From a45bb655f48d152a750f0e4a30d445c5bea92593 Mon Sep 17 00:00:00 2001
From: Paul Mercat <mercatp@yahoo.fr>
Date: Fri, 8 Jul 2016 19:45:26 +0200
Subject: [PATCH] Add a function zero_complete() for FastAutomaton, a function
 shift for BetaAdicMonoid (not well tested) and correct some little things.

---
 src/sage/combinat/words/automataC.c   | 58 ++++++++++++++++++++++++++-
 src/sage/combinat/words/automataC.h   |  5 ++-
 src/sage/combinat/words/cautomata.pyx | 38 ++++++++++++++----
 src/sage/monoids/beta_adic_monoid.pyx | 36 ++++++++++++++++-
 4 files changed, 126 insertions(+), 11 deletions(-)

diff --git a/src/sage/combinat/words/automataC.c b/src/sage/combinat/words/automataC.c
index cf7fd4d3f9c..123ba900501 100644
--- a/src/sage/combinat/words/automataC.c
+++ b/src/sage/combinat/words/automataC.c
@@ -30,6 +30,13 @@ PyMODINIT_FUNC initdautomata(void)
 
 typedef Automate Automaton;
 
+/*
+void printAutomaton (Automaton a)
+{
+	printf("Automate ayant %d lettres, %d états, état initial %d.\n", a.na, a.n, a.i);
+}
+*/
+
 Dict NewDict (int n)
 {
 	Dict r;
@@ -550,6 +557,12 @@ bool IsCompleteAutomaton (Automaton a)
 //return true iff a state was added
 bool CompleteAutomaton (Automaton *a)
 {
+/*
+	if (a->n == 0)
+	{
+		AddEtat(a, false); //ajoute un état
+	}
+*/
 	int ne = a->n; //nouvel état
 	int i,j;
 	bool add_etat = false;
@@ -772,8 +785,13 @@ void Product_rec(Automaton r, int i1, int i2, Automaton a1, Automaton a2, Dict d
 	}
 }
 
-Automaton Product(Automaton a1, Automaton a2, Dict d)
+Automaton Product (Automaton a1, Automaton a2, Dict d, bool verb)
 {
+	if (verb)
+	{
+		printAutomaton(a1);
+		printAutomaton(a2);
+	}
 	//printf("a1.na=%d, a2.na=%d\n", a1.na, a2.na);
 	//compte le nombre de lettres de l'alphabet final
 	int i, na=0;
@@ -1708,6 +1726,44 @@ Automaton Duplicate (Automaton a, InvertDict id, int na2, bool verb)
 	return r;
 }
 
+void ZeroComplete_rec (Automaton a, int etat, bool *vu, int l0, bool verb)
+{
+	if (verb)
+		printf("etat %d ..\n", etat);
+	vu[etat] = true;
+	int i, e;
+	for (i=0;i<a.na;i++)
+	{
+		e = a.e[etat].f[i];
+		if (e != -1)
+		{
+			if (!vu[e])
+				ZeroComplete_rec(a, e, vu, l0, verb);
+			if (i == l0 && a.e[e].final)
+				a.e[etat].final = true;
+		}
+	}
+}
+
+void ZeroComplete (Automaton a, int l0, bool verb)
+{
+	if (verb)
+		printf("l0 = %d\n", l0);
+	if (a.i == -1)
+		return;
+	bool *vu = (bool *)malloc(sizeof(bool)*a.n); //liste des sommets vus
+	if (!vu)
+	{
+		printf("Out of memory !\n");
+		exit(25);
+	}
+	int i;
+	for (i=0;i<a.n;i++)
+		vu[i] = false;
+	ZeroComplete_rec(a, a.i, vu, l0, verb);
+	free(vu);
+}
+
 int compteur = 0;
 bool emonde_inf_rec (Automaton a, int etat)
 {
diff --git a/src/sage/combinat/words/automataC.h b/src/sage/combinat/words/automataC.h
index d7f59c283d8..9ccc908697a 100644
--- a/src/sage/combinat/words/automataC.h
+++ b/src/sage/combinat/words/automataC.h
@@ -30,7 +30,7 @@ bool equalsAutomaton (Automaton a1, Automaton a2); //détermine si les automates
 inline int contract (int i1, int i2, int n1);
 inline int geti1 (int c, int n1);
 inline int geti2 (int c, int n1);
-Automaton Product(Automaton a1, Automaton a2, Dict d);
+Automaton Product (Automaton a1, Automaton a2, Dict d, bool verb);
 void AddEtat (Automaton *a, bool final);
 
 struct Etats
@@ -114,6 +114,9 @@ Automaton DeterminiseN (NAutomaton a, bool puits);
 //the result is assumed deterministic !!!!
 Automaton Duplicate (Automaton a, InvertDict id, int na2, bool verb);
 
