Merge pull request #6643 from roed314/cox_search

Author: jenpaulhus

lmfdb/groups/abstract/main.py

@@ -49,7 +49,7 @@
     sparse_cyclotomic_to_mathml,
     integer_to_mathml,
 )
-from lmfdb.utils.search_parsing import (parse_multiset, search_parser)
+from lmfdb.utils.search_parsing import (parse_multiset, search_parser, collapse_ors)
 from lmfdb.utils.interesting import interesting_knowls
 from lmfdb.utils.search_columns import SearchColumns, LinkCol, MathCol, CheckCol, SpacerCol, ProcessedCol, MultiProcessedCol, ColGroup
 from lmfdb.api import datapage
@@ -104,6 +104,7 @@ def yesno(val):
 
 def deTeX_name(s):
     s = re.sub(r"[{}\\$]", "", s)
+    s = s.replace("Orth", "O").replace("Unitary", "U")
     return s
 
 @cached_function
@@ -114,20 +115,25 @@ def group_families(deTeX=False):
     # Here, we're directly adding the individual Chevalley group families (i.e. 'A(n,q)', 'B(n,q)', ...) to the group families list
     # (doing this here to avoid manually adding new families to the data; this avoids re-duplicating data which is already stored in the database)
     chev_index = [t[0] for t in L].index("Chev")+1
-    for f in ['An','Bn','Cn','Dn','En','F4', 'G2']:
+    for f in ['An','Bn','Cn','Dn','En','F4','G2']:
         L.insert(chev_index, ("Chev"+f[0], "$"+f[0]+"({"+f[1]+"}, {q})$"))
         chev_index += 1
     twistchev_index = [t[0] for t in L].index("TwistChev")+1
     for f in ['2An','2B2','2Dn','3D4','2E6','2F4','2G2']:
         L.insert(twistchev_index, ("TwistChev"+f[:2], "$^{"+f[0]+"}{"+f[1]+"}({"+f[2]+"},{q})$"))
         twistchev_index += 1
+    # Adding the individual irreducible Coxeter group families
+    cox_index = [t[0] for t in L].index("Cox")+1
+    for f in ['A','B','D','E','F']:
+        L.insert(cox_index, ("Cox"+f[0], "$W("+f+"_{{n}})$"))
+        cox_index += 1
 
     if deTeX:
         # Used for constructing the dropdown
         return [(fam, deTeX_name(name)) for (fam, name) in L]
 
     def hidden(fam):
-        return fam not in ["C", "S", "D", "A", "Q", "GL", "SL", "PSL", "Sp", "SO", "Sporadic"]
+        return fam not in ["C", "S", "D", "A", "Q", "GL", "SL", "PSL", "Sp", "SO", "Sporadic", "Cox"]
     L = [(fam, name, "fam_more" if hidden(fam) else "fam_always", hidden(fam)) for (fam, name) in L]
     return L
 
@@ -203,6 +209,16 @@ def parse_family(inp, query, qfield):
         query[qfield] = {'$in':list(db.gps_special_names.search({'family':"Chev", 'parameters.fam':inp[4]}, projection='label'))}
     elif inp[:9] == 'TwistChev' and len(inp) == 11:
         query[qfield] = {'$in':list(db.gps_special_names.search({'family':"TwistChev", 'parameters.twist':int(inp[9]), 'parameters.fam':inp[10]}, projection='label'))}
+    # Searching for Coxeter families should include all dihedral groups and all symmetric S_n for n >= 2
+    elif inp == 'Cox':
+        labels = list(db.gps_special_names.search({'family': {'$or': ['Cox', 'CoxH']}}, projection='label'))
+        collapse_ors(["$or", [{"dihedral":True}, {"label": {"$in": labels}}]], query)
+    # Case of CoxI2 (return all dihedral groups D_n)
+    elif inp == 'CoxI':
+        query["dihedral"] = True
+    # Case to check if family is one of the individual irreducible Coxeter families
+    elif inp[:3] == 'Cox' and inp[3] != "H":
+        query[qfield] = {'$in':list(db.gps_special_names.search({'family':"Cox", 'parameters.fam':inp[3]}, projection='label'))}
 
