Add functions split(), shift1OP() and unshift1() to FastAutomaton and…

… correct some bugs.

src/sage/combinat/words/automataC.c

@@ -208,9 +208,10 @@ void ReallocAutomaton (Automaton *a, int n)
 	*/
 }
 
-Automaton CopyAutomaton (Automaton a)
+Automaton CopyAutomaton (Automaton a, int nalloc, int naalloc)
 {
-	Automaton r = NewAutomaton(a.n, a.na);
+	//a.n, a.na
+	Automaton r = NewAutomaton(nalloc, naalloc);
 	int i,j;
 	for (i=0;i<a.n;i++)
 	{
@@ -494,6 +495,8 @@ bool emptyLangage_rec (Automaton a, int e)
 //détermine si le langage de l'automate est vide
 bool emptyLangage (Automaton a)
 {
+	if (a.i == -1)
+		return true;
 	bool res = emptyLangage_rec(a, a.i);
 	//remet les états finaux
 	int i;

src/sage/combinat/words/automataC.h

@@ -14,7 +14,7 @@ void printDict (Dict d);
 void dictAdd (Dict *d, int e); //ajoute un élément au dictionnaire (même s'il était déjà présent)
 Automaton NewAutomaton (int n, int na);
 void FreeAutomaton (Automaton *a);
-Automaton CopyAutomaton (Automaton a);
+Automaton CopyAutomaton (Automaton a, int nalloc, int naalloc);
 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

@@ -40,7 +40,7 @@ cdef extern from "automataC.h":
 
     Automaton NewAutomaton (int n, int na)
     void FreeAutomaton (Automaton *a)
-    Automaton CopyAutomaton (Automaton a)
+    Automaton CopyAutomaton (Automaton a, int nalloc, int naalloc)
     void init (Automaton *a)
     void printAutomaton (Automaton a)
     void plotTikZ (Automaton a, const char **labels, const char *graph_name, double sx, double sy)
@@ -559,6 +559,62 @@ cdef class FastAutomaton:
         #r = r.minimise()
         return r.emonde().minimise()
 
+    #split the automaton with respect to a
+    def split (self, FastAutomaton a, verb=False):
+        #complete the automaton a
+        sig_on()
+        CompleteAutomaton(a.a)
+        sig_off()
+
+        #make the product
+        d = {}
+        for l in self.A:
+            if l in a.A:
+                d[(l,l)] = l
+
+        cdef Automaton ap
+        cdef Dict dC
+        r = FastAutomaton(None)
+        r2 = FastAutomaton(None)
+        Av = []
+        sig_on()
+        dv = imagProductDict(d, self.A, a.A, Av=Av)
+        sig_off()
+        if verb:
+            print "Av=%s"%Av
+            print "dv=%s"%dv
+        sig_on()
+        dC = getProductDict(d, self.A, a.A, dv=dv, verb=verb)
+        sig_off()
+        if verb:
+            print "dC="
+            printDict(dC)
+        sig_on()
+        ap = Product(self.a[0], a.a[0], dC)
+        FreeDict(dC)
+        sig_off()
+
+        #set final states for the intersection
+        cdef int i,j
+        cdef n1 = self.a.n
+        for i in range(n1):
+            for j in range(a.a.n):
+                ap.e[i+n1*j].final = self.a.e[i].final and a.a.e[j].final
+
+        #complementary of a in self
+        cdef Automaton ap2
+        ap2 = CopyAutomaton(ap, ap.n, ap.na)
+        #set final states
+        for i in range(n1):
+            for j in range(a.a.n):
+                ap2.e[i+n1*j].final = self.a.e[i].final and not a.a.e[j].final
+
+        r.a[0] = ap
+        r.A = Av
+        r2.a[0] = ap2
+        r2.A = Av
+        return [r.emonde().minimise(), r2.emonde().minimise()]
+
     #return the automaton recognizing the langage shifted
     def shift (self, verb=False):
         #détermine la liste des successeurs de l'état initial
@@ -582,6 +638,26 @@ cdef class FastAutomaton:
             b = b.emonde().minimise()
             a = a.union(b)
         return a
+
+    #modify the automaton to recognize the langage shifted by a (letter given by its index)
+    def shift1OP (self, int a, verb=False):
+        if self.a.i != -1:
+            self.a.i = self.a.e[self.a.i].f[a]
+
+    def unshift1 (self, int a):
+        r = FastAutomaton(None)
+        sig_on()
+        cdef Automaton aut
+        aut = CopyAutomaton(self.a[0], self.a.n+1, self.a.na)
+        cdef int i
+        cdef int ne = self.a.n
+        for i in range(aut.na):
+            aut.e[ne].f[i] = -1
+        aut.e[ne].f[a] = self.a.i
+        aut.i = ne
+        r.a[0] = aut
+        r.A = self.A
+        return r
 
