Questions tagged [sagemath]

For questions concerning the mathematical software system SageMath.

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14
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486 views

Genus of the graph $K_{4,2,2,2}$.

What is the genus of the complete $4-$partite graph $K_{4,2,2,2}$? What i know: Since $K_{4,4,2}$ is a subgraph of $K_{4,2,2,2}$, and genus of $K_{4,4,2}$ is 2, $K_{4,2,2,2}$ has genus greater than ...
5
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265 views

p-adic liftings on SAGE

I asked a question the other day: Multidimensional Hensel lifting which @Hurkyl kindly and very elegantly answered. A follow-on from this is that I have tried to implement exactly the "algorithm" ...
4
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0answers
64 views

What happens with subdivisions of normal fans in Sage?

I've been trying to compute specific subdivisions of a particular 4D complete fan, to try to speed up computations I have started looking into using Sage. The problem I'm having is that I would like ...
4
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0answers
90 views

Computing center of an algebra

Let us define an associative algebra over $\mathbb{C}$ with generators $x, y, z$ and the following relations: $x^2=x, y^2=y, z^2=z, 2yxy=y, 3zyz=z, xz=zx$. I am interested in finding center of this ...
4
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0answers
111 views

$\mathbb{Q}$ isn't a number field for SAGE

This is more a question about the weird behavior of SAGE: ...
4
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0answers
1k views

SAGE vs. Mathematica for Lie algebras / groups?

What math software is better for working with Lie algebras and Lie groups, SAGE or Mathematica?
4
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0answers
101 views

Using sage to test for squares in residue fields

Let $K$ be a number field, $x \in \mathcal{O}_K$, and $\mathfrak{p} $ a prime of $K$. I want to find out using sage whether or not the reduction of $x$ modulo $\mathfrak{p}$ is a square in the ...
3
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0answers
240 views

Computing Galois groups of function fields in sage

I found documentation on how to compute galois groups for number fields in sage. Is it possible to do the same for function field extensions? I only need it in the simple case of $t - f(x)$ over $k(t)$...
3
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251 views

Software for computing generators of the invariant rings of the symmetric groups

(Please skip to the last paragraph if you are interested in just the question) I wish to compute the generators of the ring of invariants for a symmetric group acting on a polynomial ring using a ...
3
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0answers
95 views

Squares of finite fields (mod p*q)

Lets say we have $\mathbb{Z}_p$, where $p$ is prime. For each element ($x$) we have two squares ($y$) so that $y^2=x$, i.e., if $p=7$ for $x=4$ we have $y_1=2,y_2=7-2=5,y=\pm2 $. Let's have $\mathbb{...
3
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0answers
268 views

Modular forms on $\Gamma_0(N)$ with character in Sage

I'm trying to work with modular forms on $\Gamma_0(N)$ with character in Sage. In particular, I've been using the following: ...
2
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0answers
96 views

How to compute the ray class field of $\mathbb{Q}(i)$?

I want to verify Thm 5.6 in Silvermans Advanced Topics in the Arithmetic of Elliptic Curves that says $K(j(E),h(E[\mathbb{c}])$ is the ray class filed of $K$ modulo $\mathbb{c}$. I choose $K= \mathbb{...
2
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35 views

Sage: Torsion parameter in elliptic_curves db

I'm cross-posting from StackOverflow because I didn't get any answers Looking at the Tables of elliptic curves of a given rank documentation page and at Mazur's Theorem, a question pops out at me: ...
2
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1answer
70 views

Directed Graphs on at most 9 vertices with some properties

Let $\mathcal{F}$ be the family of strongly connected digraphs with $\leq 9$ vertices, up to isomorphism. Asuume that a directed edge from vertex $v$ to $w$, if exists, is unique; and in this case, ...
2
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0answers
86 views

Construction of formula in Sagemath program

Let $P_k:= \mathbb{F}_2[x_1,x_2,\ldots ,x_k]$ be the polynomial algebra in $k$ variables with the degree of each $x_i$ being $1,$ regarded as a module over the mod-$2$ Steenrod algebra $\mathcal{A}.$ ...
2
votes
1answer
318 views

Plot Cayley graphs for generic element groups

I'm a beginner in Abstract Algebra, currently trying to solve all exercises in "A Book of Abstract Algebra" by Pinter. I was wondering if there is a way to draw Cayley graphs for generic element ...
2
votes
1answer
590 views

Finite field and its element with symbols [Sage / Python / …]

I have a finite field $T=GF(2^3)$, normal basis $(a, a^2, a^4)$ and polynomial $f$ from field $T$, which contains unknown variables / symbols. Is it possible to get vector with coordinates of f in ...
2
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0answers
43 views

Can SAGE or othe software compute or guess growth rates of infinite discrete groups?

