Algebra

Reverse-Process Synthetic Data Generation for Math Reasoning

Training LLMs on mathematical reasoning by inverting easy-to-solve problems: generate derivatives, reverse them into integration exercises with full step-by-step solutions.

A Book of Abstract Algebra

Abstract Algebra

Alga: Algebraic Parser Composition through Monadic Design A C++20 Template Library for Type-Safe Text Processing

Algebraic Cipher Types: Computing on Encrypted Data While Preserving Structure

A functorial framework that lifts algebraic structures into the encrypted domain, enabling secure computation that preserves mathematical properties.

An Algebraic Framework for Language Model Composition: Unifying Projections, Mixtures, and Constraints

Language Calculus: An Algebraic Framework for LLM Composition

A mathematical framework that treats language models as algebraic objects with compositional structure.

Algebraic Hashing A Modern C++20 Library for Composable Hash Functions Version 2.0

Algebraic Hashing: Composable Hash Functions Through XOR

A C++ library for composable hash functions using algebraic structure over XOR, with template metaprogramming.

algebraic.mle: MLEs as Algebraic Objects

An R package that treats MLEs as algebraic objects. They carry Fisher information, compose through independent likelihoods, and propagate uncertainty correctly.

algebraic.dist: Distributions as Algebraic Objects in R

An R package that treats probability distributions as algebraic objects. They compose through standard operations. The algebra preserves distributional structure.

Polynomials as Euclidean Domains

The same GCD algorithm works for integers and polynomials because both are Euclidean domains. One structure, many types, same algorithms.

Modular Arithmetic as Rings

Integers modulo N form a ring, an algebraic structure that determines which algorithms apply. Understanding this structure unlocks algorithms from cryptography to competitive programming.