Allow multiple intermediate fields in number field search (LMFDB#6827)

The "Intermediate field" search box now accepts a comma-separated list of
subfields (polynomials, field labels, or nicknames, freely mixed). The search
returns number fields containing every listed subfield, i.e. the AND of the
containment conditions (equivalently, fields containing their compositum).
This makes it easy to search for e.g. Q(sqrt2, sqrt3, sqrt5) without first
computing a defining polynomial for the compositum.

parse_subfield splits the input on commas and parses each piece with the
existing input_to_subfield helper, emitting {"$contains": [...]} on the
text[] subfields column. This compiles to a single "subfields @> ARRAY[...]"
Postgres containment test (no per-row recomputation) -- the same operator the
single-subfield search already used, so single-field behavior is unchanged.
Whitespace is stripped by the search parser, so "x^2-2, x^2-3" works too. A
malformed entry raises the existing clean SearchParsingError. Help text and a
test were added.

Verified with the flask test client: single label/polynomial (unchanged),
multiple polynomials and multiple labels both returning the compositum, three
quadratics correctly excluding the degree-4 field, and malformed input giving
a flashed error rather than a 500.

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

Author: roed314

lmfdb/number_fields/number_field.py

@@ -1316,7 +1316,8 @@ def __init__(self):
             label="Intermediate field",
             knowl="nf.intermediate_fields",
             example_span="2.2.5.1 or x^2-5 or a "
-                + display_knowl("nf.nickname", "field nickname"),
+                + display_knowl("nf.nickname", "field nickname")
+                + ", or a comma-separated list, e.g. x^2-2,x^2-3",
             example="x^2-5")
         completion = TextBox(
             name="completions",

lmfdb/number_fields/test_numberfield.py

@@ -46,6 +46,18 @@ def test_search_multiple_fields(self):
         self.check_args('/NumberField/?jump=Qsqrt5%2c+x%5E2-3&search=Go', '2.2.5.1')
         self.check_args('/NumberField/?jump=Qsqrt5%2c+x%5E2-3&search=Go', '2.2.12.1')
 
+    def test_search_subfield(self):
+        # Single intermediate field (unchanged behavior): fields containing Q(sqrt2)
+        self.check_args_with_timeout('/NumberField/?subfield=x%5E2-2', '4.0.256.1')
+        # Multiple intermediate fields: a comma-separated list matches fields
+        # containing every listed subfield (the compositum).  Q(sqrt2,sqrt3) =
+        # 4.4.2304.1 contains both Q(sqrt2) and Q(sqrt3).
+        self.check_args_with_timeout('/NumberField/?subfield=x%5E2-2%2Cx%5E2-3', '4.4.2304.1')
+        # Same search given by field labels instead of polynomials
+        self.check_args_with_timeout('/NumberField/?subfield=2.2.8.1%2C2.2.12.1', '4.4.2304.1')
+        # A malformed entry in the list gives a clean error, not a 500
+        self.check_args('/NumberField/?subfield=x%5E2-2%2Cnotafield', 'not a valid field nickname or label')
+
     def test_search_disc(self):
         self.check_args('/NumberField/?discriminant=1988-2014', '401') # factor of one of the discriminants
 

lmfdb/utils/search_parsing.py

@@ -1615,9 +1615,18 @@ def notq():
 
 @search_parser  # see SearchParser.__call__ for actual arguments when calling
 def parse_subfield(inp, query, qfield):
-    sf = input_to_subfield(inp)
-    if sf:  # Might return none
-        query[qfield] = {"$contains": sf}
+    if "," in inp:
+        # A comma-separated list of subfields means AND of the containment
+        # conditions, i.e. fields containing every listed subfield (equivalently,
+        # their compositum).  input_to_subfield may return None for empty pieces
+        # (e.g. a trailing comma), which we drop.
+        sfs = [sf for sf in (input_to_subfield(f) for f in inp.split(",")) if sf]
+        if sfs:
+            query[qfield] = {"$contains": sfs}
+    else:
+        sf = input_to_subfield(inp)
+        if sf:  # Might return none
+            query[qfield] = {"$contains": sf}
 
 @search_parser  # see SearchParser.__call__ for actual arguments when calling
 def parse_nf_string(inp, query, qfield):