Improvements to hypergeometric motives

[kedlaya]

In the wake of #23671, a meta-ticket to record some proposed improvements to hypergeometric motives. Please add suggestions to this list, and make individual tickets for individual changes.

• Euler factors at tame primes. These are implemented in Magma and involve Jacobi motives (Jacobi motives #29040). (See Implement hypergeometric Euler factors for tame primes #37881.)
• Euler factors at wild primes. This is rather complicated.
• Good Euler factors for parameter in a number field.
• Optimizations to speed up padic_H_value. Some occur at Speed up p-adic Gamma by caching Dwork expansion coefficients #24433 (cache coefficients of the Dwork exponential series) and Housekeeping for hypergeometric motives #28458 (eliminate redundant Gauss sum calls).
• Recode the computation of Gauss sums and/or the hypergeometric trace formula in Cython. (See Cythonize hypergeometric trace formula #28902, Another speedup of hypergeometric trace formula #29893.)
• Speed up possible_hypergeometric_data for fixed weight. (See Iterator for hypergeometric motives #23953 for one step: returning an iterator instead of a list.)
• Add the computation of the Frobenius structure on the hypergeometric equation, which can be more efficient than the trace formula when the degree is large.
• Refactor: should this really be under modular?

Component: algebraic geometry

Keywords: hypergeometric motives

Issue created by migration from https://trac.sagemath.org/ticket/23952

[simonbrandhorst]

Changed keywords from none to sd91

[kedlaya]

Changed keywords from sd91 to hypergeometric motives

[mkoeppe]

comment:12

Batch modifying tickets that will likely not be ready for 9.1, based on a review of the ticket title, branch/review status, and last modification date.

[mkoeppe]

comment:15

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.