Computational algebraic number theory
Computer Algebra and Symbolic Computation System for Combinatorics and Algebraic Number Theory for JavaScript
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.
A formalization of quadratic number fields in Lean 4
Formalising the Ring of Integers in Quadratic Fields in the Lean proof assistant.
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.
Circular units of real abelian fields with four ramified primes.
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.
A Go-based symbolic algebra engine for parsing, simplifying, and manipulating mathematical expressions. Designed for compilers, research tooling, and symbolic computation. A symbolic math expression simplifier and optimizer.
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)
Proof package for a certified pointwise lower bound in the Erdős unit-distance problem
An implementation of some mathematics of "Class group of Positive-definite Binary Quadratic Forms" in Python 3
continued fractions tools
Computational verification of Pisot pruning across the trinomial family x^n = x + 1 — three-test suite for the algebraic foundation of Pisot Dimensional Theory.
Leopoldt's conjecture via p-adic regulator persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.
Verification code for "Arithmetic Geometry at the Pisot Boundary" — five arithmetic theorems and the Dimensional Norm-Hodge Theorem for the PDT polynomials