Questions tagged [sagemath]

For questions concerning the mathematical software system SageMath.

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Simplifying rational function in Sage

Let $g\geq 1$ be an integer and define three rational functions and their sum by \begin{align*} H(q,t) &= f_1(q,t) + f_2(q,t) + f_3(q,t) \\ &:= \frac{t^{8g-4}q^{2g-1}(1+tq)^{2g-1}(1+q^2t^3)^{...
Bailey's user avatar
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2 votes
1 answer
37 views

Testing compositeness of the order of an elliptic curve over a prime field

Assume an elliptic curve equation in short Weierstrass form $y^2=x^3+a\,x+b$ in a prime field $\mathbb F_p$ for small given $a,b$ (e.g. $a=3$, $b=2$) and given large primes $p$ (e.g. 256-bit). We want ...
fgrieu's user avatar
  • 1,758
0 votes
1 answer
27 views

Alternating Frobenius form in Sage

Given an alternating, non-degenerate matrix $A$ over the integers, I need to compute the matrix "closest" to the standard symplectic form that can be obtained from $A$ by an integer change ...
Oliver Miller's user avatar
1 vote
1 answer
68 views

How to read labels of character tables in SageMath (and GAP)?

Note: SageMath's Group.character_table() method is built as a wrapper for GAP's CharacterTable() function. Let $G = \text{Sym}_4$...
Gutiérrez's user avatar
1 vote
1 answer
59 views

Check finiteness of ring map with SAGE

(I asked this question in a SAGE-specialized forum --see here--, but did not received an answer there sofar. I therefore decided to post the question also here.) Let $R \rightarrow S$ be a ring map. I ...
AlexIvanov's user avatar
1 vote
1 answer
89 views

How to check if two integer-valued polynomials have a common power?

Let $p, q \in \mathbb{Z}[x]$ be two integer-valued polynomial. Is there a (hopefully efficient) algorithm that checks whether $p^n = q^m$ for some $n,m \geq 1$? I need such an algorithm for a program ...
RB1995's user avatar
  • 319
0 votes
1 answer
142 views

Sagemath: Solving linear equation symbolically takes a lot of time [closed]

I have a set of polynomials $\lbrace p_{ij}|i,j\in\lbrace 1,...,n\rbrace \rbrace$ with $p_{ij}\in \mathbb{Z}[x]$ as well as degree $n$ and a given constant real vector $b\in\mathbb{R}^n$. The ...
Jfischer's user avatar
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1 vote
1 answer
87 views

Determining the size of an $m$-torsion group of elliptic curves over finite fields

In this paper by De Feo the following is stated (in proposition 4): Let $E$ be an elliptic curve defined over a field $k$, and let $m\neq 0$ be an integer. The $m$-torsion group of $E$, denoted by $E[...
jorisperrenet's user avatar
1 vote
1 answer
60 views

Algorithm and program for modelling a Free Nilpotent Lie algeabra

I need to compute in a Free Nilpotent Lie Algebra $L$ given by a finite list of generators. For example, put the generators $\{A, B\}$. So, the linear generators for the space of $L$ is $$\{A, B, [A,B]...
mechvel's user avatar
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3D graphing the parameter space

3D parameter spaceHi there I was given the equation X'= [a,b c,0]X and was asked to graph the parameter space as "a" changes. I tried but I'm not completely sure this is what they were ...
user1251629's user avatar
0 votes
1 answer
115 views

Jacobi sum of power residue symbol in Sagemath

I’m computing Jacobi sum of power residue symbol as follows: ...
user682141's user avatar
1 vote
0 answers
60 views

Using Sage to compute facts about modules

I am new to programming in general but in my project, I am required to work with a finite set $S = \{A_1,...,A_n\}$ of $m \times n$ matrices over a finite ring $R$, and the submodule $M$ they generate....
JBuck's user avatar
  • 681
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1 answer
122 views

Help explore parametric system in SageMath

i could use some help in presenting a good solution for this problem : Problem Assume the system of equations in $x, y, z, t$ $ax+y+z+t=1$ $x+ay+z+t=b$ $x+y+az+t=b^2$ $x+y+z+at=b^3$ where $a, b$ are ...
PanMath's user avatar
1 vote
1 answer
91 views

Variant of Segre embedding

We work over a field $k$. We know that there is the Segre embedding $\def\P{\mathbb{P}} \P^2 \times \P^1 \to \P^5$. Now I want an embedding of $\P^2 \times \def\A{\mathbb{A}}\A^1$ into some projective ...
Johann Birnick's user avatar
0 votes
1 answer
26 views

$U(24)$: internal direct product and generators of a subgroup of a full symmetric group

I'm being confused by the following question: Build a permutation representation of U(24). List a representation of each element. Then, construct the group as a subgroup of a full symmetric group ...
pedropedro's user avatar
2 votes
0 answers
56 views

Which two elements of $Z_2 \times Z_4$ might you use to generate all of $Z_2 \times Z_4$? [closed]

