https://github.com/andrusovn/elliptic_surfaces
A tool for calculating elliptic surfaces properties such as Zeta-function
Science Score: 13.0%
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Low similarity (4.3%) to scientific vocabulary
Repository
A tool for calculating elliptic surfaces properties such as Zeta-function
Basic Info
- Host: GitHub
- Owner: AndrusovN
- Language: C++
- Default Branch: master
- Size: 20.5 KB
Statistics
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
- Releases: 0
Metadata Files
README.md
A tool for calculating elliptic surface properties such as Zeta-function
Elliptic curves are commonly used in cryptography,
at the same time there are a lot of unresolved mathematical questions
behind this topic. This tool is developed to help
investigating properties of elliptic curves by adding a
parameter t - a new variable in the standard elliptic equation.
So, instead of usual equation (let's say we had an elliptic curve in Weierstrass form, but it's not necessary)
y^2 = x^3 + ax + b
We have an equation describing an elliptic surface:
p(t)y^2 = q(t)x^3 + f(t)x + g(t)
This additional parameter makes a surface from a curve, which is layered with elliptic curves.
One of important properties of a surface (or a curve) is number of points on this surface over a Galois (a.k.a. finite) field. Such numbers form a zeta-function (if assumed a power series with these coefficients) and other algebraic properties. That's why it's important to count number of points on a surface (or a curve) over a Galois field.
This tool helps with finding points over a Galoid field of an algebraic surface.
Currently it's in an early development stage, so the documentation is incomplete :)
Owner
- Name: Nikita Andrusov
- Login: AndrusovN
- Kind: user
- Location: Moscow, Russia
- Website: t.me/n_andrusov
- Repositories: 3
- Profile: https://github.com/AndrusovN
I'm passioned with math and problem solving!