Bibliography

calculator index · sources

Sources

Mathematical Sources

Article-level sources and software references used while building the Pure Math Toolkit. These notes record where each source influenced implementation, both for proper credit and for future debugging. This is a partial bibliography: some references may be missing, and AI-assisted code may reflect algorithms or conventions learned from sources that were not explicitly named.

References

  1. Vincent Delecroix, Johannes Schmitt, and Jason van Zelm. admcycles -- a Sage package for calculations in the tautological ring of the moduli space of stable curves. J. Softw. Algebra Geom. 11 (2021), 89--112. DOI: 10.2140/jsag.2021.11.89. arXiv:2002.01709.

    Used for computing divisors of the dual graph in the Mosaic Calculator.

  2. Roger Howe, Eng-Chye Tan, and Jeb F. Willenbring. Stable branching rules for classical symmetric pairs. Trans. Am. Math. Soc. 357 (2005), no. 4, 1601--1626. DOI: 10.1090/S0002-9947-04-03722-5. arXiv:math/0311159.

    Stable branching formulas and Littlewood-Richardson coefficient conventions currently realized in the Young Diagram Calculator.

  3. I. G. Macdonald. Symmetric products of an algebraic curve. Topology 1 (1962), 319--343. DOI: 10.1016/0040-9383(62)90019-8.

    Used for the Sym^m(C) variety type in the Sheaf Calculator, including Hodge numbers and tangent/cotangent Chern-class formulas.

  4. Sean Quinlan and Oussama Khatib. Elastic Bands: Connecting Path Planning and Control. Proceedings of the 1993 IEEE International Conference on Robotics and Automation, vol. 2 (1993), 802--807. DOI: 10.1109/ROBOT.1993.291936.

    Conceptual source for the Mosaic Calculator's basis-cord length minimization, contraction direction, and elastic-band neighborhood model, adapted here to quotient surfaces and homology constraints.

  5. youmnam. pp-ElasticBand: an implementation of the elastic band method for robot navigation. GitHub repository. github.com/youmnam/pp-ElasticBand.

    Architectural implementation reference for the Mosaic Calculator's elastic-band optimizer. The solver was independently adapted rather than copied literally.

  6. Brian Vincent Mirtich. Impulse-based Dynamic Simulation of Rigid Body Systems. Ph.D. thesis, University of California, Berkeley, 1996. Author's project and thesis page.

    General reference for impulse-based rigid-body collision response and changing rolling, sliding, and contact modes in Topological Billiards.

  7. David Kazhdan and George Lusztig. Representations of Coxeter Groups and Hecke Algebras. Invent. Math. 53 (1979), no. 2, 165--184. DOI: 10.1007/BF01390031.

    Primary source for the Kazhdan--Lusztig basis and polynomials used by the Strand Diagram Calculator.

  8. H. N. V. Temperley and E. H. Lieb. Relations between the 'Percolation' and 'Colouring' Problem and Other Graph-Theoretical Problems Associated with Regular Planar Lattices: Some Exact Results for the 'Percolation' Problem. Proc. R. Soc. Lond. A 322 (1971), no. 1549, 251--280. DOI: 10.1098/rspa.1971.0067.

    Original source associated with the Temperley--Lieb algebra represented diagrammatically in the Strand Diagram Calculator.

  9. Vaughan F. R. Jones. Hecke Algebra Representations of Braid Groups and Link Polynomials. Ann. Math. 126 (1987), no. 2, 335--388. DOI: 10.2307/1971403.

    Reference for the braid-to-Hecke framework and link-polynomial context of the Strand Diagram Calculator.

  10. David A. Cox, John B. Little, and Henry K. Schenck. Toric Varieties. Graduate Studies in Mathematics 124, American Mathematical Society, 2011. AMS book page.

    General reference for toric cones, fans, character lattices, affine charts, and torus orbits in the Higher-Dimensional Slice Calculator.

  11. Diane Maclagan and Bernd Sturmfels. Introduction to Tropical Geometry. Graduate Studies in Mathematics 161, American Mathematical Society, 2015. DOI: 10.1090/gsm/161.

    General reference for tropical polynomials, their corner loci, and dominance regions in the Higher-Dimensional Slice Calculator.