     else:
         query[qfield] = {'$in':list(db.gps_special_names.search({'family':inp}, projection='label'))}
@@ -1116,14 +1132,54 @@ def group_jump(info):
     elif len(labs) == 2:
         return redirect(url_for(".index", name=jump.replace(" ", "")))
     # by special name
+    def int_try(x):
+        if x.isdigit():
+            return int(x)
+        return x
+    def valid_params(fam, params):
+        n = ZZ(params.get("n"))
+        q = ZZ(params.get("q"))
+        if fam in ["Q", "SD", "OD"]:
+            return n.is_power_of(2)
+        if fam == "F":
+            return n.is_prime_power()
+        elif fam == "He":
+            return n > 2 and n.is_prime()
+        elif fam in ["Sp", "PSp", "SOPlus", "SOMinus", "GOPlus", "GOMinus", "OmegaPlus", "OmegaMinus", "PSOPlus", "PSOMinus", "PGOPlus", "PGOMinus", "POmegaPlus", "POmegaMinus", "SpinPlus", "SpinMinus", "CSp", "CSOPlus", "CSOMinus", "COPlus", "COMinus", "PSigmaSp", "ASigmaSp"]:
+            return n % 2 == 0
+        elif fam in ["SO", "PSO", "GO", "Omega", "PGO", "POmega", "Spin", "CSO", "CO"]:
+            return n % 2 == 1
+        elif fam == "CoxH":
+            return n in [3,4]
+        elif fam in ["Cox", "Chev"]:
+            if params["fam"] == "E":
+                return n in [6,7,8]
+            elif params["fam"] == "F":
+                return n == 4
+            elif params["fam"] == "G":
+                return n == 2
+        elif fam == "TwistChev":
+            if params["fam"] == "A":
+                return params["twist"] == 2
+            elif params["fam"] == "B":
+                return n == 2 and params["twist"] == 2 and q.is_power_of(2) and not q.is_power_of(4)
+            elif params["fam"] == "D":
+                return params["twist"] == 2 or (params["twist"] == 3 and n == 4)
+            elif params["fam"] == "E":
+                return n == 6 and params["twist"] == 2
+            elif params["fam"] == "F":
+                return n == 4 and params["twist"] == 2 and q.is_power_of(2) and not q.is_power_of(4)
+            elif params["fam"] == "G":
+                return n == 2 and params["twist"] == 2 and q.is_power_of(3) and not q.is_power_of(9)
     for family in db.gps_families.search():
         m = re.fullmatch(family["input"], jump)
         if m:
-            m_dict = dict([a, int(x)] for a, x in m.groupdict().items()) # convert string to int
+            m_dict = dict([a, int_try(x)] for a, x in m.groupdict().items()) # convert string to int
             lab = db.gps_special_names.lucky({"family":family["family"], "parameters":m_dict}, projection="label")
             if lab:
                 return redirect(url_for(".by_label", label=lab))
-            else:
+            elif valid_params(family["family"], m_dict):
+                # Only display this messages for groups that exist
                 flash_error("The group %s has not yet been added to the database." % jump)
                 return redirect(url_for(".index"))
     flash_error("%s is not a valid name for a group or subgroup; see %s for a list of possible families" % (jump, display_knowl('group.families', 'here')))
@@ -1237,18 +1293,23 @@ def group_postprocess(res, info, query):
     for rec in res:
         rec["tex_cache"] = tex_cache
     if "family" in info:
-        if info["family"] == "any":
+        family = info["family"]
+        if family == "any":
             fquery = {}
 
         # Special case to convert the family "ChevX" (for X = A..G) to just "Chev" for the database query
-        elif info["family"][:4] == "Chev":
+        elif family[:4] == "Chev":
             fquery = {"family": "Chev"}
         # Also special case to convert the family "TwistChevNX" to just "TwistChev" for the database query
-        elif info["family"][:9] == "TwistChev":
+        elif family[:9] == "TwistChev":
             fquery = {"family": "TwistChev"}
-
+        # Convert "CoxX" to: ("Cox" or "S" or "D") for database query
+        elif family == "Cox":
+            fquery = {"family": {"$or": ["Cox", "CoxH", "CoxI"]}}
+        elif family[:3] == "Cox" and family[3] not in "HI":
+            fquery = {"family": "Cox"}
         else:
-            fquery = {"family": info["family"]}
+            fquery = {"family": family}
         fams = {rec["family"]: (rec["priority"], rec["tex_name"]) for rec in db.gps_families.search(fquery, ["family", "priority", "tex_name"])}
         fquery["label"] = {"$in":[rec["label"] for rec in res]}
         special_names = defaultdict(list)
@@ -1262,11 +1323,14 @@ def group_postprocess(res, info, query):
 
