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2013-01-28 00:56:44 -0500 | 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 13:23:38 -0500 | 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. |

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2012-04-22 04:24:16 -0500 | asked a question | Quotients of finite abelian groups Sage supports finite abelian groups (see here) as well as quotients of |

2012-03-27 02:52:39 -0500 | received badge | ● Scholar (source) |

2012-03-27 02:52:39 -0500 | 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: |

2012-03-27 02:52:37 -0500 | commented answer | Find specific linear combination in multivariate polynomial ring Thanks! |

2012-03-26 03:33:21 -0500 | received badge | ● Student (source) |

2012-03-25 05:01:23 -0500 | 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. |

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2012-03-25 01:59:30 -0500 | 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 01:53:55 -0500 | 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 and test with 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. |

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