Add a function piece to FastAutomaton, add intersection2 and intersec…

…t to BetaAdicMonoid

src/sage/combinat/words/automataC.c

@@ -313,6 +313,51 @@ Automaton CopyAutomaton (Automaton a, int nalloc, int naalloc)
 	return r;
 }
 
+//donne un automate reconnaissant w(w^(-1)L) où L est le langage de a partant de e
+Automaton PieceAutomaton (Automaton a, int *w, int n, int e)
+{
+	//printf("n = %d, e=%d\n", n, e);
+	int i, j, f;
+	Automaton r = NewAutomaton(a.n+n, a.na);
+	//met les sommets pour le mot w
+	for (i=0;i<n;i++)
+	{
+		for (j=0;j<a.na;j++)
+		{
+			r.e[i].f[j] = -1;
+		}
+		r.e[i].f[w[i]] = i+1;
+		r.e[i].final = false;
+		f = a.e[e].f[w[i]];
+		e = f;
+	}
+	if (n > 0)
+		r.e[n-1].f[w[n-1]] = e+n;
+	//teste si vide
+	if (f == -1)
+	{
+		FreeAutomaton(&r);
+		return NewAutomaton(0, a.na);
+	}
+	//met les sommets de l'automate a
+	for (i=0;i<a.n;i++)
+	{
+		for (j=0;j<a.na;j++)
+		{
+			if (a.e[i].f[j] == -1)
+				r.e[i+n].f[j] = -1;
+			else
+				r.e[i+n].f[j] = a.e[i].f[j]+n;
+		}
+		r.e[i+n].final = a.e[i].final;
+	}
+	if (n > 0)
+		r.i = 0;
+	else
+		r.i = a.i;
+	return r;
+}
+
 void init (Automaton *a)
 {
 	int i,j;

src/sage/combinat/words/automataC.h

@@ -22,6 +22,7 @@ void ReallocNAutomaton (NAutomaton *a, int n);
 void FreeAutomaton (Automaton *a);
 void FreeNAutomaton (NAutomaton *a);
 Automaton CopyAutomaton (Automaton a, int nalloc, int naalloc);
+Automaton PieceAutomaton (Automaton a, int *w, int n, int e); //donne un automate reconnaissant w(w^(-1)L) où L est le langage de a partant de e
 void init (Automaton *a);
 void printAutomaton (Automaton a);
 void plotTikZ (Automaton a, const char **labels, const char *graph_name, double sx, double sy);

src/sage/combinat/words/cautomata.pyx

@@ -43,6 +43,7 @@ cdef extern from "automataC.h":
     void FreeAutomaton (Automaton *a)
     void FreeNAutomaton (NAutomaton *a)
     Automaton CopyAutomaton (Automaton a, int nalloc, int naalloc)
+    Automaton PieceAutomaton (Automaton a, int *w, int n, int e)
     void init (Automaton *a)
     void printAutomaton (Automaton a)
     void plotTikZ (Automaton a, const char **labels, const char *graph_name, double sx, double sy)
@@ -1049,10 +1050,31 @@ cdef class FastAutomaton:
             return p;
 
         return p.has_empty_langage()
+
+    #donne un automate reconnaissant w(w^(-1)L) où L est le langage de a partant de e
+    def piece (self, w, e=None):
+        cdef int* l = <int*>malloc(sizeof(int)*self.a.n)
+        cdef int i
+        for i in range(len(w)):
+            l[i] = w[i]
+        if e is None:
+            e = self.a.i
+        r = FastAutomaton(None)
+        sig_on()
+        r.a[0] = PieceAutomaton(self.a[0], l, len(w), e)
+        sig_off()
+        r.A = self.A
+        return r
 
-
-
-
-
-
+    #tell if the language of the automaton is empty
+    #(this function is not very efficient)
+    def is_empty (self, ext=True):
+        if ext:
+            return self.emonde().emonde_inf().n_states() == 0
+        else:
+            return self.emonde().n_states() == 0
+
+	#determine if the languages intersect
+    def intersect (self, FastAutomaton b, ext=True):
+        return not self.intersection(b).is_empty(ext)
 

src/sage/monoids/beta_adic_monoid.pyx

@@ -2296,7 +2296,7 @@ class BetaAdicMonoid(Monoid_class):
 
     #test if 0 is an inner point of the limit set
     def ZeroInner (self, verb=False):
-        
+
         if not hasattr(self, 'ss'):
             self.ss = self.default_ss()
 
@@ -2339,7 +2339,7 @@ class BetaAdicMonoid(Monoid_class):
             self.ss = None
             print "Zero is an inner point iff the %s has non-empty interior."%self
             self.ss = ss
-
+        
     #complete the langage of a
     def complete (self, FastAutomaton a, C=None, ext=False, verb=False):
         r"""
@@ -2506,6 +2506,27 @@ class BetaAdicMonoid(Monoid_class):
 
         #compute the adherence of the new automaton
         return self.adherence(tss=a, C=C, C2=nA)
-
+
+    #calcule l'intersection des ensembles limites
+    def intersection2 (self, FastAutomaton a, FastAutomaton b, ext=True):
+        a2 = self.complete(a, ext=ext)
+        b2 = self.complete(b, ext=ext)
+        return a2.intersection(b2).emonde()
+
+    #determine if the limit sets intersect
+    def intersect (self, FastAutomaton a, FastAutomaton b, ext=True):
+        a2 = self.complete(a, ext=ext)
+        b2 = self.complete(b, ext=ext)
+        return not a2.intersection(b2).is_empty(ext)
+
+    #Dit si l'ensemble limite est connexe ou pas
+    def connexe (self, FastAutomaton a=None):
+        if a is None:
+            if hasattr(self, 'tss'):
+                a = FastAutomaton(self.tss)
+            else:
+                a = FastAutomaton(None).full(self.C)
+
+        raise ValueError("Not implemented !")