Guard PARI polgalois on unsupported number-field degrees (LMFDB#6759)

[roed-math]

Some auto-generated code snippets on number-field pages error when run (LMFDB#6759). The snippet CI harness cannot catch them because it only exercises degree <= 2 fields, so I ran every number-field snippet across a spread of fields (Q, imaginary/real quadratic, monogenic and non-monogenic cubics, a quartic, and a degree-12 field). That surfaced three genuine bugs; two of them, the Magma Galois-group assignment (= instead of :=) and Magma's collapse of a degree-1 polynomial to the rationals on the Q page, have since been fixed on main by LMFDB#7079, which represents Q as RationalsAsNumberField(). Those changes are dropped here, leaving a single rational-field strategy, and this PR now carries only the third fix.

PARI's polgalois hard-errors above degree 11 ("sorry, galois of degree higher than 11 is not yet implemented"), and it is unconditional only through degree 7: degrees 8 to 11 need the optional galdata package, which is not part of a stock PARI installation. The galois_group snippet in lmfdb/number_fields/code.yaml is now guarded so that either case returns an explanatory string instead of aborting the rest of the snippet file, while any other polgalois failure still propagates.

Verified in PARI 2.17.2 (via sage --gp) for degrees 2, 8 and 12, both with galdata present and with datadir pointed at a directory without it. The two committed gp snippet-test logs are updated for the new Galois line; their computed output is unchanged, and re-running the Magma snippet harness reports no change to the committed Magma logs. Two regression tests are added in lmfdb/number_fields/test_numberfield.py: one checks that the degree-12 gp download is guarded and never emits a bare polgalois(K.pol) line, the other pins the Magma representation of Q to RationalsAsNumberField() in both the field definition and the self-contained class-number-formula snippet.

One issue is intentionally left as a documented limitation: the PARI analytic-class-number-formula snippet overflows the default PARI stack on high-degree fields (a resource limit, not a code error), so no allocatemem directive is injected into a user-facing snippet.

Addresses LMFDB#6759.

🤖 Generated with Claude Code

[roed-math]

Updated in f6b304f to address the review. Summary of what changed and how it was checked.

1. Dropped the duplicate Magma rational-field implementation. Both DoLinearExtension := true templates are gone, so main's RationalsAsNumberField() handling (from LMFDB#7079) is again the single strategy. This was the real bug in the merge resolution: with NumberField(%s : DoLinearExtension := true) in place, the exact-string replace("NumberField(x)", "RationalsAsNumberField()") in WebNumberField.make_code_snippets() never matched, so it was dead code while the committed Magma fixtures still contained RationalsAsNumberField(). code.yaml now differs from main in exactly one line.

Re-running the Magma harness against the committed fixtures confirms no drift:

$ PATH=/Applications/Magma:$PATH sage -python lmfdb/tests/generate_snippet_tests.py test -o magma -f lmfdb/number_fields/code.yaml
No change in lmfdb/tests/snippet_tests/number_fields/code-1.1.1.1-magma.log
No change in lmfdb/tests/snippet_tests/number_fields/code-2.0.4.1-magma.log

2. Widened the PARI guard to the documented support boundary. polgalois is unconditional only through degree 7; degrees 8 to 11 need the optional galdata package. The snippet is now

if(poldegree(K.pol) > 11, "polgalois only supports degree <= 11", iferr(polgalois(K.pol), E, "polgalois in degrees 8 to 11 requires the optional galdata package", errname(E) == "e_FILE" || errname(E) == "e_PACKAGE"))

One deviation from the suggested expression, and it is deliberate: the review proposed the predicate errname(E) == "e_PACKAGE", but that is not the error PARI actually raises here. Verified against PARI 2.17.2 (sage --gp) by pointing datadir at a directory with no galdata/:

case	result
degree 2, galdata present	[2, -1, 1, "S2"]
degree 8, galdata present	[8, 1, 2, "4[x]2"]
degree 8, galdata absent	polgalois in degrees 8 to 11 requires the optional galdata package
degree 12	polgalois only supports degree <= 11
polgalois(y^2 - 1) (unrelated failure)	propagates: not an irreducible polynomial in galois

With galdata removed, iferr(polgalois(K.pol), E, errname(E), 1) returns e_FILE ("error opening galois file: .../galdata/COS8_49_45"), not e_PACKAGE. Both names are accepted so the guard also works on builds that raise e_PACKAGE, and the predicate stays narrow enough that any other polgalois failure still propagates, as the review asked.

3. Regenerated the gp fixtures. Only the echoed command line differs; the computed outputs are byte-identical, so the mathematical content of the two logs is unchanged.

$ sage -python lmfdb/tests/generate_snippet_tests.py test -o pari -f lmfdb/number_fields/code.yaml

Note for anyone reproducing: the harness intersects the -o set with the language keys in code.yaml before mapping pari to gp, so -o gp prints "No valid languages selected" and -o pari is the working invocation. The remaining diff the harness reports on the regenerated copies is the pre-existing nondeterminism in bnfinit internals and one lfunrootres float format, on lines 3 and 30, i.e. output of commands this PR does not touch.

4. Added the two regression tests in lmfdb/number_fields/test_numberfield.py:

• test_high_degree_gp_galois_download fetches /NumberField/12.4.320979616137216.3/download/gp and asserts the guard, the explanatory text for both the degree and the galdata case, and that no line is a bare polgalois(K.pol). The degree-12 field is deliberately not added to the snippet_test matrix, since the full gp download also runs the expensive analytic-class-number-formula snippet.
• test_rational_field_magma_download fetches /NumberField/1.1.1.1/download/magma and pins RationalsAsNumberField() in both the field definition and the self-contained class-number-formula block, with DoLinearExtension and NumberField(x) absent. No Magma executable needed.

$ sage -python -m pytest lmfdb/number_fields/test_numberfield.py
36 passed, 58 warnings in 1052.79s

Lint is clean (pyflakes, pylint -e W0129,W0108, ruff check --preview --select=E722).

5. Title and body now describe the final diff: the Magma assignment and Q-collapse fixes are attributed to LMFDB#7079 and this PR is just the PARI guard plus its tests. The high-degree lfunrootres stack overflow is retained as a documented limitation.

[roed314]

GPT signed off.

[roed-math]

Superseded by LMFDB#7168, opened upstream from this same branch. Closing here; review continues upstream.