+//ajoute tous les mots qui se complètent en un mot du langage en ajoutant des 0 à la fin
+void ZeroComplete (Automaton a, int l0, bool verb);
+
 //retire tous les états à partir desquels il n'y a pas de chemin infini
 Automaton emonde_inf (Automaton a, bool verb);
 
diff --git a/src/sage/combinat/words/cautomata.pyx b/src/sage/combinat/words/cautomata.pyx
index c765682fd31..575fa8f4e05 100644
--- a/src/sage/combinat/words/cautomata.pyx
+++ b/src/sage/combinat/words/cautomata.pyx
@@ -49,9 +49,10 @@ cdef extern from "automataC.h":
 	void printAutomaton (Automaton a)
 	void plotTikZ (Automaton a, const char **labels, const char *graph_name, double sx, double sy)
 	void NplotTikZ (NAutomaton a, const char **labels, const char *graph_name, double sx, double sy)
-	Automaton Product(Automaton a1, Automaton a2, Dict d)
+	Automaton Product (Automaton a1, Automaton a2, Dict d, bool verb)
 	Automaton Determinise (Automaton a, Dict d, bool noempty, bool onlyfinals, bool nof, bool verb)
 	Automaton DeterminiseN (NAutomaton a, bool puits)
+	void ZeroComplete (Automaton a, int l0, bool verb)
 	Automaton emonde_inf (Automaton a, bool verb)
 	Automaton emonde (Automaton a, bool verb)
 	Automaton emondeI (Automaton a, bool verb)
@@ -205,7 +206,7 @@ def TestProduct (a1, a2, di):
 	d = getProductDict(di, list(a1.Alphabet()), list(a2.Alphabet()))
 	print "dictionnaire du produit :"
 	printDict(d)
-	c = Product(a, b, d)
+	c = Product(a, b, d, False)
 	print "résultat :"
 	printAutomaton(c)
 
@@ -492,6 +493,7 @@ cdef class FastAutomaton:
 	
 	def setAlphabet (self, list A):
 		self.A = A
+		self.a[0].na = len(A)
 	
 	def initial_state (self):
 		return self.a.i
@@ -554,6 +556,15 @@ cdef class FastAutomaton:
 			raise ValueError("set_succ(%s, %s) : index out of bounds !"%(i,j))
 		self.a.e[i].f[j] = k
 	
+	def zero_completeOP (self, verb=False):
+		sig_on()
+		for i in range(len(self.A)):
+			if self.A[i] == 0:
+				l0 = i
+				break
+		ZeroComplete(self.a[0], l0, verb)
+		sig_off()
+	
 	def emonde_inf (self, verb=False):
 		sig_on()
 		cdef Automaton a
@@ -594,6 +605,7 @@ cdef class FastAutomaton:
 			for la in self.A:
 				for lb in b.A:
 					d[(la,lb)] = (la,lb)
+			if verb: print d
 		sig_on()
 		cdef Automaton a
 		cdef Dict dC
@@ -607,21 +619,25 @@ cdef class FastAutomaton:
 		if verb:
 			print "dC="
 			printDict(dC)
-		a = Product(self.a[0], b.a[0], dC)
+		a = Product(self.a[0], b.a[0], dC, verb)
 		FreeDict(dC)
 		r.a[0] = a
 		r.A = Av
 		sig_off()
 		return r
 	
-	def intersection (self, FastAutomaton a, verb=False):
+	def intersection (self, FastAutomaton a, verb=False, simplify=True):
 		d = {}
 		for l in self.A:
 			if l in a.A:
 				d[(l,l)] = l
 		if verb:
 			print "d=%s"%d
-		return self.product(a, d, verb=verb)
+		p = self.product(a, d, verb=verb)
+		if simplify:
+			return p.emonde().minimise()
+		else:
+			return p
 	
