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        Questions tagged [sage]

        Sage is a mathematical software system, and this tag is intended for questions involving this software in a substantive way. This tag should hardly ever be the only tag of a question; typically there should be additional tags to indicate the mathematical content of the question. Please note that questions that are purely support-questions on Sage are not a good fit for this site.

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        1answer
        137 views

        Branching to Levi subgroups in SAGE and the circle action

        In the SAGE computer package, there useful exist tools for branching representations of a simple Lie group to a Levi subgroup: http://doc.sagemath.org/html/en/reference/combinat/sage/combinat/...
        4
        votes
        2answers
        164 views

        GAP versus SageMath for branching to Lie subgroups

        Which computer package is better, GAP or SageMath, for decomposing an irreducible representation of a (simple) Lie group $G$ into representations of a Lie subgroup. I am most interested when ...
        10
        votes
        0answers
        813 views

        Euler's totient function and Riemann hypothesis

        I am looking for an upper-bound of the Euler's totient function $\varphi$ which would be equivalent to the Riemann hypothesis (RH). There is the following Nicolas' criterion about primorial numbers $...
        1
        vote
        1answer
        164 views

        Sage: Evaluation precision for elliptic curves over p-adic fields

        Consider the elliptic curve $E: y^2 = x^3 + 23x+11$ over p-adic fields. In Sage I use: k = GF(257) E = EllipticCurve(k,[23,11]) kp = Qp(257,5) # 257-adic Field with capped relative ...
        3
        votes
        0answers
        682 views

        Puzzle in 3D grid with black and white boxes, related to shelling

        Consider a $n$ by $n$ by $n$ grid represented by the set of $3$-uples $S=\{1,2,\dots, n\}^3$. A line (resp. slice) of $S$ is a subset of cardinal $n$ (resp. $n^2$) where two components (resp. one ...
        17
        votes
        4answers
        993 views

        Number of collinear ways to fill a grid

        A way to fill a finite grid (one box after the other) is called collinear if every newly filled box (the first excepted) is vertically or horizontally collinear with a previously filled box. See the ...
        5
        votes
        0answers
        152 views

        normal form for some finite groups, extending the small groups library

        I am in need of a normal (that is, canonical) form for (some) finite groups, computable with - for example - gap or sage or any other freely available package. The goal is to make finite groups ...
        11
        votes
        1answer
        352 views

        How do computer algebra packages like Sagemath implement rank of a matrix

        I am not sure if this is the right place to ask this question, but I believe there will be people here who do computations on computer algebra packages like Sage in their work. I have been using ...
        2
        votes
        1answer
        158 views

        Memory usage of Gröbner basis computation

        I've been calculating some Gröbner bases in preparation for finding non-commutative Hilbert series (and, once I recreate that, characters of group actions). Specifically, I've been using the ...
        4
        votes
        1answer
        312 views

        Existence of a non-Eulerian atomistic lattice with this property on the Möbius function

        Let $L$ be a finite lattice with least element $\hat{0}$, greatest element $\hat{1}$, and M?bius function $\mu$. Question 1: What class of lattices the following property characterizes? $$\mu(\hat{0},...
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        votes
        6answers
        1k views

        Computation of a minimal polynomial

        It is relatively easy (but sometimes quite cumbersome) to compute the minimal polynomial of an algebraic number $\alpha$ when $\alpha$ is expressible in radicals. For example, the simple query "...
        4
        votes
        0answers
        142 views

        Symmetry-finding with SAGE?

        On pp. 152-3 of Hydon's Symmetry Methods for Differential Equations (2000 ed.), he lists some computer packages for symmetry-finding. This related Mathematica StackExchange question mentions the SYM ...
        1
        vote
        1answer
        135 views

        How to return elements of a given length in a symmetric group using Sage?

        Let $S_n$ be the symmetric group over $\{1,2,\ldots,n\}$. How to return elements of length $m$ in $S_n$ using Sage? I try to find such function in Sage but didn't find one. Thank you very much. Edit: ...
        2
        votes
        0answers
        82 views

        Is the bounded coset poset of a boolean interval of finite groups, Cohen-Macaulay?

        Let $[H,G]$ be a boolean interval of finite groups and let $\hat{C}(H,G)$ be its bounded coset poset (i.e. the poset of cosets $Kg$ with $K \in [H,G]$, bounded below by $\emptyset$ and bounded above ...
        3
        votes
        0answers
        210 views

        Is there an integral simple fusion ring of multiplicity one and Frobenius type? (obvious excepted)

        To avoid any confusion, we rewrite the basic definitions for a fusion ring (already written in this post). A fusion ring is a finite dimensional complex space $\mathbb{C}\mathcal{B}$ together ...

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