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-b213-1aaaa6a691d4n%40googlegroups.com.
