I‑AIMS Institute for Artificial Intelligence
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A Neurosymbolic Framework for Geometric Reduction of Binary Forms

Ilias Kotsireas, Tanush Shaska

I-AIMS paper 2024-06 · Published in Contemp. Math. 835 (2026), 173–194 · 2026

We implement a machine learning algorithm based on Julia’s original work on reduction of binary forms.

MSC classes: Primary 11E76; Secondary 11E45, 30F45, 68T01, 68T05

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References

  1. John E. Cremona, Reduction of binary cubic and quartic forms, LMS J. Comput Math 2 (1999), 64–94.
  2. Jan-Hendrik Evertse, Estimates for reduced binary forms, J. Reine Angew. Math. 434 (1993), 159–190. (94h:11037)
  3. Gaston Julia, Etude sur les formes binaires non quadratiques `á indéterminées réelles ou complexes., Mémories de lAcadémie des Sciences de lInsitut de France 55 (1917), 1–296.
  4. T. Shaska, Reduction of superelliptic Riemann surfaces, Automorphisms of Riemann surfaces, subgroups of mapping class groups and related topics, 2022, pp. 227–247.
  5. Michael Stoll and John E. Cremona, On the reduction theory of binary forms, J. Reine Angew. Math. 565 (2003), 79–99. (2005e:11091)

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