Correct some little problems with BetaAdicMonoid.relations_automaton3…

…() and others.

src/sage/combinat/words/cautomata.pyx

@@ -652,7 +652,7 @@ cdef class FastAutomaton:
         DeleteVertexOP(self.a, i)
         sig_off()
 
-    def spectral_radius (self, verb=False):
+    def spectral_radius (self, only_non_trivial=False, verb=False):
         sig_on()
         a = self.minimise()
         if verb:
@@ -662,7 +662,7 @@ cdef class FastAutomaton:
             print "%s composantes fortement connexes."%len(l)
         r = 0 #valeur propre maximale trouvée
         for c in l:
-            if len(c) > 1:
+            if not only_non_trivial or len(c) > 1:
                 if verb:
                     print "composante ayant %s états..."%len(c)
                 b = a.sub_automaton(c)
@@ -695,7 +695,7 @@ cdef class FastAutomaton:
         sig_on()
         res = emptyLangage(self.a[0])
         sig_off()
-        return res
+        return Bool(res)
 
     def equals_langages (self, FastAutomaton a2, minimized=False):
         sig_on()
@@ -708,6 +708,7 @@ cdef class FastAutomaton:
                     break
         res = equalsLangages(self.a, a2.a, d, minimized)
         sig_off()
-        return res
-
-
+        return Bool(res)
+
+
+

src/sage/monoids/beta_adic_monoid.pyx

@@ -96,7 +96,7 @@ cdef extern from "relations.h":
 
     InfoBetaAdic allocInfoBetaAdic (int n, int na, int ncmax, bool verb)
     void freeInfoBetaAdic (InfoBetaAdic iba)
-    Automate RelationsAutomaton (InfoBetaAdic iba2, bool isvide, bool verb)
+    Automate RelationsAutomaton (InfoBetaAdic iba2, bool isvide, bool ext, bool verb)
 
 cdef getElement (e, Element r, int n):
     cdef j
@@ -152,7 +152,7 @@ cdef InfoBetaAdic initInfoBetaAdic (self, Cd=None, verb=False) except *:
     if Cd is None:
         Cd = Set([c-c2 for c in C for c2 in C])
     else:
-        Cd = [c.lift()(1/b) for c in Cd]
+        Cd = [K(c).lift()(1/b) for c in Cd]
     if verb: print "Cd = %s"%Cd
     m = dict([])
     for p in parch:
@@ -364,6 +364,8 @@ cdef BetaAdic getBetaAdic (self, prec=53, ss=None, tss=None, iss=None, transpose
     if add_letters:
         C = set(self.C)
         C.update(a.Alphabet())
+    else:
+        C = a.Alphabet()
     C = list(C)
 
     b = NewBetaAdic(len(C))
@@ -754,7 +756,7 @@ class BetaAdicMonoid(Monoid_class):
           Default values: between ``5`` and ``16`` depending on the number of generators.
         
         - ``place`` - place of the number field of beta (default: ``None``)
-          The place we should use to evaluate elements of the number field.
+          The place used to evaluate elements of the number field.
         
         - ``ss`` - Automaton (default: ``None``)
           The subshift to associate to the beta-adic monoid for this drawing.
@@ -1468,18 +1470,29 @@ class BetaAdicMonoid(Monoid_class):
         res.emonde()
         return res
 
-    def relations_automaton3 (self, isvide=False, Cd=None, verb=False):
+    def relations_automaton3 (self, isvide=False, Cd=None, ext=False, verb=False):
+        r"""
+            Compute the relation automaton of the beta-adic monoid.
+            For beta algebraic integer only.
+            If isvide is True, it only checks if the automaton is trivial or not.
+            Cd is the set of differences A-B where A and B are the alphabets to compare.
+            ext : automate des relations à l'infini ou pas.
+        """
         if Cd is None:
             Cd = Set([c-c2 for c in self.C for c2 in self.C])
         Cd = list(Cd)
+        sig_on()
         cdef InfoBetaAdic ib
         ib = initInfoBetaAdic(self, Cd=Cd, verb=verb)
         cdef Automate a
-        a = RelationsAutomaton(ib, isvide, verb)
+        a = RelationsAutomaton(ib, isvide, ext, verb)
         r = FastAutomaton(None)
         r.a[0] = a
         r.A = Cd
         freeInfoBetaAdic(ib)
+        sig_off()
+        if isvide:
+            return a.na != 0
         return r
 
     def critical_exponent_aprox (self, niter=10, verb=False):
@@ -1722,8 +1735,8 @@ class BetaAdicMonoid(Monoid_class):
 
                 sage: m = BetaAdicMonoid(1/(1+I), {0,1})
                 sage: import sage.combinat.words.cautomata
-				sage: from sage.combinat.words.cautomata import FastAutomaton
-				sage: ss0 = FastAutomaton([(0,1,0)]+[(1,1,l) for l in m.C], i=0, final_states=[1])
+                sage: from sage.combinat.words.cautomata import FastAutomaton
+                sage: ss0 = FastAutomaton([(0,1,0)]+[(1,1,l) for l in m.C], i=0, final_states=[1])
                 sage: ss1 = FastAutomaton([(0,1,1)]+[(1,1,l) for l in m.C], i=0, final_states=[1])
                 sage: ssi = m.intersection2(ss0, ss1)
                 sage: m.plot2(tss = ssi)     # long time
@@ -2228,7 +2241,43 @@ class BetaAdicMonoid(Monoid_class):
             print "Zero is an inner point iff the %s has non-empty interior."%self
             self.ss = ss
 
