Add curves as a search column for abvar/fq (LMFDB#6975)

Register a default-off Curves column on the abelian varieties over Fq
search page, displaying the first curve equation (TeXified, with the
count of remaining ones) and including the full list of equations in
search downloads.  The curves attribute of AbvarFq_isoclass now defaults
to None so that rows whose curves have not been computed (stored as NULL
and omitted from psycodict records) display an empty cell and download as
null; the TeXification of stored equations is factored out of
curve_display for reuse.  Verified with a new test in test_av.py (full
lmfdb/abvar/fq/test_av.py suite passes) plus manual checks of search
pages, all download languages, and homepage regressions.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

Author: roed314

lmfdb/abvar/fq/isog_class.py

@@ -69,6 +69,30 @@ def validate_label(label):
         raise ValueError("the final part must be of the form c1_c2_..._cg, with each ci consisting of lower case letters")
 
 
+def formatted_curve_equation(cv):
+    """
+    TeXify a curve equation as stored in the curves column of av_fq_isog,
+    appending "=0" if the stored string is a bare polynomial.
+    """
+    cv = teXify_pol(cv)
+    if "=" not in cv:
+        cv = cv + "=0"
+    return cv
+
+
+def curves_display_search(curves):
+    """
+    A compact rendering of the curves column for search results pages;
+    the full list is available on the homepage and in downloads.
+    """
+    if not curves:
+        return ""
+    disp = "$%s$" % formatted_curve_equation(curves[0])
+    if len(curves) > 1:
+        disp += " and %s more" % (len(curves) - 1)
+    return disp
+
+
 class AbvarFq_isoclass():
     """
     Class for an isogeny class of abelian varieties over a finite field
@@ -80,6 +104,8 @@ def __init__(self, dbdata):
             dbdata["hyp_count"] = None
         if "jacobian_count" not in dbdata:
             dbdata["jacobian_count"] = None
+        if "curves" not in dbdata:
+            dbdata["curves"] = None
         # New invariants: cyclicity and noncyclic primes
         if "is_cyclic" not in dbdata:
             dbdata["is_cyclic"] = None
@@ -466,10 +492,7 @@ def twist_display(self, show_all):
 
     def curve_display(self):
         def show_curve(cv):
-            cv = teXify_pol(cv)
-            if "=" not in cv:
-                cv = cv + "=0"
-            return "  <li>$%s$</li>\n" % cv
+            return "  <li>$%s$</li>\n" % formatted_curve_equation(cv)
         if hasattr(self, "curves") and self.curves:
             s = "\n<ul>\n"
             cutoff = 20 if len(self.curves) > 30 else len(self.curves)

lmfdb/abvar/fq/main.py

@@ -16,7 +16,7 @@
 from lmfdb.api import datapage
 from . import abvarfq_page
 from .search_parsing import parse_nf_string, parse_galgrp
-from .isog_class import validate_label, AbvarFq_isoclass
+from .isog_class import validate_label, AbvarFq_isoclass, curves_display_search
 from .stats import AbvarFqStats
 from lmfdb.number_fields.web_number_field import nf_display_knowl, field_pretty
 from lmfdb.utils import redirect_no_cache
@@ -706,13 +706,15 @@ def extended_code(c):
     MathCol("abvar_counts", "ag.fq.point_counts", r"$\mathbb{F}_{q^k}$ points on variety", short_title="Fq^k points on variety", default=False),
     MathCol("jacobian_count", "av.jacobian_count", "Jacobians", default=False),
     MathCol("hyp_count", "av.hyperelliptic_count", "Hyperelliptic Jacobians", default=False),
+    ProcessedCol("curves", "ag.jacobian", "Curves", curves_display_search, default=False,
+                 download_desc="Equations of curves whose Jacobians are in the isogeny class.  For a base field GF(p^r) with r > 1, the variable a denotes a generator of the base field over its prime field.  The list may be empty or missing if no such curves are known."),
     MathCol("twist_count", "av.twist", "Num. twists", default=False),
     MathCol("max_twist_degree", "av.twist", "Max. twist degree", default=False),
     MathCol("geometric_extension_degree", "av.endomorphism_field", "End. degree", default=False),
     ProcessedCol("number_fields", "av.fq.number_field", "Number fields", lambda nfs: ", ".join(nf_display_knowl(nf, field_pretty(nf)) for nf in nfs), default=False),
     SearchCol("galois_groups_pretty", "nf.galois_group", "Galois groups", download_col="galois_groups", default=False),
     SearchCol("decomposition_display_search", "av.decomposition", "Isogeny factors", download_col="decompositionraw")],
-    db_cols=["label", "g", "q", "poly", "p_rank", "p_rank_deficit", "is_simple", "is_geometrically_simple", "simple_distinct", "simple_multiplicities", "is_primitive", "primitive_models", "curve_count", "curve_counts", "abvar_count", "abvar_counts", "jacobian_count", "hyp_count", "number_fields", "galois_groups", "slopes", "newton_elevation", "twist_count", "max_twist_degree", "geometric_extension_degree", "angle_rank", "angle_corank", "is_supersingular", "has_principal_polarization", "has_jacobian", "is_cyclic", "noncyclic_primes"])
+    db_cols=["label", "g", "q", "poly", "p_rank", "p_rank_deficit", "is_simple", "is_geometrically_simple", "simple_distinct", "simple_multiplicities", "is_primitive", "primitive_models", "curve_count", "curve_counts", "curves", "abvar_count", "abvar_counts", "jacobian_count", "hyp_count", "number_fields", "galois_groups", "slopes", "newton_elevation", "twist_count", "max_twist_degree", "geometric_extension_degree", "angle_rank", "angle_corank", "is_supersingular", "has_principal_polarization", "has_jacobian", "is_cyclic", "noncyclic_primes"])
 
 def abvar_postprocess(res, info, query):
     gals = set()

lmfdb/abvar/fq/test_av.py

@@ -158,6 +158,24 @@ def test_download_curves(self):
         page = self.tc.get('Variety/Abelian/Fq/download_curves/5.3.ac_e_ai_v_abl', follow_redirects=True)
         assert 'No curves for abelian variety isogeny class 5.3.ac_e_ai_v_abl' in page.get_data(as_text=True)
 
+    def test_curves_search_column(self):
+        r"""
+        Test the curves column on search results pages, including downloads.
+        """
+        # The column is available in the column dropdown
+        page = self.tc.get("/Variety/Abelian/Fq/?q=4&g=1").get_data(as_text=True)
+        assert '<option value="curves">' in page
+        # A single curve is displayed as is, longer lists are truncated
+        page = self.tc.get("/Variety/Abelian/Fq/?q=4&g=1&showcol=curves").get_data(as_text=True)
+        assert "$y^2+y=x^3+a$" in page
+        assert "$y^2+a y=x^3$ and 1 more" in page
+        # Search downloads contain the full lists
+        data = self.tc.get("/Variety/Abelian/Fq/?q=4&g=1&showcol=curves&Submit=sage&download=1&query=%7B%27q%27%3A+4%2C+%27g%27%3A+1%7D").get_data(as_text=True)
+        assert '["y^2+a*y=x^3", "y^2+(a+1)*y=x^3"]' in data
+        # Classes for which curves have not been computed display an empty cell
+        page = self.tc.get("/Variety/Abelian/Fq/?q=729&g=2&showcol=curves").get_data(as_text=True)
+        assert "2.729.aee_gmg" in page
+
     def test_cyclic_group_of_points_display(self):
         r"""
         Check that the cyclic group of points information is displayed