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Choose an area to find its mathematical lessons, library guides, reference material, implementation accounts and benchmark reports. An article can belong to several areas; every link opens its one canonical treatment.
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Article outline by topic
Getting started
- A hole appears and disappears Mathematical lesson — When does a hole appear and disappear, and how can I read its interval?
- Optional integrations Task recipe — Which dependency activates the optional capability I need?
Persistence and filtered complexes
- A hole appears and disappears Mathematical lesson — When does a hole appear and disappear, and how can I read its interval?
- Finite encodings: recovering a module from finite data Mathematical lesson — How can finite data recover a module over an infinite parameter domain?
- Persistence modules over posets Mathematical lesson — How do vector spaces and compatible maps describe persistence?
- Why two parameters change the problem Mathematical lesson — Why do two parameters require spaces and maps beyond a barcode?
- Choosing views and inspecting intervals Library guide — Which view lets me investigate the mathematical object I have computed?
- From inputs to computed objects Library guide — Which construction route should I choose, and what object will it return?
- Ordinary persistent homology Library guide — Which ordinary persistence construction and retained output answer my question?
- Explain a distance through its matching Task recipe — Which matched and unmatched intervals account for a computed diagram distance?
- Ordinary persistence: TamerOp and PHAT Benchmark report — What does the scoped comparison with PHAT establish?
- Vietoris–Rips persistence: TamerOp and Ripser.py Benchmark report — What does the fixed comparison with Ripser.py establish for ordinary Rips barcodes, cocycles and landmark workflows?
Finite descriptions and parameter queries
- Categories, encodings, and derived computations Mathematical lesson — In which category does a computation take place, and when can its result be transported?
- Finite encodings: recovering a module from finite data Mathematical lesson — How can finite data recover a module over an infinite parameter domain?
- 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?
- 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?
- Why two parameters change the problem Mathematical lesson — Why do two parameters require spaces and maps beyond a barcode?
- Choosing and inspecting resolutions Library guide — Which resolution or Betti computation answers my question without computing unnecessary terms?
- Choosing views and inspecting intervals Library guide — Which view lets me investigate the mathematical object I have computed?
- Exact coverage-depth windows Library guide — How can I restrict coverage depth while preserving the required module?
- Exact matching distance in a finite window Library guide — Which finite-window matching question can I compute, and what does the result establish?
- Exact multicover computation Library guide — How do I choose an exact multicover construction and interpret its output?
- 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?
- Ingestion options and their mathematical effects Library guide — Which input and construction choices change the represented module?
- Inspection and explicit computation Library guide — What is already retained, and what extra computation does my next query request?
- Options must affect the requested computation API reference — Which options change mathematical meaning, computation, or storage?
Modules, maps and derived algebra
- 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?
Geometric inputs and filtrations
- Exact coverage-depth windows Library guide — How can I restrict coverage depth while preserving the required module?
- Exact multicover computation Library guide — How do I choose an exact multicover construction and interpret its output?
- Exact rhomboid grades Library guide — Which filtration coordinates remain exact through queries, plots and saving?
- From inputs to computed objects Library guide — Which construction route should I choose, and what object will it return?
- Ingestion options and their mathematical effects Library guide — Which input and construction choices change the represented module?
- Ordinary persistent homology Library guide — Which ordinary persistence construction and retained output answer my question?
- Concurrent polyhedral computations Task recipe — How can I safely run polyhedral computations concurrently?
Invariants, slices and distances
- Exact matching distance in a finite window Library guide — Which finite-window matching question can I compute, and what does the result establish?
- Explain a distance through its matching Task recipe — Which matched and unmatched intervals account for a computed diagram distance?
Features and data analysis
- Ordinary persistent homology Library guide — Which ordinary persistence construction and retained output answer my question?
Visualization and interaction
- A hole appears and disappears Mathematical lesson — When does a hole appear and disappear, and how can I read its interval?
- Inspect spaces and maps Mathematical lesson — How does the computed encoding recover the square and its spaces and maps?
- Choosing and inspecting resolutions Library guide — Which resolution or Betti computation answers my question without computing unnecessary terms?
- Choosing views and inspecting intervals Library guide — Which view lets me investigate the mathematical object I have computed?
- Exploring spaces and maps Library guide — How do I investigate a constructed object and request deeper information when needed?
- Ordinary persistent homology Library guide — Which ordinary persistence construction and retained output answer my question?
- Explain a distance through its matching Task recipe — Which matched and unmatched intervals account for a computed diagram distance?
- Optional integrations Task recipe — Which dependency activates the optional capability I need?
- Visualization reference API reference — Which visual specifications, sessions, renderers and exports are supported?
- From visual specifications to renderers and exports Implementation account — Which representations and algorithms underlie from visual specifications to renderers and exports, and why?
Data, saving and interchange
- Exact rhomboid grades Library guide — Which filtration coordinates remain exact through queries, plots and saving?
- Ordinary persistent homology Library guide — Which ordinary persistence construction and retained output answer my question?
- Optional integrations Task recipe — Which dependency activates the optional capability I need?
Fields, grades and numerical arithmetic
- Exact rhomboid grades Library guide — Which filtration coordinates remain exact through queries, plots and saving?
- Numerical derived algebra Library guide — How do tolerances affect derived algebra, and how should I assess the answer?
- Exact rational coordinates Implementation account — Which representations and algorithms underlie exact rational coordinates, and why?
Performance and comparisons
- Inspection and explicit computation Library guide — What is already retained, and what extra computation does my next query request?
- Concurrent polyhedral computations Task recipe — How can I safely run polyhedral computations concurrently?
- Finite-module algebra: TamerOp and QPA Benchmark report — What does the scoped comparison with QPA establish?
- Ordinary persistence: TamerOp and PHAT Benchmark report — What does the scoped comparison with PHAT establish?
- Vietoris–Rips persistence: TamerOp and Ripser.py Benchmark report — What does the fixed comparison with Ripser.py establish for ordinary Rips barcodes, cocycles and landmark workflows?
- Benchmarking TamerOp Contributor guide — How do I measure a meaningful computation and report what the evidence supports?
- Designing a comparison that can finish Contributor guide — How do I design a bounded, semantically matched comparison and finish it?
- Visual style for benchmark reports Contributor guide — How should a benchmark report look and explain its measured evidence?
Documentation and navigation
- Build the teaching site Contributor guide — How do I build and review canonical lessons, downloads and site pages?
- Maintaining the API inventory and documentation backlog Contributor guide — How do I reconcile runtime bindings with intended API documentation?
- Maintaining the article inventory Contributor guide — How do I maintain article identities, boundaries, topic membership and migration intent?
- Visual style for benchmark reports Contributor guide — How should a benchmark report look and explain its measured evidence?
- Writing documentation that teaches Contributor guide — How do I write precise, connected and approachable TamerOp documentation?
Development and maintenance
- Benchmarking TamerOp Contributor guide — How do I measure a meaningful computation and report what the evidence supports?
- Build the teaching site Contributor guide — How do I build and review canonical lessons, downloads and site pages?
- Contributing to TamerOp Contributor guide — How can I contribute a useful change or report?
- Designing a comparison that can finish Contributor guide — How do I design a bounded, semantically matched comparison and finish it?
- Maintaining the API inventory and documentation backlog Contributor guide — How do I reconcile runtime bindings with intended API documentation?
- Releasing TamerOp Contributor guide — How do I validate and publish one release candidate?
- Running correctness tests Contributor guide — Which correctness checks are appropriate for a change or release?