Fix belyi dessin images 7026

lmfdb/belyi/templates/belyi_galmap.html

@@ -145,9 +145,8 @@ <h2>{{ KNOWL('nf.embedding', title="Embeddings") }}</h2>
     <div class="knowl"><div><div class="knowl-content">
       <strong>Dessin d&rsquo;enfant</strong>
       {% for g in data.embeddings_and_triples %}
-        {% set svg_idx = loop.index0 if loop.index0 < data.dessin_svgs|length else 0 %}
         <div id="dessin-svg-{{ loop.index0 }}" class="dessin-svg-item" style="display:none;">
-          {{ data.dessin_svgs[svg_idx]|safe }}
+          {{ data.dessin_svgs[loop.index0]|safe }}
         </div>
       {% endfor %}
       <p style="font-size:0.85em; margin-top:0.75em;">

lmfdb/belyi/test_belyi.py

@@ -1,4 +1,11 @@
+import gzip
+import os
+from collections import defaultdict
+
 from lmfdb.tests import LmfdbTest
+from lmfdb import db
+from lmfdb.belyi import web_belyi
+from lmfdb.belyi.web_belyi import get_belyi_images, _belyidb_to_lmfdb_plabel
 
 
 class BelyiTest(LmfdbTest):
@@ -12,6 +19,85 @@ def test_random(self):
     def test_by_galmap_label(self):
         self.check_args("/Belyi/6T15-5.1_4.2_4.2-b", "A_6")
 
+    # dessin images (#7026)
+
+    def test_belyidb_to_lmfdb_plabel_orbit_letters(self):
+        # missing orbit-letter component defaults to "a"
+        assert _belyidb_to_lmfdb_plabel("4T2-[2,2,2]-22-22-22-g0") == "4T2-2.2_2.2_2.2-a"
+        # distinct orbit letters must map to distinct labels, across a
+        # spread of degrees, genera and letters (not just a single example)
+        cases = [
+            ("4T2-[2,2,2]-22-22-22-g0-a", "4T2-2.2_2.2_2.2-a"),
+            ("5T1-[5,5,5]-5-5-5-g0-c", "5T1-5_5_5-c"),
+            ("6T15-[5,5,5]-51-51-51-g1-d", "6T15-5.1_5.1_5.1-d"),
+            ("7T6-[7,7,322]-7-7-322-g1-c", "7T6-7_7_3.2.2-c"),
+            ("9T23-[6,6,6]-621-621-621-g1-a", "9T23-6.2.1_6.2.1_6.2.1-a"),
+            ("9T23-[6,6,6]-621-621-621-g1-b", "9T23-6.2.1_6.2.1_6.2.1-b"),
+        ]
+        for belyidb_label, expected in cases:
+            assert _belyidb_to_lmfdb_plabel(belyidb_label) == expected
+        # too few components is not a valid label
+        assert _belyidb_to_lmfdb_plabel("4T2-[2,2,2]") is None
+
+    def test_belyidb_to_lmfdb_plabel_roundtrips_for_every_shipped_image(self):
+        # regression test for #7026: parse every raw BelyiDB label in the
+        # shipped image dump and check that the conversion is (a) injective
+        # -- distinct orbits must never collide onto the same LMFDB label,
+        # the root cause of #7026 -- and (b) actually resolves to a real
+        # galmap in the database, for the whole dataset, not just an example
+        images_path = os.path.abspath(os.path.join(
+            os.path.dirname(web_belyi.__file__), "..", "static", "images", "belyi_images.txt.gz"))
+        raw_labels = []
+        with gzip.open(images_path, "rt", encoding="utf-8") as f:
+            for i, line in enumerate(f):
+                if i < 2:  # header rows
+                    continue
+                parts = line.rstrip("\n").split("|", 2)
+                if len(parts) == 3:
+                    raw_labels.append(parts[1])
+        assert len(raw_labels) > 1000  # sanity: dump did not go missing/truncated
+
+        converted = [_belyidb_to_lmfdb_plabel(label) for label in raw_labels]
+        assert all(c is not None for c in converted)
+        assert len(set(converted)) == len(converted), "orbit collision: two BelyiDB labels mapped to the same LMFDB label"
+
+        real_labels = set(db.belyi_galmaps.search({}, projection="label"))
+        missing = [c for c in converted if c not in real_labels]
+        assert not missing
+
+    def test_dessin_images_distinct_across_orbits(self):
+        # regression test for #7026: galmaps sharing a passport but in
+        # different Galois orbits must not be served the same dessin
+        # images. Check every multi-orbit passport in the database (not
+        # just one hand-picked example), pairwise within each passport.
+        orbits_by_passport = defaultdict(list)
+        for galmap in db.belyi_galmaps.search({}, projection=["label", "plabel"]):
+            orbits_by_passport[galmap["plabel"]].append(galmap["label"])
+        multi_orbit_passports = {p: labels for p, labels in orbits_by_passport.items() if len(labels) > 1}
+        assert len(multi_orbit_passports) > 50  # sanity: this is exercising a lot of passports
+
+        checked_pairs = 0
+        for plabel, labels in multi_orbit_passports.items():
+            images = {label: get_belyi_images(label) for label in labels}
+            present = [label for label in labels if images[label]]
+            for i in range(len(present)):
+                for j in range(i + 1, len(present)):
+                    a, b = present[i], present[j]
+                    assert images[a] != images[b], "orbits {} and {} of passport {} share dessin images".format(a, b, plabel)
+                    checked_pairs += 1
+        assert checked_pairs > 50  # sanity: the loop actually compared something
+
+    def test_dessin_image_counts_match_embeddings(self):
+        # every galmap that has dessin images must have exactly one image
+        # per embedding, since the template indexes into the image list by
+        # embedding position with no fallback (see PR #7189 review)
+        mismatches = []
+        for galmap in db.belyi_galmaps.search({}, projection=["label", "triples_cyc"]):
+            images = get_belyi_images(galmap["label"])
+            if images and len(images) != len(galmap["triples_cyc"]):
+                mismatches.append((galmap["label"], len(images), len(galmap["triples_cyc"])))
+        assert not mismatches, mismatches
+
     def test_passport_label(self):
         self.check_args("/Belyi/5T4-5_3.1.1_3.1.1-a", "5T4-5_3.1.1_3.1.1")
 

