Validate Euler factor links to abelian varieties over Fq on L-function pages#29
Validate Euler factor links to abelian varieties over Fq on L-function pages#29roed-math wants to merge 2 commits into
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…FDB#4535, LMFDB#4922) The isogeny class column of the L-function Euler factor table (added in LMFDB#6573) derived (g, q) from the factor's leading coefficient via nth_root, which raises ValueError (a 500 page) when the coefficient is not a perfect g-th power, and produced garbage labels for factors that are not genuine Weil polynomials (negative lead, non-self-dual). Add Lfactor_to_gq, which checks that the factor is the reciprocal Weil polynomial of an abelian variety over F_p (even degree, integral, constant term 1, leading coefficient p^g, self-duality a_{2g-i} = q^{g-i} a_i) and pass the row's prime in from lfuncEPhtml, leaving the cell empty otherwise; out-of-range (g, q) still shows a plain unlinked label. Also defer the AbvarFqStats query from module import to first use. Verified on 11.a (links 1.2.c at p=2, matching 5 = #E(F_2)), genus 2 curve 169.a (2.2.d_f at p=2, the reduced Jacobian, matching av_fq_isog.poly and 19 points), an EC/NF and degree 6/8 CMF pages (labels beyond av/Fq coverage stay unlinked), and EC/G2C isogeny class pages; new tests in test_lfunctions.py plus the full suite (25 passed) and pyflakes are clean. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
…v/Fq links (LMFDB#4535) Lfactor_to_gq checked reciprocity but not the root condition, so self-dual non-Weil factors like [1, 10, 2] (x^2 + 10x + 2 violates the Hasse bound at p = 2) produced links to wrong or nonexistent isogeny classes. Now the reversal must pass Sage's exact is_weil_polynomial (Sturm's theorem, no floating point; 26-53us per call for g = 1..6). For proper prime powers, where Weil does not imply realizable (x^2 + 25 over F_25, Honda-Tate), the link emitter confirms the label against av_fq_isog; pages always pass a prime, where Weil is exactly Honda-Tate, so page renders add no queries. polynomial_unroll now rejects empty/non-list payloads with ValueError (previously IndexError escaped to a 500) and gives prod an initial polynomial so exponent-0 factorizations no longer raise; Lfactor_to_gq catches these and returns None. Verified: new must-reject unit tests ([1,10,2], boundary (x+2)^2, malformed flat/factored payloads); av/Fq link counts on six real L-function pages (EC/Q 11.a, G2C 169.a, EC/NF deg 4, deg 6, deg 8) identical before/after; full lfunctions suite 27 passed; pyflakes clean. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Addressed both of the external review's P2 findings: commit b0a99a2. Weil condition: the validator now requires the reversed factor to pass Sage's Beyond the review: while verifying, the agent found that Weil ⟹ exists-in-DB only holds for prime q (Honda–Tate): x²+25 is Weil but 1.25.a doesn't exist. Labels for proper prime-power q are now confirmed against av_fq_isog before linking — a cold path, since current pages always pass prime p, so zero added queries on real pages. Empty/malformed payloads: 27/27 lfunctions tests pass; av/Fq links verified identical before/after on six real pages (11.a→1.2.c etc.). |
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L-function pages of motivic weight 1 link each good-prime Euler factor to the corresponding
isogeny class of abelian varieties over F_p (feature introduced in LMFDB#6573). This PR hardens that
linking: a new
Lfactor_to_gqcheck confirms the factor is genuinely the reciprocal Weilpolynomial of an abelian variety over F_p (even degree, integral, lead p^g, self-dual) before a
label is displayed, so malformed or non-Weil factors now give an empty cell instead of a
ValueError-driven 500 or a wrong/garbage label, while out-of-range (g,q) still shows a plain
unlinked label. The av/Fq coverage lookup now happens lazily at first use instead of at module
import, and the row's prime is passed in so the label can be checked against it. Verified
against av_fq_isog data (11.a links 1.2.c at p=2 with 5 = #E(F_2) points; genus 2 curve 169.a
links 2.2.d_f, its reduced Jacobian) and covered by new tests in test_lfunctions.py; the full
lfunctions suite passes.
Addresses LMFDB#4535.
Addresses LMFDB#4922.
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