Partitions
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. Click a GIF preview or use the direct link to open its working page.
Representation Theory
Work with pairs of partitions, tensor products, Littlewood-Richardson data, and fixed-rank Lie types.
Open calculatorHigher-Dimensional Geometry
Move an affine frame through regular polytopes, spheres, Cartesian frames, and points; compare projection with exact 2D slices.
Open calculatorKnots, Links, and Surfaces
Build hexagonal or square mosaics for knots, links, dual graphs, and glued background surfaces; inspect invariants, cusps, and surface types.
Open calculatorLinear Algebra
Edit matrices and compute standard linear algebra outputs inside the shared applet interface.
Open calculatorAlgebraic Geometry
Assemble varieties, maps, and sheaves, then compute characteristic classes and pushforward-style data.
Open calculatorLie Theory
Switch between classical and exceptional Dynkin types and inspect their diagram and root-system data.
Open calculatorPrototypes
Prototype Websites
Early versions kept for future development. These pages may be incomplete, rough, or missing demonstration media.
Mathematical workspace
Open workspace-native calculators beside a session Assets explorer for varieties, sheaves, and maps.
Open workspaceMathematics
Sketch categories, opposite categories, symbolic morphism templates, and covariant or contravariant functors.
Open prototypeMathematics
Build a dependency graph of theorem, lemma, conjecture, and reference nodes.
Open prototypeNumber Theory
Explore how rational primes split or ramify in selected number-field examples.
Open prototypeSymmetric Groups
Build adjacent-transposition strand diagrams and compare word, cycle, one-line, matrix, and export forms.
Open prototypeAcknowledgements
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
The single Young diagram calculator follows this original combinatorics applet most directly.
Open archived appletYoung Diagram2, Higher-Dimensional Slices, and Dynkin Diagram
Lievis guided the two-dimensional slice visualization in the double Young diagram calculator, informed the Higher-Dimensional Slice Calculator, and also influenced the Dynkin diagram calculator.
Open LievisHigher-Dimensional Slices · Ramified Minigames · Mosaic Calculator
These projects contributed interaction, puzzle, and explanatory ideas across the Higher-Dimensional Slice Calculator, Ramified Minigames, and the Mosaic Calculator.
Mosaic Calculator Archive
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
Pieter Belmans' cohomology tables were a direct reference for the sheaf calculator's algebraic geometry viewpoint.
Open cohomology tablesTheorem Graph Calculator
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's database style and number-theory organization were a direct reference for the place ramification calculator.
Open LMFDB betaBroader List
A larger collection of databases, atlases, and mathematical web tools is kept in the recommendation page.
Open recommendation listSources
Article-level sources and notes on where they were used while building the toolkit.
Open bibliography