Some little improvements (add Cd argument in sage.monoids.beta_adic_m…

…onoid BetaAdicMonoid.relations, change the style of the arrows for plotting automaton using TikZ)

src/sage/combinat/words/automata.pyx

@@ -498,8 +498,11 @@ class Automaton (DiGraph):
         self.allow_multiple_edges(True)
         for u,v,l in self.edges():
             self.delete_edge(u, v, l)
-            for l2 in d[l]:
-                self.add_edge(u, v, l2)
+            if d.has_key(l):
+                for l2 in d[l]:
+                    self.add_edge(u, v, l2)
+            else:
+                print "Key %s not in the dictionary !"%l
         self.A = [a for A in d.values() for a in A]
 
     def determinize_rec (self, S, A, a, nof, noempty, verb):

src/sage/combinat/words/automata_tools.c

@@ -29,7 +29,7 @@ void TikZ (const char *data, const char *graph_name, double sx, double sy)
 		printf("start...\n");
 	fprintf(f, "digraph %s\n{\n"\
 	"	node[fontsize=20]"\
-	"	edge[fontsize=20]"\
+	"	edge[fontsize=20, arrowhead = open]"\
 	"	rankdir = LR;\n"\
 	"	size = \"%lf, %lf\";\n"\
 	"	center = 1;\n"\

src/sage/monoids/beta_adic_monoid.pyx

@@ -931,7 +931,7 @@ class BetaAdicMonoid(Monoid_class):
                 di[current_state][e] = c
         return di
 
-    def relations_automaton (self, ext=False, ss=None, noss=False, verb=False, step=100, limit=None, niter=None):
+    def relations_automaton (self, ext=False, ss=None, noss=False, Cd=None, verb=False, step=100, limit=None, niter=None):
         r"""
         Compute the relations automaton of the beta-adic monoid (with or without subshift).
         See http://www.latp.univ-mrs.fr/~paul.mercat/Publis/Semi-groupes%20fortement%20automatiques.pdf for a definition of such automaton (without subshift).
@@ -1066,7 +1066,8 @@ class BetaAdicMonoid(Monoid_class):
         if verb: print "places: "; print parch; print pultra
 
         #calcule les bornes max pour chaque valeur absolue
-        Cd = Set([c-c2 for c in self.C for c2 in self.C])
+        if Cd is None:
+            Cd = Set([c-c2 for c in self.C for c2 in self.C])
         if verb: print "Cd = %s"%Cd
         m = dict([])
         for p in parch:
@@ -1108,7 +1109,7 @@ class BetaAdicMonoid(Monoid_class):
         if verb: print "Avant emondation : %s"%res
 
         res.I = [K.zero()]
-        res.A = Set([c-c2 for c in self.C for c2 in self.C])
+        res.A = Cd #Set([c-c2 for c in self.C for c2 in self.C])
         if verb: print "Emondation..."
         if not ext:
             res.F = [K.zero()]