Implementation bibliography

Academic and software references cited in the implementation accounts.

Nemo and Hecke

Claus Fieker, William Hart, Tommy Hofmann, and Fredrik Johansson. Nemo/Hecke: Computer Algebra and Number Theory Packages for the Julia Programming Language. ISSAC 2017, 157–164. DOI: 10.1145/3087604.3087611 · Open manuscript · Matrix API.

Role: directly used software and its architecture. TamerOp delegates selected exact matrix operations to Nemo; this paper explains its combination of Julia algorithms and specialized native libraries. Use in the coordinate account.

FLINT

The FLINT team. FLINT: Fast Library for Number Theory. Project and citation guidance · Rational matrices · Rational reconstruction.

Role: exact-arithmetic implementation used through Nemo, and a precise reference for reconstruction bounds. The online matrix manual describes multiple solving algorithms; listing them is not a claim about which one a particular TamerOp request invokes. Use in the coordinate account.

Rational reconstruction

Paul S. Wang, M. J. T. Guy, and J. H. Davenport. P-adic reconstruction of rational numbers. ACM SIGSAM Bulletin 16(2), 2–3, 1982. DOI: 10.1145/1089292.1089293 · Paper scan.

Role: mathematical background for a technique implemented locally: reconstructing small rational numbers from modular residues. It supports the uniqueness argument; the implementation additionally checks the original matrix equation. No claim of direct code derivation is made. Use in the coordinate account.

Dixon lifting

John D. Dixon. Exact solution of linear equations using p-adic expansions. Numerische Mathematik 40, 137–141, 1982. DOI: 10.1007/BF01459082.

Role: a related exact-solving method, and context for the backend's available algorithms. Lifting through powers of one prime differs from TamerOp's local independent-prime CRT route. This entry does not claim a local Dixon implementation. Use in the coordinate account.

Generalized rank

Woojin Kim and Facundo Mémoli. Generalized Persistence Diagrams for Persistence Modules over Posets. Journal of Applied and Computational Topology 5, 533–581, 2021. DOI: 10.1007/s41468-021-00075-1.

Role: the mathematical limit-to-colimit rank and generalized persistence diagram framework. TamerOp constructs finite constraint and relation matrices locally, and limits signed reconstruction to the caller's declared family.

Generalized-rank invariant landscapes

Cheng Xin, Soham Mukherjee, Shreyas N. Samaga, and Tamal K. Dey. GRIL: A 2-parameter Persistence Based Vectorization for Machine Learning. Proceedings of Machine Learning Research 221, 2023. Paper and proceedings record.

Role: the continuous worm and landscape definition. TamerOp's supported-grid implementation contracts constant fibers and searches exact critical widths; it does not reuse the paper's filtration-level zigzag implementation.

Bigraded Betti numbers and presentation diagrams

The RIVET developers. Mathematical preliminaries, RIVET documentation. Invariant definitions.

Role: mathematical and visualization context for minimal multigraded free resolutions and their Betti numbers. The finite-poset resolution views use TamerOp's own stored projective/injective terms and verification algorithms; supplied grade coordinates alone do not identify those terms with an ambient free resolution. No RIVET algorithm or code is used by the renderer. Use in the visual-specification account.