2017-10-15 20:20:44 +0200 received badge ● Famous Question (source) 2016-12-03 12:32:24 +0200 received badge ● Popular Question (source) 2014-10-11 18:04:15 +0200 received badge ● Notable Question (source) 2013-05-13 18:44:27 +0200 received badge ● Popular Question (source) 2013-01-28 07:56:44 +0200 commented question Combining intervals I see the image. It is the following formula: $\overline{(-4,1)} \cup [0,\infty) \setminus (-\infty,4) \cap [-1,3]$ (rendered...). 2013-01-27 20:23:38 +0200 asked a question Ideals of non-commutative polynomials Basically I have the same question as here, but in the non-commutative case: Given non-commutative polynomials $f_1,\dotsc,f_s \in \mathbb{Q}\langle x_1,\dotsc,x_n \rangle$, how can I test (with sage, or any other program which can do this) that some $g \in \mathbb{Q}\langle x_1,\dotsc,x_n \rangle$ satisfies $g \in \langle f_1,\dotsc,f_s \rangle$ (two-sided ideal), and find an explicit linear combination $g = \sum_i a_i f_i b_i$ which demonstrates this? In trac ticket #11068 non-commutative quotient rings were implemented. However, according to the reference manual on quotient rings, this assumes that one defines a reduce method by hand. But in my example , it is not clear how to do this. 2012-04-30 10:03:12 +0200 received badge ● Editor (source) 2012-04-22 11:24:16 +0200 asked a question Quotients of finite abelian groups Sage supports finite abelian groups (see here) as well as quotients of permutation groups (see here). What about quotients of finite abelian groups? I would like to let Sage compute the Smith Normal Form of something like $(\mathbb{Z}/n_1 \oplus \dotsc \oplus \mathbb{Z} / n_s) / \langle r_1,\dotsc,r_d \rangle$, where $r_i$ are words in the canonical generators. 2012-03-27 09:52:39 +0200 marked best answer Find specific linear combination in multivariate polynomial ring AFAIK, Singular can handle this case but the Sage wrappers restrict the coefficient domain to a field. You can work around this with the magical Singular function interface. Using the example from the previous question linked above: sage: R. = ZZ[] sage: C1= 17*x^2 + 7*y^2 - 26*y*z + 7*z^2 sage: C2= 13*y^2 - 7*y*z + 13*z^2 - 51*t^2 sage: I = (C1, C2)*R sage: f in I False sage: 221*f in I True sage: lift = sage.libs.singular.ff.lift sage: lift(I, 221*f) [ 13*x^2 + 17*y*z - 21*t^2] [-7*x^2 + 17*y^2 + 17*z^2 + 78*t^2] sage: (13*x^2 + 17*y*z - 21*t^2)*C1 + (-7*x^2 + 17*y^2 + 17*z^2 + 78*t^2)*C2 221*x^4 + 221*y^4 + 221*z^4 - 3978*t^4 sage: f x^4 + y^4 + z^4 - 18*t^4  2012-03-27 09:52:39 +0200 received badge ● Scholar (source) 2012-03-27 09:52:37 +0200 commented answer Find specific linear combination in multivariate polynomial ring Thanks! 2012-03-26 10:33:21 +0200 received badge ● Student (source) 2012-03-25 12:01:23 +0200 commented question Find specific linear combination in multivariate polynomial ring I could solve my problem by feeding sage with base fields such as $\mathbb{Q}$ and $\mathbb{F}_2$ and experimental comparing of the results, to get a correct linear combination over the base ring $\mathbb{Z}$. But I think it is interesting whether there is a general method implemented. 2012-03-25 09:00:29 +0200 received badge ● Supporter (source) 2012-03-25 08:59:30 +0200 commented question Find specific linear combination in multivariate polynomial ring There is a related question http://ask.sagemath.org/question/1064/explicit-representation-of-element-of-ideal which answers my question if the base ring was a field. 2012-03-25 08:53:55 +0200 asked a question Find specific linear combination in multivariate polynomial ring Assume that I have given a sequence of polynomials $f_1,\dotsc,f_s$ in a multivariate polynomial ring (over $\mathbb{Z}$, if that matters) and want to decide whether a given polynomial $g$ can be written as $g = \lambda_1 f_1 + \dotsc + \lambda_s f_s$. Then in Sage I just let I = Ideal([f_1,...,f_s])  and test with g in I  If this returns True, how can I get Sage to display some possible $\lambda_1,\dotsc,\lambda_s$? As for my specific problem, I have already tried it by hand, but this is hard: My polynomial ring has $15$ indeterminates and there are $s = 250$ polynomials.