In Judson Abstract Algebra: Theory and Applications, p. 176, one can read: Build the permutation representation of $Z_2 \times Z_4$ described in Cayley’s Theorem [...] I got to this point with Sage (...
pedropedro's user avatar
0 votes
1 answer
20 views

Removing simplices from a simplicial complex in sage

The context for this problem is this: given a simplicial complex $X$ and a simplex $\sigma \subseteq X$, I want to define a new simplicial complex $Y_\sigma$ to be the subcomplex of $X$ with vertex ...
Joe Wells's user avatar
  • 1,110
3 votes
1 answer
99 views

Problem about the Galois group elements in Sage

I am computing a Galois group as below in Sage. K.<a> = NumberField(x^4-2) L = K.galois_closure('b') G=L.galois_group() Here, $G=\text{Gal}(L/\mathbb{Q)} \...
Ninja's user avatar
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1 vote
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81 views

discrete_log in elliptic curve torsion basis using sage

I want to solve a discrete log problem on elliptic curve using sagemath. Given a basis of E[D], denoted as P and Q. How to solve aP + bQ = R where R is a point of order D.
matthew's user avatar
  • 71
3 votes
1 answer
93 views

Plücker relations in Sagemath from Macaulay2

I am trying to implement the Plücker relations in Sagemath. Sage has an interface for Macaulay2, and this latter has a command Grassmannian(k-1, n-1) for computing ...
Dario Antolini's user avatar
0 votes
1 answer
41 views

Reduced form of symbolic expressions in sagemath

I am working in symbolic ring with two symbols: q and h. The relation between them is $q=e^h$. I want to do some algebra of matrices with symbolic entries. The entries of the input matrices consist of ...
Shruti's user avatar
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1 vote
0 answers
41 views

Computing the cohomology of a complex over $F[x,y]$

Is there a method for computing the generators of the cohomology of a chain complex over the ring $R=F[x,y]$? When $R$ is a PID one can use Smith normal form and there are libraries in Sage that ...
ali's user avatar
  • 2,225
0 votes
0 answers
35 views

Representations of $G=\mathrm{SL}_2(\mathbb{Z}/4\mathbb{Z})$ on SAGE/GAP

Let $G=\mathrm{SL}_2(\mathbb{Z}/4\mathbb{Z})$. I want to use SAGE/GAP to write a code that prints image of all irreducible representations of $G$, when applied on the matrix $\begin{pmatrix} 1 & 1\...
dragoboy's user avatar
  • 1,879
1 vote
0 answers
73 views

Finding and Identifying Finite Subgroups in SageMath

I have a finite subgroup, which I determined to be finite using the is_finite() function. The cardinality() function helped me ...
j.doe's user avatar
  • 217
3 votes
0 answers
88 views

Infinite Groups in SageMath(or in GAP)

I am once again asking more software-related questions, but I am happy to learn a general answer as well. I'm curious about how the is_infinite function works in SageMath (or in GAP). Does it simply ...
j.doe's user avatar
  • 217
1 vote
1 answer
73 views

Understanding whether the addition of an element to a subgroup of an infinite group will result in an infinite group or not in GAP/SageMath

This is more of a software-related question, but I wanted to ask here because I am confident that most people in this forum are well-acquainted with GAP/SageMath and can provide more insight for the ...
j.doe's user avatar
  • 217
0 votes
1 answer
58 views

Question about automorphisms of the cyclotomic field and Sagemath

Let $K = \mathbb{Q}(\zeta_5)$ be the fifth cyclotomic field. I write the following code in sage ...
Ninja's user avatar
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2 votes
1 answer
69 views

Central Products in SageMath

I would like to compute the Central Product of two groups in SageMath. I cannot find any builtins and I'm not sure what group theory packages for Sage may exist. Is there anything out there or am I ...
Spamakin's user avatar
0 votes
1 answer
51 views

Generators of a Galois group in SAGEMath

I have a (potentially silly) question about a problem I've been having with SAGEMath. Let $K$ be the maximal totally real subfield of the cyclotomic field of conductor $24$, i.e. the number field with ...
Chris's user avatar
  • 678
2 votes
1 answer
43 views

Making card configurations in Sagemath

I'm following SageMath's tutorial on Combinatorics and one of the exercizes is to calculate the set of Four of a Kind hands (in card games a hand containing four cards of the same value is called a ...
Luisz's user avatar
  • 21
0 votes
0 answers
29 views

Multi-graded hilbert series in sage

Is there a way to compute the multi-graded Hilbert series in sage? I know that one can do it in Macaulay2, see https://mathoverflow.net/questions/20263/software-for-computing-multi-graded-hilbert-...
Light man's user avatar
0 votes
0 answers
15 views

Hilbert series of superpolynomial ring

I am recently trying to compute Hilbert series involving Grassmann variables. This means I have to deal with super-polynomials. Is there a way to compute the corresponding Hilbert series in sage once ...
Light man's user avatar
1 vote
1 answer
78 views

Different results on Hilbert series in sage and Macaulay2

I am recently trying to compute some complicated Hilbert series. I tried sage and Macaulay2. More precisely, I tried the following command in M2: SS = QQ[ x1, x2, x3, x7, x8, x9, x13, x14, x17, x4, ...
Light man's user avatar
4 votes
1 answer
103 views

How to obtain explicit formula of coefficients for generating functions?