I am interested in the growth rate of some finitely generated (infinite, non-abelian) discrete groups. Knowing very little about geometric group theory, I am wondering if I can plug them into sage and ...
2
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0answers
109 views

Finding newforms with Sage

I am new to Sage and modular forms. I have some conceptual questions. When I write sage: S = CuspForms(Gamma0(55),2,prec=14) sage: S.new_subspace().basis() ...
1
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67 views

Remainder of multivariate division of polynomials

Consider a homogeneous polynomial of several variables $f(x_1,x_2,\ldots,x_n)$ with the leading term (with respect to lex ordering) having the maximum degree of any $x_i$s to be $k$. Take the ideal I ...
1
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0answers
64 views

Cauchy Integral in Sage Math

I am relatively new to complex analysis and I am trying to write down the following integral in Sage Math: $$ I(k) = \frac{1}{2i\pi}\oint\frac{(1-t^2)}{(1-t)^n}\frac{dt}{t^{k+1}} $$ from a paper that ...
1
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1answer
32 views

Help with sage math defining function of two variables

Hello I need help regarding sage math, since I cant find anything about it on the manuals. So I have a function of the form $F(r,t) = 2r H(t)$ and then i want to perform an operation on it ...
1
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0answers
90 views

A group theoretic interpretation of Lagarias inequality

Let $G$ be a finite group, $S \subset G$ a generating set. Set $\sigma(G):=\sum_{U \subset G} |U| $, where the sum runs over all subgroups $U$ of $G$. Set $H_G := \sum_{g \in G} \frac{1}{|g|+1}$, ...
1
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0answers
43 views

Generating words in a finitely presented group in SAGE

I'm trying to get a list of all words of length $n$ (in the word metric sense) in some finitely presented group. I have tried some very naive enumerations but it is very slow. Is there an efficient ...
1
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1answer
55 views

Understanding Output in SageMath Regarding Dirichlet Characters

p=7 G = DirichletGroup(p); G m=3; n=ZZ((p-1)/m); print m,n c=G[1] c1=c^n;c1 The output is: ...
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30 views

Minimum Spanning set for a given vector

I have a matrix $M \in \mathbb{Q}_{r \times c}$, where $r << c$ and I want to know what is the minimum number $s$ such that some $s$ columns of the matrix span a given vector $v \in \mathbb{Q}^r$...
1
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0answers
194 views

Get primitive root of 1024 bit prime number in sage

How to find the primitive root of a 1024 bit prime number in sage? primitive_root(p) takes forever to calculate.
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0answers
63 views

Boston's “Spaces of constant rank matrices over $\mathrm{GF}(2)$”

Let’s recall what is spaces of matrices of constant rank, that is, in spaces of matrices in which every nonzero matrix has the same rank. The case is, i’m reading journal by NIGEL BOSTON titled “...
1
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1answer
201 views

Linear combination of elements of sets- finding “basis” and implementation in Python/SAGE

I actually have a question concerning both linear algebra and SAGE (or just Python) implementation. Consider for example set with $6$ elements $a,b,c,d,e,f$ and I know some relations that hold ...
1
vote
1answer
54 views

Determining a limsup value

what is meant by 'lim sup' value? is it the convergence value of a sequence when $n$ goes to infinity? What is the answer for, $$\limsup \left(\frac{4}{3n}\right)^{1/n}?$$ can someone help me please?
1
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0answers
36 views

Holomorph of a group in Sage

i want to calculate the holomorph of a group on SageMath, for example G=CyclicPermutationGroup(6) $\\$ H=G.holomorph()$\\$ G.list() , H$\\$ and i get this result: ([(), (1,2,3,4,5,6), (1,3,5)(2,...
1
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0answers
264 views

Breaking ElGammal by solving discrete logarithm in subgroups with Sage

I'm working in the context of ElGamal encryption problem as describe in the second image of this post. In my problem, I work on $\mathbb{Z}_p^*$ with p prime. I'm told that I should look for subgroups ...
1
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0answers
486 views

How to use CVXOPT to solve an semidefinite programming problem

I'm using Sage to solve a problem and would like to use cvxopt to solve a sdp problem. Specifically, I have a list of expressions of the form $$c + \sum_{i,j} a_{i,j} q_{i,j}$$ where each $c$ and all ...
1
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0answers
507 views

Finding equilibrium points of a system of nonlinear differential equations

I am currently working on a spatially explicit ODE model with dispersion to study the population dynamics of mosquitoes. I wish to compute the equilibrium values of the populations as functions of the ...
1
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0answers
393 views

Bezout Coefficient for polynomials in sage?

