Questions tagged [sagemath]
For mathematical questions involving the mathematical software system SageMath. Note that this tag should not be used for technical support.
435 questions
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Finding isogeny is Sage
I have this elliptic curve $E$ over $\mathbb{Q}(\sqrt{2})$ given by Weierstrass equation ${y}^2+a{y}={x}^{3}-{x}^{2}-19{x}-27$ where $a=\sqrt{2}$. This is a $\mathbb{Q}$-curve, meaning that it is ...
- 1,799
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Volcano of $2$-isogenies of elliptic curves with prescribed shape.
I want to construct a volcano of $2$-isogenies such that it is a binary tree (of depth $3$ in my example below).
Based on Theorem 70, page 28 and Theorem 22.11 page 7, I need to find a discriminant $\...
- 61
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SageMath's Automaton method number_of_words error
Consider the language of those $w\in \{a,b,c,d\}^*$ that contain $ab$. Corresponding DFA is (written in SageMath):
...
- 12.7k
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How to translate direct product of groups tuple notation to Sagemath compatible form
I am trying to understand how to get from a cartesian view point of the direct product of finite groups to the usage in sagemath.
For example, I want to analyze the direct product of $S_4$ with itself,...
- 1,113
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Closest point in high dimensions
Is there an algorithm to find the closest point, not the distance, to a given point $x_0$ from a surface defined by a system of linear equations?
If we have $A_{1,3} \times x_{3,1} = B_{1,1}$, that's ...
- 123
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90
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Visualizing the winding index of complex curves (sagemath, matplotlib) [closed]
I'm working on visualizing the winding number of complex curves using SageMath/Matplotlib. At this point, I already have the curve plotted:
Plotted lissajous curve
Colorization of different regions of ...
- 29
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31
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Write an element of an ideal in a number field as a linear combination of the generators in sage
Suppose I have, in sage, a number field $K$ and an ideal $I$ of $\mathcal{O}_K$ given by generators $I = (x_1, \ldots, x_r)$. Given an element $x \in I$, how can I find the elements $\lambda_1, \ldots,...
- 111
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Investigating subgroups of finitely presented groups in SageMath
Investigating the subgroups of a finitely presented group in SageMath seems to be problematic.
Simple questions like is_normal() do not work for them.
In this question I am specifically interested in ...
- 7,908
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134
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Elliptic curve $y^2=x^3+ax^3+bx$ with rational 2-torsion in Magma/Sage
Let $E/\mathbb{Q}: y^2=x^3+ax+b$ be an elliptic curve with $E(\mathbb{Q})[2]\cong \mathbb{Z}/2\mathbb{Z}$. I know that we can rewrite the equation of $E/\mathbb{Q}$ in the form $y^2=x^3+a'x^2+b'x$ (...
- 6,877
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What does the finite group $4_1 \cdot L_3(4)$ mean?
I recently came across a paper (Table 1) that makes reference to a finite linear group $4_1 \cdot L_3(4)$.
I understand that $L_n(q)$ is used as shorthand to refer to $PSL_n(q)$. But I am not sure how ...
3
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90
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$\pi$-adic expansions and constants in SAGE
I am trying to use SAGE to compute some $\pi$-adic expansions of units in the field $\mathbb{Q}_p(\mu_p)$ where $\pi=\zeta-1$. The issue I'm having is as follows: For each element $\epsilon$ of $\mu_{...
- 311
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How to ask Sage for $6\times6$ matrices $A$, $B$, $C$, $D$ of a certain form over a ring, such that $AC=BD=AD+BC=0$, $AD\ne0$, $BC\ne0$?
Let $R$ be a ring. Suppose
$$M(R)= \left \{\;\begin{bmatrix}
a & d & 0 & 0 & 0 & 0 \\
0 & b & 0 & 0 & 0 & 0 \\
0 & 0 & c & e & 0 & 0 \\
0 &...
- 845
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182
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Number of preceding edges for green subpaths of a maximal Dyck path for $r\geq 3$ and $n\geq 6$
In order to understand Theorem 9 from https://arxiv.org/pdf/1106.0952 I like to check with SageMath that
$$ x_{n} = \frac{1+x_{n-1}^r}{x_{n-2}}, \ \ \text{for any}\ n\geq 4, \ r\geq 2\ \text{ with ...
- 2,569
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Error with semidirect_product in GAP
EDIT: problem is resolved, it was my mistake.
Following code snippet produces:
GAPError: Error, no method found! Error, no 1st choice method found for `SemidirectProduct' on 3 arguments
The 2nd ...
- 7,908
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Multiplication table of $\mathbb{F_2}[\mathcal{Q_8}]$ in sagemath
Let $\mathbb{F_2}$ be the ring of integers modulo 2 and $\mathcal{Q_8}$ be the group of quaternions such that $\mathcal{Q_8}= \{e,\bar{e},i,\bar{i},j,\bar{j},k,\bar{k}\}$. Then $\mathbb{F_2}[\mathcal{...
- 845