lmfdb/belyi/web_belyi.py

@@ -5,14 +5,15 @@
 from lmfdb.utils import (names_and_urls, prop_int_pretty, raw_typeset,
         web_latex, compress_expression)
 from flask import url_for
+import gzip
 import re
 import os
 
 from lmfdb import db
 
 
 ###############################################################################
-# Belyi dessin images from belyi_images.txt
+# Belyi dessin images from belyi_images.txt.gz
 ###############################################################################
 
 _belyi_images = None
@@ -22,11 +23,11 @@ def _load_belyi_images():
     if _belyi_images is not None:
         return _belyi_images
     _belyi_images = {}
-    txt_path = os.path.join(os.path.dirname(__file__), '..', 'static', 'images', 'belyi_images.txt')
+    txt_path = os.path.join(os.path.dirname(__file__), '..', 'static', 'images', 'belyi_images.txt.gz')
     txt_path = os.path.abspath(txt_path)
     if not os.path.exists(txt_path):
         return _belyi_images
-    with open(txt_path, encoding='utf-8') as f:
+    with gzip.open(txt_path, 'rt', encoding='utf-8') as f:
         for i, line in enumerate(f):
             if i < 2:  # skip header rows
                 continue
@@ -76,7 +77,10 @@ def _new_height(m):
 
 
 def _belyidb_to_lmfdb_plabel(belyidb_label):
-    # "4T2-[2,2,2]-22-22-22-g0" -> "4T2-2.2_2.2_2.2"
+    # "4T2-[2,2,2]-22-22-22-g0" -> "4T2-2.2_2.2_2.2-a"
+    # "9T23-[6,6,6]-621-621-621-g1-b" -> "9T23-6.2.1_6.2.1_6.2.1-b"
+    # (the optional 7th, orbit-letter component distinguishes galmaps within
+    # a passport; passports with a single orbit omit it, defaulting to "a")
     parts = belyidb_label.split('-')
     if len(parts) < 5:
         return None
@@ -85,12 +89,13 @@ def _belyidb_to_lmfdb_plabel(belyidb_label):
     sigma0 = '.'.join(list(parts[2]))
     sigma1 = '.'.join(list(parts[3]))
     sigmaoo = '.'.join(list(parts[4]))
-    return '{}-{}_{}_{}'.format(group, sigma0, sigma1, sigmaoo)
+    letter = parts[6] if len(parts) >= 7 else 'a'
+    return '{}-{}_{}_{}-{}'.format(group, sigma0, sigma1, sigmaoo, letter)
 
 
-def get_belyi_images(plabel):
-    """Return list of SVG strings for the given LMFDB passport label, or []."""
-    return _load_belyi_images().get(plabel, [])
+def get_belyi_images(label):
+    """Return list of SVG strings for the given LMFDB galmap label, or []."""
+    return _load_belyi_images().get(label, [])
 
 
 ###############################################################################
@@ -383,8 +388,17 @@ def __init__(self, galmap, triple=None):
         if galmap.get('plane_map_constant_factored'):
             data['plane_map_constant_factored'] = galmap['plane_map_constant_factored']
 
-        # Dessin images (one per embedding, or a single shared one)
-        data['dessin_svgs'] = get_belyi_images(galmap['plabel'])
+        # Dessin images (one per embedding), looked up per galmap orbit so
+        # that different orbits within the same passport don't share images.
+        # An empty list means no images are available for this galmap; a
+        # nonempty list must have exactly one SVG per embedding, since the
+        # template indexes into it by embedding position with no fallback.
+        data['dessin_svgs'] = get_belyi_images(galmap['label'])
+        if data['dessin_svgs']:
+            assert len(data['dessin_svgs']) == len(data['embeddings_and_triples']), (
+                "dessin image count ({}) does not match embedding count ({}) for {}".format(
+                    len(data['dessin_svgs']), len(data['embeddings_and_triples']), galmap['label'])
+            )
 
         # Properties
         self.plot = db.belyi_galmap_portraits.lucky({"label": galmap['label']},