3
votes
1answer
68 views

On Hilbert Class Polynomial

Is there any open source software which computes Hilbert Class polynomial of an imaginary quadratic fields? Thank you in advance
1
vote
0answers
26 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 ...
6
votes
0answers
184 views

Math-related open source software to contribute to

I'm interested in finding a math-related open source project that I can contribute to. I've studied maths and stats at undergraduate level, but I'm a professional software developer and I'll have some ...
3
votes
1answer
238 views

Programmatically solving a system of nonlinear equations over GF(2)

I have the following relatively large system of nonlinear equations over $GF(2)$: $ 0 = w7x7 + w7x5 + w7x4 + w7x0 + w6x6 + w6x5 + w6x1 + w5x7 + w5x6 + w5x2 + w4x7 + w4x3 + w3x4 + w2x5 + w1x6 + w0x7 ...
5
votes
2answers
210 views

Find the rational points on $1 + 18 x + 81 x^2 + 44 x^3 = y^2$ with Sage

I'm trying to use Sage on-line,but I meet some trouble with the code of it. I want to find the rational points on an ellipse curve,such as $$1 + 18 x + 81 x^2 + 44 x^3 = y^2,\tag1$$ I know that ...
5
votes
1answer
156 views

Finding irreducible representations of the following group using GAP

Given the following group of order 24, $$ G = \langle a,b \mid a^2=b^3=(abab^2)^2=1\rangle$$ how can one find (all) the irreducible representations using GAP? Since I have not installed GAP yet, I ...
1
vote
1answer
559 views

In Sage, how to extract coefficient of a polynomial in a ring

For instance, $f=x^2y^2+1$ is an element of $\mathbb{C}[x,y]$, I want to extract the coefficient of $x^2$, which is $y^2$. However "f.coefficient(x,2)" only works for symbolic expressions, are there ...
0
votes
1answer
149 views

How to define a polynomial with abstract coefficients in Sage

Let $f=ax^2+b$ be a polynomial in $Q[x]$, how to define $f$ in sage?
4
votes
0answers
73 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
votes
1answer
193 views

A question about modular forms in SAGE

I was trying to solve Exercise 1.4.5 in Alvaro Lozano-Robledo's book Elliptic Curves, Modular Forms and Their L-functions, which is about representations of integers as sums of 6 squares and its ...
22
votes
1answer
7k views

Is Sage on the same level as Mathematica or Matlab for graph theory and graph visualization?

The context: I'm going to start working on a project that involves running predefined algorithms (and defining my own) for very big graphs (thousands of nodes). Visualization would also be welcome if ...
1
vote
2answers
202 views

Help need in Mathematica or Sage

I want to find the common positive solutions of two polynomials $f_{a,b}(x,y)$, $g_{a,b}(x,y)$ where $a,b$ runs from 0 to 1 with an interval 0.01. Let $(x_0,y_0)$ be a common positive solution. Then ...