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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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### 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/...
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### 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 ...
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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 $... 1answer 164 views ### Sage: Evaluation precision for elliptic curves over p-adic fields Consider the elliptic curve$E: y^2 = x^3 + 23x+11$over p-adic fields. In Sage I use: k = GF(257) E = EllipticCurve(k,[23,11]) kp = Qp(257,5) # 257-adic Field with capped relative ... 0answers 682 views ### Puzzle in 3D grid with black and white boxes, related to shelling Consider a$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 ... 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 ... 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 ... 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 ... 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 ... 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},... 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 "... 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 ... 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: ... 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 ... 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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