I want to find the bezout coefficient for those 2 polynomials : $f = 1+x-x^2-x^4+x^5$ and $g = -1+x^2+x^3-x^6$ when I use the gcd function in sage the output is : ...
1
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0answers
78 views

In Sage, how to look at orbits of conjugation in GL(2,q). Actually, their image in PGL(2,q)?

I have a matrix $A$ in $\text{GL}(2,q)$ or order $m$. The cyclic group of order $m$ acts upon $\text{GL}(2,q)$ by conjugation powers of $A$ (choose a generator of the cyclic group to act by ...
1
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0answers
213 views

Necessary and sufficient conditions for Hensel lifting in the multidimensional case

in Multidimensional Hensel lifting, @Hurkyl gave a neat sufficient condition for the existence of $p$-adic liftings in the multidimensional case. I have finally gotten around (but please also see p-...
1
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0answers
54 views

Running gp in sage how do I access. e.g.. e.j

I am new to sage and I am trying to run the gp interface. In gp I can define an elliptic curve e and then access j by e.j ...
1
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2answers
42 views

Irreducibility criterions for polynomials over $\mathbb{Z}$ or $\mathbb{Q}$

Given a polynomial with "large" coefficients and powers over $\mathbb{Z}$ or $\mathbb{Q}$, how can we check the irreducibility of it? For example, let us have the following polynomial in $\mathbb{Z}[...
0
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2answers
38 views

Patterns from an Algorithm

Consider the following algorithm: pick an integer $n> 0$. If $n$ is even, divide by 2. If $n$ is odd, find the least perfect square $m^2$ greater then $n$ and add $m^2$+n. Repeat step 2. with ...
0
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0answers
58 views

Problem with a system of equation

What is the solution of these equations $\begin{align}a1 - 2*b1*b3 - b2^2 - b4^2 - 2*b5*b6=0 \\ a2=0 \\ a3 - b3^2=0 \\ a4 - 2*b3*b4 - b6^2=0 \\ a5=0 \\ a6=0 \\ b1^2=0 \\ b1*b2=0 \\ b1*b4 + 1/2*b5^2=0 ...
0
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0answers
27 views

Kerr metric in SageMath causal visualization

I am studying the Kerr Metric via the SageMath manifolds module and would like to visualize the casual surfaces generated by light cones. Like the circles in this picture: Can anybody provide clues ...
0
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1answer
25 views

Cartesian Product of Graphs Algorithm

I am not quite sure what I am asking but I am having trouble finding the proper context in Google. I wanted to take the Cartesian Product of a certain graph using Sagemath; however, I think either I ...
0
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0answers
30 views

Plotting complicated function on sagemath

I am not sure if this is the right place to ask about coding a program sagemath. But it is the only math online community I know, so I hope I can get some suggestions here. The problem is I want to ...
0
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0answers
35 views

Algebra using sage

Can anyone help in writing a code to find the list of idempotent and primitive elements of a group algebra, the examples goes like this. Let $p$ be an odd prime such that $\bar2$ generates $U(\mathbf{...
0
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0answers
56 views

Find the Order of an Elliptic Curve

I have an Elliptic Curve represented by the following equation and values: Elliptic Curve: y^2 = x^3 + A*x + B mod M ...
0
votes
0answers
10 views

periodicity of a word

I have the following code to create words. sage: M. = FreeMonoid(3) sage: Word(x^3yxz^2x) word: xxxyxzzx I want find the periodicity of a given word. For example ababab has periodicity 3 and ...
0
votes
1answer
44 views

Solving Cauchy's problem with a discontinuous function

I have the Cauchy problem: $$\begin{cases} f'=g(t)+2(f-5) \\ f(0)=2\end{cases}$$ Now $g(t)$ is a periodic function: $$g(t)=\begin{cases} 0,t\in(24k,24k+8)\\ 2,t\notin(24k,24k+8) \end{cases}$$ for $k=...
0
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0answers
91 views

Minimizing function with inequality constraints in R^n

I have a point $p$ in $R^n$, and I need to find the point $q$ which minimizes a distance function $f(p,q)$ with a number of constraints on $q$ (namely, $q$ needs to represent a probability ...
0
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0answers
24 views

sage : plotting graph with dotted edges

I need to draw a graph in which some edges are usual and some edges are dotted. I know how to make all the edges dotted (using the option "dotted" for the parameter edge_style of plot). But I need ...