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2 years ago
gh-36190: establish interface for instantiated classical modular polynomials Generic modular polynomials (i.e., as elements of $\mathbb Z[X,Y]$) grow very big very quickly. However, most algorithmic applications only require evaluations $\Phi_\ell(j,Y)$ of those polynomials. There are algorithms to compute such evaluations faster than computing-then- evaluating the full modular polynomial, for example due to [Sutherland](https://arxiv.org/abs/1202.3985). PARI implements both kinds of algorithms in `polmodular()`. This patch adds a common interface for (1) accessing Kohel's database of modular polynomials if available, (2) calling PARI's `polmodular()` to compute generic modular polynomials, and (3) calling PARI's `polmodular()` to compute instantiated modular polynomials. Results are opportunistically cached and reused whenever this seems to make sense. URL: https://github.com/sagemath/sage/pull/36190 Reported by: Lorenz Panny Reviewer(s): Lorenz Panny, Travis Scrimshaw
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