AxiomForge

AxiomForge — Build, Verify & Visualize Finite Algebra

AxiomForge is a dedicated lab for exploring finite algebraic structures. Define groups, rings, and fields from element sets and Cayley tables, then verify axioms, study homomorphisms, and visualize structure behavior — all in one polished mobile workspace. Verify Axioms Automatically Run a full axiom inspection with one tap. AxiomForge checks closure, associativity, identity elements, inverses, commutativity, distributivity, and field conditions. Each result is reported clearly as passed, failed, or not applicable, with an inferred structure type when possible.

Study Homomorphisms & Isomorphisms Define mappings between structures and test whether they preserve operations. Instantly see whether a map is a homomorphism, isomorphism, injection, or surjection, with detailed violation messages when conditions fail.

Advanced Algebraic Tools Go beyond basic verification with quotient subgroup coset computation, direct products, free monoids, and free groups. Explore normal subgroups, build quotient tables, and generate sample reduced words from custom generators.

Live Visualization in the Lab Turn abstract tables into clear visuals. View neon-styled Cayley tables and operation relation graphs that update as you build, making structure behavior easier to understand at a glance.

Designed for Learners & Enthusiasts AxiomForge combines a sleek dark neon interface with a clean mathematical workflow. Five focused modules — Home, Lab, Verify, Maps, and Tools — keep every feature within easy reach. Share feedback anytime to help shape future updates.

Whether you are studying abstract algebra, preparing coursework, or experimenting with finite structures out of curiosity, AxiomForge gives you a practical lab for building, testing, and seeing algebra in action.