Is there any function in python or sage to obtain explicit formula of coefficients for generating functions. For example, Catalan generating function is given as $${\displaystyle c(x)={\dfrac {1-{\...
Rjda's user avatar
  • 41
0 votes
0 answers
96 views

Counting the number of points on a curve over a finite field by calculators

I want to count the number of points on a algebraic curve $C:y^2=x^5-x+1$ over $\mathbb{F}_{3^n} (n=2,3,4,...)$ by calculators (Pari/GP, Sage, Magma,...). Can you give me a command that solves the ...
user682141's user avatar
0 votes
0 answers
49 views

Finding Elements with Prime Power Orders in the Ring of Integers Modulo 463

Let $\mathbb{Z}^*_{463}$ the ring of integers modulo 463 without the $0$ element. I need to find an element of $(\mathbb{Z}^*_{463},\cdot)$ which have as order a power of a prime. For example, let 27 ...
Dan_Mir's user avatar
  • 11
0 votes
1 answer
92 views

Declaring constants in Sagemath

I want to find the Groebner base of a ideal,the ideal is generated by some polynomials with constant coefficients, but they do not have numerical values. ...
johnyy's user avatar
  • 31
0 votes
0 answers
54 views

Strange Sage behavior grobner bases

I have the following code in Sage ...
johnyy's user avatar
  • 31
-4 votes
2 answers
236 views

How to find generators of $\mathbb{Z}_p$ in Sage [closed]

I don't know anything about Sage, but I need to compute generators of $\mathbb{Z}_p$, $p=463$. How can I do?
Dan_Mir's user avatar
  • 11
0 votes
0 answers
41 views

How can i write $\sqrt[4]{y}$ in sagemath

Well i know i that can write the square root as sqrt(y) but i want to be able to write $\sqrt[4]{y}$ and can't find any information anywhere about how it's done. Hope somebody knows if it's possible ...
Mohammed's user avatar
1 vote
1 answer
67 views

Singular and Sage Grobner bases

Does the function grobner_basis in Sage (which I think comes from the implementation in Singular) compute a reduced Grobner base for an ideal? Or is it just a Grobner base with no special property ?
johnyy's user avatar
  • 31
0 votes
0 answers
38 views

Sagemath -- finding Eigenvalues of a matrix representation of a tensor

I am using sagemath to compute Einstein tensors of a non-standard spacetime. The output is something horrid and non-diagonal. I need to find the Eigenvalues of this tensor... which is represented as a ...
Deepdoop's user avatar
2 votes
0 answers
23 views

Minimal generators for the ring of quasi-symmetric polynomials

Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ of characteristic 0. Then the ring of symmetric polynomials in $R$ is generated (as a $K$-algebra) by the minimal ...
Mare's user avatar
  • 2,322
0 votes
0 answers
54 views

How to substitute unevaluated expression in SageMath?

I have an expression x*y. I want to convert it to latex, while substituting numbers instead of variables. So if I want to substitute 10 instead of ...
g00dds's user avatar
  • 187
0 votes
1 answer
151 views

Is there a way to get SageMath to completely simplify this family of expressions, particularly for $n = 5$?

I am using SageMath for the first time. I have the following long expression, which I want to simplify for integer values of n from 0 to 5: ...
Lawton's user avatar
  • 1,675
1 vote
1 answer
129 views

How can I get Sagemath to simplify the following? [closed]

I am new to sage. If I provide the following instructions to sagemath ...
ebenezer's user avatar
0 votes
0 answers
39 views

How to visualize a polyhedron with faces consisting of different number of vertices?

For each face of a polyhedron, I have a list of all vertices being a part of said face. Example data for a polyhedron consisting of $13$ vertices and $9$ faces, where vertices are numbered from $0$: <...
pakut2's user avatar
  • 101
2 votes
1 answer
184 views

Implementation of Schoof's algorithm on SageMath

I wish to see how Schoof's algorithm of counting points on elliptic curves over finite fields is implemented on SageMath. I have came across this answer https://math.stackexchange.com/a/3722724/...
Soumik Mukherjee's user avatar
0 votes
0 answers
55 views

Plotting trees on sagemath

I'm an undergraduate student doing an independent research on trees, and I want to generate trees and plot them. I'm using a sage notebook with the ipynb extension (using my university's remote ...
lifeisfun's user avatar
  • 143
0 votes
1 answer
195 views

Comparing "diff" in Sagemath and Sympy

I am currently testing two programs of symbolic computation, one written in Sage and one in Sympy, which do similar computations. After running both of them, I found that the one written in Sympy is ...
Miguel Mars's user avatar
  • 1,007

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