Allow group names in abstract-group label search boxes (LMFDB#6397)

[roed-math]

Search boxes in the abstract groups section that take group labels (center, commutator, central quotient, abelianization, automorphism group, outer automorphism group, Frattini subgroup; subgroup/ambient/quotient in the subgroup search; group/image in the complex character search) now also accept group names, e.g. C6, S4, D8, Q8, C2^3, C2xC4, SL(2,7), GL(2,3), 8T3, and light TeX variants like C_2^3 or C_2\times C_4. Names are resolved to labels by a new name_to_label helper that reuses the jump box's resolution paths (stored names, cyclic products via primary invariants, special family names, transitive labels), so a name works in a search box iff it works in the jump box. Comma-separated lists may mix labels, names, and (where previously allowed) orders; only top-level commas split the list, so a family name whose parameters contain a comma stays in one piece, and unbalanced delimiters or empty entries give the section's search-input error. A + inside a name such as SO+(4,2) is preserved, while a leading unary + on an order or label is still accepted. Unknown or ambiguous names produce a search-input error naming the offending entry. Adds tests pairing each name search with the existing sibling label test so the two stay in sync. Addresses LMFDB#6397.

🤖 Generated with Claude Code

[roed-math]

Pushed 4f231530a, which fixes the comma-splitting bug found in review.

The bug. Both new parsers tokenized with inp.split(","), so a family name whose parameters contain a comma was chopped up before resolution: SL(2,7) became SL(2 and 7) and never reached name_to_label. Every name the description advertises with parameters (SL(2,7), GL(2,3), ...) was broken, and none of the new tests exercised one. Separately, parse_group_label_or_order_or_name kept prep_plus=True, which deletes every + in the input; that was harmless when the box took only labels and orders, but it mangles the stored name SO+(4,2) (= 72.40) now that names are accepted.

The fix (lmfdb/groups/abstract/main.py):

• split_group_search_terms splits only at commas outside (), [] and {}, and raises SearchParsingError for unbalanced delimiters or empty entries (C2,,C3, trailing comma) so those land on the section's normal search-input error page instead of being reported as a truncated name. Both parse_group_label_or_order_or_name and parse_group_label_or_name use it, so the complete name is preserved before resolution rather than being patched up inside name_to_label. split_top_level_commas in search_wrapper.py is deliberately lenient (it hands unbalanced input on to the jump logic), so it isn't reused here.
• prep_plus=True is replaced by strip_unary_plus, applied per entry: +8 and +8.3 keep working, and an internal + reaches name_to_label unchanged.

Tests (lmfdb/groups/abstract/test_browse_page.py) — three tests, all of which fail on 6bcfa82a8 and pass on 4f231530a:

• test_search_by_name_with_commas — aut_group=GL(2,3) (label-only box), commutator_label=SL(2,7) (order-or-name box), ambient=SL(2,7) in the subgroup search, the mixed list aut_group=GL(2,3),C6, and an order mixed with a comma-bearing name, commutator_label=8,SL(2,7)&order=336 → 336.114 (from the name) plus 336.169/336.170/336.213 (from the order).
• test_search_by_name_with_plus — central_quotient=SO%2B(4%2C2)&order=144 → 144.115, 144.186; center_label=%2B8 and center_label=%2B8.1 still behave as before.
• test_search_by_bad_name — extended so that unbalanced SL(2,7 gives the right error title in all three searches and does not report the truncated SL(2, and C2,,C6 is rejected.

Verification. sage -python -m pytest lmfdb/groups/ → 83 passed against devmirror; the three tests above → 3 failed on the previous head, pass here; pyflakes clean. Full CI is running on the push.

[roed314]

GPT signed off.

[roed-math]

Superseded by LMFDB#7173, opened upstream from this same branch. Closing here; review continues upstream.