# Questions tagged [sagemath]

For questions concerning the mathematical software system SageMath.

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### How does “substituting $x=x$” change the behavior of this Sage function?

TL/DR: Why do the Sage functions defined below behave differently? Consider the following recursively-defined sequence of functions, $g_n: \mathbb{R}\to\mathbb{R}$: $$g_0(x) = 1,$$ and for $n\geq 1$...
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### How to avoid nested loops intelligently with the computer when solving Diophantine equations with finite range of variables?

I have 59 quadratic equations in 59 variables $\{x_1, ..., x_{59}\}$ and I'm interested in the integer solutions of this equation system, where all $x_i$ can have values only between $-100$ and $+100$....
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### Mordell Weil group (and other elliptic curves) computations using SageMath(jupyter or offline version)

I apologise in advance if the question of this sort is not appropriate for this site. I am new to SageMath and have been exploring computations related to elliptic curves with it, this hasn't been a ...
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### Is there a CAS that can compute a direct product decomposition of modular group algebras?

Let $G$ be a finite group and $k$ be a finite field of characteristic $p>0$ such that $p\mid |G|$. Is there a computer algebra system which can compute a direct product decomposition of such ...
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### What are matrix spaces used for in Sage?

What are some computations/ calculations in Sagemath which are done better/ more elegantly because of the existence of matrix spaces? Most of the times it seems to me that constructing matrices with <...
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### Casting and Partial Fractions for symbolic generating function?

This is probably a silly question, but I can't seem to find an answer anywhere. It seems odd to me that Sage should allow us to get a series expansion for a generating function, but won't allow us to ...
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### Are results found of an Elliptic Curve by SageMathCell proven (does there exists no more solutions)?

Well, I have for example the following SageMathCell-code: ...
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### Numerical Integration over region with singularities

I am trying to integrate the following $$\int_0^{2\pi}\frac{1}{\sqrt{1-\cos(x)}}dx$$ and I am stuck on how to proceed using Matlab or Sage.
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### Numerical Integration with constants

I am having trouble trying to integrate the following integral numerically because of the constant z $$\int_{-5}^5(x^2+z^2)^{-1}(x^2+25+z^2)^{-0.5}dx$$ Is there any way to evaluate this integral on ...