Partitions
Young Diagram Calculator
Draw a partition by cells and read off hooks, conjugates, tableaux counts, weights, and related data.
Open calculatorMenu
Constructed Websites
A compact directory for the browser-side mathematical tools in this folder. Each entry has a GIF preview slot and a direct link to the working page.
Representation Theory
Young Diagram2 Calculator
Work with pairs of partitions, tensor products, Littlewood-Richardson data, and fixed-rank Lie types.
Open calculatorKnots, Links, and Surfaces
Mosaic Calculator
Build hexagonal or square mosaics for knots, links, dual graphs, and glued background surfaces; inspect invariants, cusps, and surface types.
Open calculatorLinear Algebra
Matrix Calculator
Edit matrices and compute standard linear algebra outputs inside the shared applet interface.
Open calculatorAlgebraic Geometry
Sheaf Calculator
Assemble varieties, maps, and sheaves, then compute characteristic classes and pushforward-style data.
Open calculatorLie Theory
Dynkin Diagram Calculator
Switch between classical and exceptional Dynkin types and inspect their diagram and root-system data.
Open calculatorAcknowledgements
References Followed Directly
The applets here were not designed in isolation. These are the websites I used most directly as models or mathematical references when asking AI to help construct the pages.
Young Diagram Calculator
Lauren Williams' Young Diagram Applet
The single Young diagram calculator follows this original combinatorics applet most directly.
Open archived appletYoung Diagram2 and Dynkin Diagram
Lievis
Lievis guided the two-dimensional slice visualization in the double Young diagram calculator, and also influenced the Dynkin diagram calculator.
Open LievisMosaic Calculator Archive
Hexapipes, KnotFolio, and KnotInfo
Hexapipes suggested the main canvas interaction, KnotFolio suggested the idea of identifying drawn knots, and KnotInfo supplied knot naming conventions and database context.
Sheaf Calculator
Cohomology Tables
Pieter Belmans' cohomology tables were a direct reference for the sheaf calculator's algebraic geometry viewpoint.
Open cohomology tablesTheorem Graph Calculator
q.uiver
The arrow type controls and endpoint vocabulary in the theorem graph calculator learned a lot from q.uiver's diagram editor.
Open q.uiverPlace Ramification Calculator
LMFDB Beta
LMFDB's database style and number-theory organization were a direct reference for the place ramification calculator.
Open LMFDB betaBroader List
Database and Atlas Recommendations
A larger collection of databases, atlases, and mathematical web tools is kept in the recommendation page.
Open recommendation listSources
Bibliography
Article-level sources and notes on where they were used while building the toolkit.
Open bibliographyPrototypes
Prototype Websites
Early versions kept for future development. These pages may be incomplete, rough, or missing demonstration media.
Mathematics
Category Calculator
Sketch categories, opposite categories, symbolic morphism templates, and covariant or contravariant functors.
Open prototypeMathematics
Theorem Graph Calculator
Build a dependency graph of theorem, lemma, conjecture, and reference nodes.
Open prototypeAlgebraic Geometry
Sheaf Complex Calculator
Strengthen the sheaf calculator with editable LaTeX chain complexes and filtrations.
Open prototypeNumber Theory
Place Ramification Calculator
Explore how rational primes split or ramify in selected number-field examples.
Open prototypeGames
Ramified Minigames
Play small surface-aware games, beginning with a glued-boundary 2048 variant.
Open prototype