             # Special case to deal with individual Chevalley families
             # (e.g. querying the "A(n,q)" family should ensure the "B(n,q)" family names don't show up under "Family name" search column)
-            if (info["family"][:4] == "Chev") and (len(info["family"]) == 5):
-                if name[0] != info["family"][4]:
+            if (family[:4] == "Chev") and (len(family) == 5):
+                if name[0] != family[4]:
+                    continue
+            elif (family[:9] == "TwistChev") and (len(family) == 11):
+                if name[3:5] != family[9:11]:
                     continue
-            if (info["family"][:9] == "TwistChev") and (len(info["family"]) == 11):
-                if name[3:5] != info["family"][9:11]:
+            elif (fam == "Cox" and family[:3] == "Cox" and len(family) == 4):
+                if params["fam"] != family[3]:
                     continue
 
             special_names[rec["label"]].append((fams[fam][0], params.get("n"), params.get("q"), name))
@@ -2894,7 +2958,7 @@ def __init__(self):
         )
         family = SelectBox(
             name="family",
-            options=[("", "")] + group_families(deTeX=True) + [("any", "any")],
+            options=[("", ""), ("any", "any")] + group_families(deTeX=True),
             knowl="group.families",
             label="Family",
         )

lmfdb/templates/base.html

@@ -81,22 +81,24 @@
   "\\AGL": '{\\textrm{AGL}}',
   "\\ASp": '{\\textrm{ASp}}',
   "\\Sp": '{\\textrm{Sp}}',
-  "\\GSp": '{\\textrm{GSp}}',
   "\\PSp": '{\\textrm{PSp}}',
   "\\SO": '{\\textrm{SO}}',
   "\\PSO": '{\\textrm{PSO}}',
-  "\\PGO": '{\\textrm{PGO}}',
+  "\\PO": '{\\textrm{PO}}',
+    "\\PGO": '{\\textrm{PO}}',
   "\\SU": '{\\textrm{SU}}',
   "\\PSU": '{\\textrm{PSU}}',
   "\\SOPlus": '{\\textrm{SO}^+}',
   "\\SOMinus": '{\\textrm{SO}^-}',
     "\\GO": '{\\textrm{O}}',
   "\\Orth": '{\\textrm{O}}',
     "\\GOPlus": '{\\textrm{O}^+}',
+  "\\OPlus": '{\\textrm{O}^+}',
   "\\OrthPlus": '{\\textrm{O}^+}',
     "\\GOMinus": '{\\textrm{O}^-}',
   "\\OrthMinus": '{\\textrm{O}^-}',
-    "\\GU": '{\\textrm{U}}',
+  "\\OMinus": '{\\textrm{O}^-}',
+  "\\GU": '{\\textrm{GU}}',
   "\\Unitary": '{\\textrm{U}}',
     "\\CSp": '{\\textrm{GSp}}',
   "\\GSp": '{\\textrm{GSp}}',
@@ -109,7 +111,7 @@
     "\\CSU": '{\\textrm{GSU}}',
   "\\GSU": '{\\textrm{GSU}}',
     "\\CO": '{\\textrm{GO}}',
-  "\\Gorth": '{\\textrm{GO}}',
+  "\\GOrth": '{\\textrm{GO}}',
     "\\COPlus": '{\\textrm{GO}^+}',
   "\\GOrthPlus": '{\\textrm{GO}^+}',
     "\\COMinus": '{\\textrm{GO}^-}',
@@ -122,10 +124,13 @@
   "\\SpinPlus": '{\\textrm{Spin}^+}',
   "\\SpinMinus": '{\\textrm{Spin}^-}',
   "\\PSOPlus": '{\\textrm{PSO}^+}',
-  "\\PGOPlus": '{\\textrm{PGO}^+}',
-  "\\PGU": '{\\textrm{PGU}}',
+  "\\POPlus": '{\\textrm{PO}^+}',
+    "\\PGOPlus": '{\\textrm{PO}^+}',
+  "\\PU": '{\\textrm{PU}}',
+    "\\PGU": '{\\textrm{PU}}',
   "\\PSOMinus": '{\\textrm{PSO}^-}',
-  "\\PGOMinus": '{\\textrm{PGO}^-}',
+  "\\POMinus": '{\\textrm{PO}^-}',
+    "\\PGOMinus": '{\\textrm{PO}^-}',
   "\\POmega": '{\\textrm{P}\\Omega}',
   "\\POmegaPlus": '{\\textrm{P}\\Omega^+}',
   "\\POmegaMinus": '{\\textrm{P}\\Omega^-}',