Computational algebraic number theory

Advanced Combinatorics and Algebraic Number Theory Symbolic Computation library for JavaScript, Python

An introduction to the basic ideas of commutative algebra

High-performance integer factorization suite implementing GNFS, MPQS, and QS algorithms with optimized lattice reduction, vectorization, GPU acceleration, and tensor-based linear algebra. Features automatic algorithm selection, NUMA-aware scheduling, and checkpoint/restore for computational number theory research and cryptanalytic analysis.

Repository for the FermulerPy core package. Fermulerpy is useful for problems related to various fields of Number Theory.

This repository presents Version 4.0 of a formal, type-theoretic, and fully machine-verifiable proof of the Birch and Swinnerton-Dyer (BSD) Conjecture, built upon the framework of Collapse Theory and the AK High-Dimensional Projection Structural Theory (AK-HDPST) v14.5.

WORK IN PROGRESS: This grew out of the visualization of imaginary quadratic integer rings project.

Here we give an algorithm to determine Shintani domains for non-totally complex number fields from the signed fundamental domains given in the works of Diaz y Diaz, Espinoza and Friedman. We also present some explicit examples of Shintani domains.

Circular units of real abelian fields with four ramified primes.

Examples of Shintani domains for complex quartic number fields. Moreover, we propose in the folder "Algorithm" an implementation to obtain Shintani domains in complex quartic fields (restriction: unit group without torsion)

An implementation of some mathematics of "Class group of Positive-definite Binary Quadratic Forms" in Python 3

Abelian unramified geometric class field theory

Shintani domain for totally complex quartic number fields considering the action of units group with torsion. Including some examples.

continued fractions tools