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.
56 questions
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Compute generators for group of totally positive units of a number field?
Given a number field $K$, I would like to compute (in Sage) generators for the group of totally positive units of $K$.
Update: I've tried some code (details below), which I've received some help on in ...
- 111
13
votes
3
answers
4k
views
Is there any fast implementation of four color theorem in Python?
I'm now using scipy.spatial.Voronoi to generate a Voronoi graph, as shown here: voronoi graph. I'd like to apply the four color theorem on it, so that no adjcent regions share the same color. I ...
- 1
25
votes
7
answers
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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 ...
- 224
1
vote
0
answers
90
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Can computer algebra system compute Galois group/splitting field of a polynomial over $p$-adic number field of higher degree?
I am looking for a computer algebra system that checks if the splitting fields of two polynomials over a $p$-number field are the same or not. At least, knowing their splitting fields are isomorphic ...
- 195
1
vote
0
answers
133
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Hall-Littlewood polynomials with sage
I need to make some computations with Sage involving Hall-Littlewood polynomials. I couldn't find any satisfying information in the Sage manuals/tutorials that I found on the internet. What I found is ...
- 161
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3
answers
782
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Computer program for counting graph homomorphisms
I would like to ask is there a computer program for counting graph homomorphisms?
- 75
2
votes
1
answer
134
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On a efficient algorithm for factoring bivariate polynomials modulo composite modulus assuming the solution is unique
We found and implemented in sage efficient algorithm for factoring
bivariate polynomials modulo composite modulus assuming the solution is unique up to a constant factor.
More formally let $K=\mathbb{...
- 25.4k
4
votes
0
answers
127
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Minimal Model for $\mathbb{CP}^2 \# \mathbb{CP}^2 \# \mathbb{CP}^2$
I'm a grad student studying non-negative curvature on simply-connected manifolds and the conjectured relationship with rational homotopy theory.
The rational homotopy groups (and so the number of ...
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1
vote
1
answer
141
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Factorial series $j(D)=\sum_{n=1}^\infty \frac{1}{(n^D)!}$ and hypergeometric functions
For positive integer $D$, define $j(D)=\sum_{n=1}^\infty \frac{1}{(n^D)!}$.
For $D \le 6$, sage finds closed form in terms of hypergeometric functions
at algrebraic arguments and fails to find closed ...
- 14k
1
vote
1
answer
118
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Re: Vertices of hyperbolic triangle with given angles [closed]
I'm working on visualizing hyperbolic triangles given angles following a previous discussion on MathOverflow. The algorithm, as outlined in this MathOverflow answer, involves computing the side ...
- 1,986
0
votes
0
answers
112
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Software for Intersection of Ideals in Noncommutative Polynomial algebra
I am looking for software which can compute an intersection of ideals (in particular right ideals) in a noncommutative polynomial algebra and then find its Gröbner Basis.
Most software somehow does ...
- 12.9k
19
votes
1
answer
711
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Discrepancy in Magma's calculation and Sage's of elliptic curve?
$\DeclareMathOperator\Sha{Sha}$I calculated the Tate–Shafarevich group $\Sha(E/K)[2]$ of the elliptic curve $E:y^2=x^3+17x$ over $K=\Bbb{Q}(\sqrt{-37})$.
I calculated that by hand and I reached the ...
- 8,945
3
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1
answer
201
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Computations of half-integer forms in SAGE/Magma
I am currently going through Shimura's paper on half-integer weight modular forms. I would like to understand given a 𝑞-expansion of half-integral weight modular forms of arbitrary level and ...
- 20.8k
1
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0
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205
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Units in group rings in SAGE
Is there a recorded/known SAGE code to compute units in integral group rings for finite abelian groups ?
I would be happy with a code that only works for cyclic groups. I sort of know how to ...
- 15.9k
3
votes
0
answers
152
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Disconnected reductive algebraic groups in Sage
All simply connected split simple groups have been implement on Sage and it is possible to find their highest roots, fundamental weights, Dynkin diagrams or compute the tensor of two of their ...
- 370
4
votes
0
answers
193
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Is it possible to compute Lie bialgebra structures with SageMath?
Is it possible to use SageMath (or some Linux open source program) to compute the bialgebra structures on a given finite dimensional Lie algebra? I wonder if such program can compute all the ...
- 12.9k
0
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1
answer
663
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How does Sage order the elements of the symmetric group?
In Sage, the symmetric group is a list. For instance if G = SymmetricGroup(3), we have
\begin{align*}
G[0] & = e \\
G[1] & = (1,3,2)\\
G[2] & = (1,2,3) \\
G[3] &= (2,3)\\
G[4] &= (...
- 9,720
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votes
1
answer
319
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Construction of skew-Hadamard matrix of order 292
I am currently looking into how to construct a skew-Hadamard matrix of order 292. Where can I find such construction?
According to multiple papers (e.g. Koukouvinos and Stylianou - On skew-Hadamard ...
- 14k
8
votes
2
answers
754
views
How to get the dimension of Atkin-Lehner eigenspace or do you have any data already obtained?
I need the dimensions of the Atkin-Lehner eigenspace for the paper I'm writing.
As is well known, the cuspidal space $S_{k}(\Gamma_{0}(N))$ can be decomposed by Atkin Lehner involution. For example, ...
- 37k
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votes
3
answers
546
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Why mpmath computes $\sum_{n=2}^\infty (-1)^n\log(n)=\log\left(\frac1 2 \sqrt{2} \sqrt{\pi}\right)$
Working with precision 500 decimal digits, mpmath in sage computes:
$$\sum_{n=2}^\infty (-1)^n\log(n)=\log\left(\frac1 2 \sqrt{2} \sqrt{\pi}\right).\tag{1}\label{1}$$
We believe the LHS of \eqref{1} ...
