2020-09-21 23:25:03 -0500 | received badge | ● Good Answer (source) |

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2020-09-20 01:10:38 -0500 | commented answer | Which subgroups do conjugacy_classes_subgroups() return You're welcome. You can accept an answer using the checkmark button on the left of the answer. |

2020-09-19 09:28:26 -0500 | received badge | ● Nice Answer (source) |

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2020-09-19 06:38:19 -0500 | answered a question | How to express elements in a field of prime order and power of a prime order using the same function? This method is currently available only for the Givaro and NTL implementations of finite fields. You can specify the implementation using the In theory, this method could easily be added to all implementations. You might open a trac ticket for it and/or bring it up on the sage-devel mailing list. |

2020-09-19 04:43:07 -0500 | answered a question | Which subgroups do conjugacy_classes_subgroups() return The method calls GAP's ConjugacyClassesSubgroups to get the conjugacy classes and then GAP's `Representative` to get a representative of each. This does not have the property you want. For example`SymmetricGroup(4).conjugacy_classes_subgroups()` includes both $K=\langle (1,3)(2,4)\rangle$ and $L=\langle (3,4), (1,2)(3,4) \rangle$ where a conjugate of $K$ is a subgroup of $L$ but $K$ is not a subgroup of $L$.See symmetric group: get back conjugacy class from its generators if you want the actual conjugacy classes as GAP objects; you will be able to call the methods `Representative()` and`AsList()` on them, and on each subgroup you can also call`IsSubgroup(H)` .I am not a group theorist but your algorithm seems fine to me.
Edit: Maybe I don't have to tell you this but, caveat: being conjugate in a subgroup is a stronger requirement than being conjugate in the full group (because there are fewer elements to conjugate by). |

2020-09-19 03:45:23 -0500 | answered a question | How to force numerical coefficients for non-polynomials? I'm pretty sure it can't be done with a built-in function, but I have written one (rather, a class) as an answer to a previous (slightly different) question: is it possible to round numbers in symbolic expression. Here I added an exception for integers, so it works in your use case: Or in the definition of It could be a nice idea to have such a class included in SageMath. |

2020-09-19 03:18:47 -0500 | answered a question | Functions in polynomials rings You want to access the generators of If you want to use some strange alternative indexing, then you can achieve it with a function. |

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2020-09-12 14:05:14 -0500 | commented question | Triple integrals in a specific region of space Are the inequalities always polynomial? Probably you can use cylindrical algebraic decomposition. |

2020-09-12 06:17:33 -0500 | commented question | Triple integrals in a specific region of space Numerically or symbolically? |

2020-09-12 03:48:12 -0500 | received badge | ● Nice Answer (source) |

2020-09-11 16:35:02 -0500 | commented answer | Changing Parent on multivariable polynomial ring You're welcome. You can accept the answer by pressing the check mark button under the voting arrows (also on all of your other answered questions). |

2020-09-11 14:40:57 -0500 | commented question | Changing Parent on multivariable polynomial ring By the way, |

2020-09-11 14:35:46 -0500 | answered a question | Changing Parent on multivariable polynomial ring If you do explicit division of polynomials with (If you have an element |

2020-09-05 13:08:45 -0500 | answered a question | Extracting terms of polynomial of certain powers Polynomial rings have monomial orderings (in this case it is degrevlex by default), and the terms of polynomials are automatically ordered from greatest to smallest (with respect to the monomial ordering), as you can see e.g. with You can get the exponents you want like this: Or the indices of the respective terms (again, with respect to the monomial ordering): Or the terms themselves: A bit more efficiently: |

2020-09-03 12:11:39 -0500 | received badge | ● Nice Answer (source) |

2020-09-03 11:28:27 -0500 | answered a question | Inconsistency with Groebner basis There is no inconsistency or bug, but a misunderstanding: the linear equation for The coefficient of |

2020-08-16 12:04:31 -0500 | commented question | Lattice of subspaces of a finite field vector space |

2020-08-16 04:18:19 -0500 | answered a question | Why can't I solve a simple root equation? I don't know what's hard about it (can't answer that part), but you can use some of the options that |

2020-08-13 17:03:40 -0500 | commented answer | Algebraic to symbolic expression The first thing this method does is compute |

2020-08-12 09:52:34 -0500 | commented answer | Algebraic to symbolic expression You're welcome :) This approach is not exact but if for an algebraic number |

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2020-08-12 04:43:43 -0500 | commented answer | A 2-codim polynomial ideal of normal-basis [0], meaning? In the example in the answer, the vanishing locus $V(I)$ of $I$ is the intersection of the cylinder $x^2+y^2=1$ and the plane $z=0$, so it is just a circle in the plane, i.e. a 1-dimensional algebraic variety (and this dimension is the same as the Krull dimension of the quotient ring). The quotient ring can be identified with the ring of polynomial functions on $V(I)$, i.e. the set of polynomial functions on the circle. On the one hand the circle is 1-dimensional (Krull dimension of the quotient), but on the other hand the functions $1, y, y^2, y^3 \ldots$ on the circle are all linearly independent because there is no equation that could relate them (they are part of an infinite normal basis, so the vector space dimension of the quotient is infinite). |

2020-08-12 04:27:38 -0500 | commented answer | A 2-codim polynomial ideal of normal-basis [0], meaning? By the dimension of an ideal $J$, I (and Sage and Singular) mean the Krull dimension of the ring modulo $J$. Yes, the Krull dimension of the quotient is 2, but (hence) the vector space dimension of the quotient is $\infty$. The normal basis is a basis of the quotient as a vector space, so it is infinite. A "witness" of the fact that the Krull dimension of the quotient is (at least) 2 would be: a chain of prime ideals of length 2 in the quotient. |

2020-08-12 03:46:31 -0500 | commented answer | A 2-codim polynomial ideal of normal-basis [0], meaning? You have indeed found a bug in Singular and/or SageMath. According to the documentation of Singular's kbase it should return |

2020-08-12 02:52:50 -0500 | answered a question | How to get a solution from an ideal in a polynomial ring when it is nonzero codimensional? If you change |

2020-08-11 16:45:40 -0500 | answered a question | Algebraic to symbolic expression I'm not sure how Output: It can be used to find minimal polynomials Edit: The uncertainty of |

2020-08-11 11:44:02 -0500 | commented answer | How to get a solution from an ideal in a polynomial ring when it is nonzero codimensional? The hyperplane trick works, but |

2020-08-11 11:18:19 -0500 | answered a question | A 2-codim polynomial ideal of normal-basis [0], meaning? This output should never occur, because If In the above output |

2020-08-11 02:15:20 -0500 | commented answer | Constant coefficient of symbolic expression You're welcome! (I updated the answer to make the substitution method more readable.) |

2020-08-11 02:05:13 -0500 | answered a question | Constant coefficient of symbolic expression You can set all variables to zero: If you are working with polynomials, consider using polynomial ring instead: Also you can convert back and forth between symbolic expressions and polynomials: |

2020-08-10 12:12:20 -0500 | commented question | Solving equation with algebraic numbers It seems Maxima can't handle the symbolic wrapper around |

2020-08-10 09:08:59 -0500 | commented question | Solving equation with algebraic numbers You can convert algebraic numbers to symbolic expressions using |

2020-08-09 06:56:20 -0500 | received badge | ● Necromancer (source) |

2020-08-07 18:12:05 -0500 | commented question | solve with "excess" equations Excess variables are interpreted as parameters, and only solutions that are valid for |

2020-08-01 15:42:10 -0500 | edited answer | Symbolic Equation 0=0 The value of Here |

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