiMnqQiacyNWA%40mail.gmail.com.