     def determinise_proj (self, dict d, noempty=True, onlyfinals=False, nof=False, verb=False):
         sig_on()
@@ -795,7 +871,7 @@ cdef class FastAutomaton:
     def copy (self):
         sig_on()
         r = FastAutomaton(None)
-        r.a[0] = CopyAutomaton(self.a[0])
+        r.a[0] = CopyAutomaton(self.a[0], self.a.n, self.a.na)
         r.A = self.A
         sig_off()
         return r

src/sage/monoids/beta_adic_monoid.pyx

@@ -106,7 +106,7 @@ cdef getElement (e, Element r, int n):
 
 cdef InfoBetaAdic initInfoBetaAdic (self, Cd=None, verb=False) except *:
     #compute all the data in sage
-    K = NumberField((1/self.b).minpoly(), 'b', embedding=QQbar(self.b))
+    K = NumberField((1/self.b).minpoly(), 'b', embedding=QQbar(1/self.b))
     b = K.gen()
     C = [c.lift()(1/b) for c in self.C]
     if verb:
@@ -502,7 +502,7 @@ class BetaAdicMonoid(Monoid_class):
                 else:
                     return "Monoid of b-adic expansion with b root of %s and numerals set %s"%(K.modulus(),self.C) + str
 
-    def default_ss (self):
+    def default_ss (self, C=None):
         r"""
         Returns the full subshift (given by an Automaton) corresponding to the beta-adic monoid.
 
@@ -512,7 +512,8 @@ class BetaAdicMonoid(Monoid_class):
             sage: m.default_ss()
             Finite automaton with 1 states
         """
-        C = self.C
+        if C is None:
+            C = self.C
         ss = Automaton()
         ss.allow_multiple_edges(True)
         ss.allow_loops(True)
@@ -2345,15 +2346,18 @@ class BetaAdicMonoid(Monoid_class):
         if verb:
             print "Cd=%s"%Cd
         a = self.relations_automaton3(Cd=Cd, ext=ext)
-        if step == 1:
-            return a
         if verb:
             print " -> %s"%a
-        a = a.emonde_inf()
-        if step == 2:
+        if step == 1:
             return a
+        if ext:
+            a = a.emonde_inf()
+        else:
+            a = a.emonde()
         if verb:
             print " Après émondation : %s"%a
+        if step == 2:
+            return a
         d={}
         for c1 in C2:
             for c2 in C:
@@ -2368,7 +2372,7 @@ class BetaAdicMonoid(Monoid_class):
             print a2
         if step == 3:
             return a2
-        ap = tss.product(FastAutomaton(self.default_ss()), verb=verb)
+        ap = tss.product(FastAutomaton(self.default_ss(C=C)), verb=verb)
         if step == 4:
             return ap
         a2 = ap.intersection(a2)
@@ -2407,7 +2411,10 @@ class BetaAdicMonoid(Monoid_class):
     def move (self, t, FastAutomaton tss=None, list C=None, step=None):
         if tss is None:
             if hasattr(self, 'tss'):
-                tss = FastAutomaton(self.tss)
+                if isinstance(self.tss, FastAutomaton):
+                    tss = self.tss
+                else:
+                    tss = FastAutomaton(self.tss)
             else:
                 tss = FastAutomaton(self.default_ss())
         if C is None:

src/sage/monoids/relations.c

@@ -107,6 +107,9 @@ void initHash ()
 void freeInfoBetaAdic (InfoBetaAdic iba)
 {
 	int i;
+	free(pile);
+	free(thash);
+	free(iba.cM);
 	for (i=0;i<iba.ncmax;i++)
 	{
 		FreeElement(iba.c[i]);