Re: [sage-support] Subalgebra membership in a polynomial algebra
Thanks, Dima, that's helpful. I will open a ticket; I hope this will be an easy thing for people familiar with the Singular interfaces. -- John On Tuesday, September 6, 2022 at 3:31:08 PM UTC-7 dim...@gmail.com wrote: > On Tue, Sep 6, 2022 at 10:32 PM John H Palmieri > wrote: > > > > Let R = k[x_1, x_2, ..., x_n] be a polynomial ring over a field k of > characteristic p. Given elements a_1, a_2, ..., a_m and b in R, I would > like to know if b is in the subalgebra generated by a_1, ..., a_m.My > impression from a superficial skim of the literature (Shannon and Sweedler, > https://www.sciencedirect.com/science/article/pii/S0747717188800476, for > example) is that this problem has been solved using Grobner bases. Is there > something already in Sage that can easily perform this test? I couldn't > find any method "in_subalgebra" or "in_subring" or any obviously relevant > "__contains__", or even a method for constructing a subalgebra of a > polynomial ring, but maybe I'm missing something obvious. > > in Singular it is available: > https://www.singular.uni-kl.de/Manual/4-3-1/sing_1247.htm#SEC1328 > So the question is to make an interface. > > > > > (I don't actually care about representing b inside the subalgebra, I > just want to know if it's there, in case that helps.) > > > > -- > > John > > > > -- > > You received this message because you are subscribed to the Google > Groups "sage-support" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to sage-support...@googlegroups.com. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-support/e69e3952-57bf-4d8e-b213-16a691d4n%40googlegroups.com > . > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/25a3294a-15bb-4a05-a081-bb9407176d59n%40googlegroups.com.
Re: [sage-support] Subalgebra membership in a polynomial algebra
On Tue, Sep 6, 2022 at 10:32 PM John H Palmieri wrote: > > Let R = k[x_1, x_2, ..., x_n] be a polynomial ring over a field k of > characteristic p. Given elements a_1, a_2, ..., a_m and b in R, I would like > to know if b is in the subalgebra generated by a_1, ..., a_m.My impression > from a superficial skim of the literature (Shannon and Sweedler, > https://www.sciencedirect.com/science/article/pii/S0747717188800476, for > example) is that this problem has been solved using Grobner bases. Is there > something already in Sage that can easily perform this test? I couldn't find > any method "in_subalgebra" or "in_subring" or any obviously relevant > "__contains__", or even a method for constructing a subalgebra of a > polynomial ring, but maybe I'm missing something obvious. in Singular it is available: https://www.singular.uni-kl.de/Manual/4-3-1/sing_1247.htm#SEC1328 So the question is to make an interface. > > (I don't actually care about representing b inside the subalgebra, I just > want to know if it's there, in case that helps.) > > -- > John > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-support/e69e3952-57bf-4d8e-b213-16a691d4n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/CAAWYfq2DG6ZDT372rF%2B12%2BhM4cykPmKyabL19Wq2qJA9TTLZiQ%40mail.gmail.com.
[sage-support] Subalgebra membership in a polynomial algebra
Let R = k[x_1, x_2, ..., x_n] be a polynomial ring over a field k of characteristic p. Given elements a_1, a_2, ..., a_m and b in R, I would like to know if b is in the subalgebra generated by a_1, ..., a_m.My impression from a superficial skim of the literature (Shannon and Sweedler, https://www.sciencedirect.com/science/article/pii/S0747717188800476, for example) is that this problem has been solved using Grobner bases. Is there something already in Sage that can easily perform this test? I couldn't find any method "in_subalgebra" or "in_subring" or any obviously relevant "__contains__", or even a method for constructing a subalgebra of a polynomial ring, but maybe I'm missing something obvious. (I don't actually care about representing b inside the subalgebra, I just want to know if it's there, in case that helps.) -- John -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/e69e3952-57bf-4d8e-b213-16a691d4n%40googlegroups.com.