 	#determine if the automaton is complete (i.e. with his hole state)
 	def is_complete (self):
@@ -682,7 +698,7 @@ cdef class FastAutomaton:
 			print "dC="
 			printDict(dC)
 		sig_on()
-		ap = Product(self.a[0], a.a[0], dC)
+		ap = Product(self.a[0], a.a[0], dC, verb)
 		FreeDict(dC)
 		sig_off()
 		
@@ -732,7 +748,7 @@ cdef class FastAutomaton:
 			print "dC="
 			printDict(dC)
 		sig_on()
-		ap = Product(self.a[0], a.a[0], dC)
+		ap = Product(self.a[0], a.a[0], dC, verb)
 		FreeDict(dC)
 		sig_off()
 		
@@ -786,7 +802,7 @@ cdef class FastAutomaton:
 		if self.a.i != -1:
 			self.a.i = self.a.e[self.a.i].f[a]
 	
-	def unshift1 (self, int a):
+	def unshift1 (self, int a, final=False):
 		r = FastAutomaton(None)
 		sig_on()
 		cdef Automaton aut
@@ -796,6 +812,7 @@ cdef class FastAutomaton:
 		for i in range(aut.na):
 			aut.e[ne].f[i] = -1
 		aut.e[ne].f[a] = self.a.i
+		aut.e[ne].final = final
 		aut.i = ne
 		r.a[0] = aut
 		r.A = self.A
@@ -1071,6 +1088,11 @@ cdef class FastAutomaton:
 		cdef i
 		for i in range(self.a.n):
 			self.a.e[i].final = not self.a.e[i].final
+	
+	def complementary (self):
+		a = self.copy()
+		a.complementaryOP()
+		return a
 			
 	def included (self, FastAutomaton a, bool verb=False, step=None):
 		d = {}
diff --git a/src/sage/monoids/beta_adic_monoid.pyx b/src/sage/monoids/beta_adic_monoid.pyx
index 43aedf42be3..f7848368f9b 100644
--- a/src/sage/monoids/beta_adic_monoid.pyx
+++ b/src/sage/monoids/beta_adic_monoid.pyx
@@ -2602,7 +2602,15 @@ class BetaAdicMonoid(Monoid_class):
 		return self.adherence(tss=a, C=C, C2=nA)
 	
 	#donne l'automate décrivant le translaté de +t de a, avec les chiffres A au départ et B à l'arrivée, le tout dans l'ensemble décrit par b
-	def move2 (self, t, FastAutomaton a, FastAutomaton b=None, list A=None, list B=None, verb=False):
+	def move2 (self, t, FastAutomaton a=None, FastAutomaton b=None, list A=None, list B=None, verb=False):
+		if a is None:
+			if hasattr(self, 'tss'):
+				if isinstance(self.tss, FastAutomaton):
+					a = self.tss
+				else:
+					a = FastAutomaton(self.tss)
+			else:
+				a = FastAutomaton(self.default_ss())
 		if b is None:
 			if hasattr(self, 'tss'):
 				if isinstance(self.tss, FastAutomaton):
@@ -2630,6 +2638,32 @@ class BetaAdicMonoid(Monoid_class):
 		ai = ai.determinise_proj(d, verb=verb)
 		return ai.minimise()
 	
+	#Not well tested !!!!
+	#return the automaton recognizing the division by beta and translation t
+	def shift (self, FastAutomaton aa, FastAutomaton bb, t=0, verb=False):
+		#détermine la liste des successeurs de l'état initial
+		cdef int i
+		cdef int e
+		l = set()
+		for j in range(aa.a.na):
+			e = aa.a.e[aa.a.i].f[j]
+			if e != -1:
+				l.add(j)
+		l = list(l)
+		if verb:
+			print "états à considérer : %s"%l
+		#calcule l'union des automates translatés
+		a = FastAutomaton(None)
+		A = aa.Alphabet()
+		a.setAlphabet(A)
+		for i in range(0, len(l)):
+			a2 = aa.copy()
+			a2.set_initial_state(aa.a.e[aa.a.i].f[l[i]])
+			a2 = a2.emonde().minimise()
+			a2 = self.move2(t=-(A[l[i]]-t)/self.b, a=a2, b=bb)
+			a = a.union(a2)
+		return a
+	
 	#calcule l'intersection des ensembles limites
 	def intersection2 (self, FastAutomaton a, FastAutomaton b, ext=True):
 		a2 = self.complete(a, ext=ext)