Improve the completion of FastAutomaton and add complementaryOP() and…

… test of inclusion : included().

src/sage/combinat/words/automataC.c

@@ -333,25 +333,38 @@ bool IsCompleteAutomaton (Automaton a)
 }
 
 //complete the automaton (i.e. add a hole state if necessary)
-void CompleteAutomaton (Automaton *a)
+//return true iff a state was added
+bool CompleteAutomaton (Automaton *a)
 {
 	int ne = a->n; //nouvel état
-	AddEtat(a, false); //ajoute l'état puits
 	int i,j;
+	bool add_etat = false;
 	for (i=0;i<ne;i++)
 	{
 		for (j=0;j<a->na;j++)
 		{
 			if (a->e[i].f[j] == -1)
+			{
 				a->e[i].f[j] = ne;
+				add_etat = true;
+			}
 		}
 	}
+	if (a->i == -1)
+	{
+		a->i = ne;
+		add_etat = true;
+	}
+	if (!add_etat)
+		return false;
+	AddEtat(a, false); //ajoute l'état puits
 	for (j=0;j<a->na;j++)
 	{
 		a->e[ne].f[j] = ne;
 	}
 	if (a->i == -1)
 		a->i = ne;
+	return true;
 }
 
 //détermine si les automates sont les mêmes (différents si états permutés)

src/sage/combinat/words/automataC.h

@@ -112,7 +112,7 @@ bool emptyLangage (Automaton a);
 bool IsCompleteAutomaton (Automaton a);
 
 //complete the automaton (i.e. add a hole state if necessary)
-void CompleteAutomaton (Automaton *a);
+bool CompleteAutomaton (Automaton *a);
 
 //copy the automaton with a new bigger alphabet
 Automaton BiggerAlphabet (Automaton a, Dict d, int nna);

src/sage/combinat/words/cautomata.pyx

@@ -69,7 +69,7 @@ cdef extern from "automataC.h":
     bool emptyLangage (Automaton a)
     void AddEtat (Automaton *a, bool final)
     bool IsCompleteAutomaton (Automaton a)
-    void CompleteAutomaton (Automaton *a)
+    bool CompleteAutomaton (Automaton *a)
     Automaton BiggerAlphabet (Automaton a, Dict d, int nna) #copy the automaton with a new bigger alphabet
     void Test ()
 
@@ -501,13 +501,14 @@ cdef class FastAutomaton:
         sig_on()
         res = IsCompleteAutomaton(self.a[0])
         sig_off()
-        return res
+        return Bool(res)
 
     #give a complete automaton (i.e. with his hole state)
     def complete (self):
         sig_on()
-        CompleteAutomaton(self.a)
+        res = CompleteAutomaton(self.a)
         sig_off()
+        return Bool(res)
 
     def union (self, FastAutomaton a, verb=False):
         #complete the automata
@@ -837,8 +838,34 @@ cdef class FastAutomaton:
         sig_off()
         r.A = nA
         return r
-
-
+
+    def complementaryOP (self):
+        self.complete()
+        cdef i
+        for i in range(self.a.n):
+            self.a.e[i].final = not self.a.e[i].final
+
+    def included (self, FastAutomaton a, bool verb=False, step=None):
+        d = {}
+        for l in self.A:
+            if l in a.A:
+                d[(l,l)] = l
+        if verb:
+            print "d=%s"%d
+        a.complete()
+        cdef FastAutomaton p = self.product(a, d, verb=verb)
+
+        #set final states
+        cdef int i,j
+        cdef n1 = self.a.n
+        for i in range(n1):
+            for j in range(a.a.n):
+                p.a.e[i+n1*j].final = self.a.e[i].final and not a.a.e[j].final
+
+        if step == 1:
+            return p;
+
+        return p.has_empty_langage()