-
+    #donne l'automate décrivant l'adhérence de l'ensemble limite avec un nouvel alphabet C
+    def adherence (self, C, tss=None, verb=False):
+        if verb:
+            print "Calcul de l'automate des relations..."
+        Cd = [c1-c2 for c1 in self.C for c2 in C]
+        if verb:
+            print "Cd=%s"%Cd
+        a = self.relations_automaton3(Cd=Cd, ext=True)
+        if verb:
+            print " -> %s"%a
+        a = a.emonde_inf()
+        if verb:
+            print " Après émondation : %s"%a
+        d={}
+        for c1 in self.C:
+            for c2 in C:
+                if not d.has_key(c1-c2):
+                    d[c1-c2] = []
+                d[c1-c2].append((c1,c2))
+        if verb:
+            print d
+        a2 = a.duplicate(d, verb=verb)
+        if verb:
+            print a2.Alphabet()
+            print a2
+            print "déterminise..."
+        d={}
+        for c1,c2 in a2.Alphabet():
+            d[(c1,c2)] = c2
+        a2 = a2.determinise_proj(d, verb=verb)
+        if verb:
+            print " -> %s"%a2
+        #a2 = a2.emonde()
+        a2 = a2.emonde_inf()
+        if verb:
+            print "Après simplification : %s"%a2
+        return a2    
 
 
 

src/sage/monoids/relations.c

@@ -152,7 +152,7 @@ bool keep (Element e)
 	int i;
 	for (i=0;i<iba.na;i++)
 	{
-		if (cnorm(eval(e, i)) >= iba.cM[i])
+		if (cnorm(eval(e, i)) + .0000001 > iba.cM[i])
 			return false;
 	}
 }
@@ -185,6 +185,17 @@ Element zeroElement ()
 	return e;
 }
 
+bool isNull (Element e)
+{
+	int i;
+	for (i=0;i<iba.n;i++)
+	{
+		if (e.c[i] != 0)
+			return false;
+	}
+	return true;
+}
+
 bool equalsElements (Element e, Element f)
 {
 	int i;
@@ -278,7 +289,7 @@ int indElement (Element e)
 }
 
 //calcule l'automate des relations
-Automate RelationsAutomaton (InfoBetaAdic iba2, bool isvide, bool verb)
+Automate RelationsAutomaton (InfoBetaAdic iba2, bool isvide, bool ext, bool verb)
 {
 	int i,j;
 
@@ -313,7 +324,7 @@ Automate RelationsAutomaton (InfoBetaAdic iba2, bool isvide, bool verb)
 		printf("parcours...\n");
 	int n = 1; //nombre d'éléments sur la pile
 	compteur = 0; //nombre d'états de l'automate
-	//état initial
+	//état initial 
 	pile[0] = zeroElement();
 	inHash(pile[0]); //ajoute l'élément à la table de hachage
 	Element e = NewElement(iba.n);
@@ -345,10 +356,12 @@ Automate RelationsAutomaton (InfoBetaAdic iba2, bool isvide, bool verb)
 				//teste si l'élément a déjà été vu et l'ajoute si non
 				if (!inHash(s))
 				{ //l'élement est nouveau et a été ajouté à la table de hachage
+					/*
 					if (isvide && !vide)
 					{ //l'automate n'est pas trivial
 						return NewAutomaton(1,0);
 					}
+					*/
 					//empile
 					pile[n] = NewElement(iba.n);
 					copy(s, pile[n]);
@@ -357,6 +370,16 @@ Automate RelationsAutomaton (InfoBetaAdic iba2, bool isvide, bool verb)
 					{
 						printf("Erreur : dépassement de la pile !!!\n");
 					}
+				}else
+				{//on retombe sur un état déjà vu
+					if (isvide)
+					{
+						//if (!isNull(e) && 
+						if (ext || isNull(s))
+						{ //l'automate émondé inf ou émondé n'est pas vide
+							return NewAutomaton(1,0);
+						}
+					}
 				}
 			}
 		}

src/sage/monoids/relations.h

@@ -32,5 +32,5 @@ InfoBetaAdic allocInfoBetaAdic (int n, int na, int ncmax, bool verb);
 void freeInfoBetaAdic (InfoBetaAdic iba);
 
 //calcule l'automate des relations
-Automate RelationsAutomaton (InfoBetaAdic iba2, bool isvide, bool verb);
+Automate RelationsAutomaton (InfoBetaAdic iba2, bool isvide, bool ext, bool verb);