# Questions tagged [sagemath]

For questions concerning the mathematical software system SageMath.

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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 ...
265 views

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" ...
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 ...
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 ...
111 views

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

This is more a question about the weird behavior of SAGE: ...
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?
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 ...
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 $k(t)$...
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 ...
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### 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: ...
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, ...
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### 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 $\mathcal{A}.$ ...
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 ...
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 ...
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 ...
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() ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 $H_G := \sum_{g \in G} \frac{1}{|g|+1}$, ...
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### 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 ...
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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### 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 $v \in \mathbb{Q}^r$...
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.
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 “...
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### 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 ...
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?
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### 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,...
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### 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 ...
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 ...
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### 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 ...
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 : ...
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### 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 ...
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### 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-...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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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{... 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 ... 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 ... 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=...
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 ...