Modules, maps and derived algebra
These treatments share a subject; their labels distinguish the questions they answer.
- Categories, encodings, and derived computations — Mathematical lesson. In which category does a computation take place, and when can its result be transported?
- Indicator presentations: building a module from regions and a matrix — Mathematical lesson. How can regions and a matrix define spaces and their maps?
- Inspect spaces and maps — Mathematical lesson. How does the computed encoding recover the square and its spaces and maps?
- Persistence modules over posets — Mathematical lesson. How do vector spaces and compatible maps describe persistence?
- Tameness and scope: when finite descriptions exist — Mathematical lesson. When do constant subdivisions, finite encodings and finite fringe presentations exist?
- Why finite computations stay tame — Mathematical lesson. Why do finite constructions and compatible maps preserve tame descriptions?
- Choosing and inspecting resolutions — Library guide. Which resolution or Betti computation answers my question without computing unnecessary terms?
- Exploring spaces and maps — Library guide. How do I investigate a constructed object and request deeper information when needed?
- From inputs to computed objects — Library guide. Which construction route should I choose, and what object will it return?
- Inspection and explicit computation — Library guide. What is already retained, and what extra computation does my next query request?
- Numerical derived algebra — Library guide. How do tolerances affect derived algebra, and how should I assess the answer?
- Options must affect the requested computation — API reference. Which options change mathematical meaning, computation, or storage?
- Exact rational coordinates — Implementation account. Which representations and algorithms underlie exact rational coordinates, and why?
- From visual specifications to renderers and exports — Implementation account. Which representations and algorithms underlie from visual specifications to renderers and exports, and why?
- Finite-module algebra: TamerOp and QPA — Benchmark report. What does the scoped comparison with QPA establish?