# 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)^{...
• 184
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### 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 ...
• 1,758
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### 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 ...
1 vote
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### 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 $G = \text{Sym}_4$...
• 310
1 vote
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### 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 ...
• 111
1 vote
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### 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 ...
• 319
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 ...
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1 vote
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### 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/...
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 ...
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