Todd-Coxeter + examples

examples/newpres.py

@@ -0,0 +1,48 @@
+import libsemigroups_cppyy
+
+from libsemigroups_cppyy.todd_coxeter import *
+
+def symgroup(n):
+    s = ["s%i"%i for i in range(n)]
+    res = []
+    for i in range(1,n):
+        res.append([[s[i],s[i]], [1]])
+    for i in range(1, n-1):
+        res.append([[s[i],s[i+1],s[i]], [s[i+1],s[i],s[i+1]]])
+    for i in range(1, n-2):
+        for j in range(i+2, n):
+            res.append([[s[i],s[j]], [s[j],s[i]]])
+    return s[1:], res
+def Hecke0(n):
+    p = ["pi%i"%i for i in range(n)]
+    res = []
+    for i in range(1,n):
+        res.append([[p[i],p[i]], [1]])
+    for i in range(1, n-1):
+        res.append([[p[i],p[i+1],p[i]], [p[i+1],p[i],p[i+1]]])
+    for i in range(1, n-2):
+        for j in range(i+2, n):
+            res.append([[p[i],p[j]], [p[j],p[i]]])
+    return p[1:], res
+
+
+N = 5
+
+gs, rs = symgroup(N)
+SG = make_cong([1]+gs, rs, identity=1)
+SG.run()
+SG.standardize(ToddCoxeter.order.shortlex)
+clSG = classes_reduced_word_cong(SG)
+
+gs, rs = Hecke0(N)
+H0 = make_cong([1]+gs, rs, identity=1)
+H0.run()
+H0.standardize(ToddCoxeter.order.shortlex)
+clH0 = classes_reduced_word_cong(H0)
+
+print (clSG == clH0)
+
+
+
+
+

libsemigroups_cppyy/todd_coxeter.py

@@ -0,0 +1,75 @@
+"""
+This file contains the interface to the implementation of the
+Todd-Coxeter algorithm for finitely presented semigroups in libsemigroups; see
+
+    https://libsemigroups.readthedocs.io/en/latest/_generated/libsemigroups__congruence__toddcoxeter.html
+
+for further details.
+
+
+"""
+import cppyy
+cppyy.include("cong.hpp")
+cppyy.include("cong-intf.hpp")
+
+lsg = cppyy.gbl.libsemigroups
+congruence_type = lsg.congruence_type
+ToddCoxeter = lsg.congruence.ToddCoxeter
+
+def make_cong(lgen, rels, identity=None):
+    """
+    Build a congruence
+
+    each generator must be hashable.
+
+    - `lgen` : the list of generators (must be unique)
+    - `rels` : a list of pairs of tuple
+    - `identity` : the identity if known
+
+    if `rels` contains a generator which is not in `lgen`, it will be appended.
+    """
+    if len(set(lgen)) != len(lgen):
+        raise ValueError("duplicate generator")
+    if identity is not None and identity not in lgen:
+        lgen.append(identity)
+    for rel in rels:
+        for w in rel:
+            for g in w:
+                if g not in lgen:
+                    lgen.append(g)
+    res = ToddCoxeter(lsg.congruence_type.twosided)
+    res.set_nr_generators(len(lgen))
+    def add_pair(a,b) :
+        # print("Adding : (%s, %s)"%(a,b))
+        res.add_pair(a,b)
+    if identity is not None:
+        idd = lgen.index(identity)
+        for ig in range(len(lgen)):
+            add_pair([ig, idd], [ig])
+            if idd != ig:
+                add_pair([idd, ig], [ig])
+    def iword(w):
+        return [lgen.index(l) for l in w]
+    for rel in rels:
+        trg = iword(rel[0])
+        for src in rel[1:]:
+            add_pair(trg, iword(src))
+    return res
+
+
+def classes_reduced_word_cong(C):
+    r"""
+    returns the list of the classes all the reduced words.
+
+    Each classes is stored as a frozenset. in the same order as the
+    index of `C`.
+    """
+    res = []
+    for nc in range(C.nr_classes()):
+        w =  C.class_index_to_word(nc)
+        Cl = []
+        for wrd in lsg.shortlex_words(C.nr_generators(), w.size(), w.size()):
+            if (C.word_to_class_index(wrd) == nc):
+                Cl.append(tuple(wrd))
+        res.append(frozenset(Cl))
+    return res