- 41.1k
1
vote
0
answers
173
views
Calculating multiplication in a finite dimensional algebra over $\mathbb{Q}$
Suppose $ L $ be an extension over $ \mathbb{Q} $ of degree $ n $. Let $\{e_{1},e_{2},\dots,e_{n}\} $ be a basis of this extension. Now I know the product $ e_{i}^{2} $ and $ e_{i}e_{j} $ . So we can ...
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0
answers
313
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Degree $8$ cyclic extension over $\mathbb{Q}$
Actually I am interested in degree $ 8 $ cyclic extension over $ \mathbb{Q} $. Let $ L $ be such extension. At first I was thinking to take basis as normal basis, as we can determine the galois group ...
- 923
1
vote
0
answers
136
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Can PARI compute class numbers without factoring the discriminant?
When calculating properties of algebraic number fields, one of the hardest steps is factorizing the discriminant of a defining polynomial. This is necessary in the Pohst-Zassenhaus algorithm for ...
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votes
1
answer
322
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How to calculate genus number of number field using sage?
I am looking to find real quadratic fields whose Hilbert class field is abelian over $\Bbb Q$. Then I learned about genus numbers and genus field of the number field. It is enough to find a number ...
- 4,713
3
votes
1
answer
356
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Understanding the implementation of the $p$-adic(?) sigma function in SageMath
I'm trying to understand the (pretty undocumented) method .sigma() method for formal groups of elliptic curves, as listed here. The source code looks like this:
<...
- 1,986
2
votes
1
answer
196
views
Software for $S$-unit equation
Is there any implementation available of an algorithm which solves in full generality the $S$-unit equation $x+y=1$ in a number field? It seems that Magma solves $ax+by=c$ but only in the algebraic ...
- 188k
6
votes
0
answers
259
views
Is there an integral simple fusion ring rank<6, FPdim>60 and Frobenius type?
A fusion ring is a finite dimensional $\mathbb{Z}$-module
$\mathbb{Z}\mathcal{B}$ together with a distinguished basis
$\mathcal{B} = \{ h_1,...,h_r\}$ and fusion rules $ h_i \cdot h_j =
\sum_k n_{ij}^...
4
votes
1
answer
486
views
All rational periodic points
I am trying to find all rational periodic points of a polynomial. To specify: a periodic point is the point that satisfy $f^n(x)=x$. It is related to dynamical systems in fact. So the current codes ...
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3
votes
2
answers
380
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How to find a solution of a large system of linear diophantine inequalities?
I need to find a solution (all solutions, or at least upper and lower bounds) in positive integer numbers to the system $Ax \ge f$, where $A$ is an integer matrix.
With SageMath, I solved it with the ...
- 34.4k
4
votes
0
answers
260
views
Indexed character tables for wreath products in Sage and GAP
I am trying to obtain character table for the Hyperoctahedral group $\mathcal{H}_n$ in Sage using GAP.
This group arises as the wreath product $\mathcal{C}_2 \wr \mathcal{S}_n$, so of course I can ...
- 41
5
votes
2
answers
392
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 ...
- 185
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votes
3
answers
896
views
What CASes say about the analytic rank of rank 8 elliptic curve '457532830151317a1'
For the rank $8$ elliptic curve with a-invariants $(0, 0, 1, -23737, 960366)$
sage 5.3 reports analytic rank $4$ in about 2.4 hours.
Almost sure this a bug, so I am interested what other CAS say on ...
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0
votes
1
answer
359
views
Mistake in SageMathCell code, finding integral points on elliptic curves [closed]
I've the following number:
$$12\left(n-2\right)^2x^3+36\left(n-2\right)x^2-12\left(n-5\right)\left(n-2\right)x+9\left(n-4\right)^2\tag1$$
Now I know that $n\in\mathbb{N}^+$ and $n\ge3$ (and $n$ has ...
4
votes
2
answers
754
views
Finding relations between invariant polynomials
Suppose I have an action of a linear reductive group ($GL(2,\mathbb{C})^2$ in this case) on a complex vector space (of dimension $16$) and I want to compute explicitly the ring of invariants of this ...
- 101
5
votes
1
answer
413
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Implementing zeta functions of algebraic varieties in SAGE
I am fairly new to sage, I was studying zeta functions of hypersurfaces over finite fields and I don't know how to compute them in Sage. Are there any packages that do most of the work, or maybe some ...
- 37k
4
votes
2
answers
423
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
...
- 2,449
4
votes
1
answer
202
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/...
- 8,597
1
vote
2
answers
361
views
Ihara zeta function (graph theory) coefficients using a line graph [closed]
I'VE COMPLETELY REVISED MY QUESTION
I wish to take a simple undirected graph (i.e. the complete graph K_4)
Arbitrarily direct said graph, and then create a line graph from the directed version of ...
- 3,597
12
votes
0
answers
1k
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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
1
answer
266
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 ...
- 2,784
3
votes
0
answers
698
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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 ...
10
votes
1
answer
531
views
Genus of the graph $K_{4,2,2,2}$
I have ask this question in math.stackexchange, here. Since, there is no answer and apart from that i feel that the problem is difficult, i would like to ask it here. The problem is to find the genus ...
- 296
5
votes
0
answers
185
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 ...
- 5,822
11
votes
1
answer
635
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 ...
- 20.2k
4
votes
1
answer
381
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 Möbius function $\mu$.
Question 1: What class of lattices the following property characterizes? $$\mu(\hat{0},...
2
votes
1
answer
286
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 ...
- 11.8k
9
votes
6
answers
4k
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
"...
- 2,753
3
votes
0
answers
247
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 ...
1
vote
1
answer
295
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: ...
- 1,961
2
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0
answers
97
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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 ...
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