critere polynome de definition Fpk

CocksPinchVariant.py

@@ -505,7 +505,7 @@ class CocksPinchVariantResult(object):
 
     """
 
-    def __init__(self,k,D,T,i,ht=Integer(0),hy=Integer(0),pre=False,l=1, allowed_cofactor = 1, allowed_size_cofactor = 5, max_trialdiv=10**6, max_B1=10**4, new_semantics=False):
+    def __init__(self,k,D,T,i,ht=Integer(0),hy=Integer(0),max_poly_coeff=0,pre=False,l=1, allowed_cofactor = 1, allowed_size_cofactor = 5, max_trialdiv=10**6, max_B1=10**4, new_semantics=False):
         kl = k * l
         fD = -fundamental_discriminant(-D)
 
@@ -515,6 +515,7 @@ class CocksPinchVariantResult(object):
         self.T = Integer(T)
         self.i = i
         self.r = cyclotomic_polynomial(kl)(T)
+        self.max_poly_coeff = max_poly_coeff
         self.allowed_size_cofactor = allowed_size_cofactor
         self.allowed_cofactor = allowed_cofactor
         self.max_trialdiv = max_trialdiv
@@ -623,6 +624,11 @@ class CocksPinchVariantResult(object):
         if pre:
             print "C=%s" % repr(self)
 
+    def u(self):
+        return self.T
+    def T(self):
+        return self.T
+
     def _prepare_E2(self):
         if self._E2 is not None:
             return
@@ -1029,6 +1035,7 @@ class CocksPinchVariantSearch(object):
         output_file="",
         T_choice="",
         hty_choice="",
+        max_poly_coeff=0,
         l=1,
         required_cofactor=1,
         allowed_cofactor = 1,
@@ -1052,6 +1059,7 @@ class CocksPinchVariantSearch(object):
           - `random`: abide by the other parameters, except that we do random picks.
           - `hamming=X`: restrict to Hamming weight equal to `X` (int, positive)
           - `2-naf=X`: restrict to 2-NAF weight equal to `X` (int, positive)
+        - `max_poly_coeff` (int):     maximum value of alpha such that x^k - alpha is irreducible
         - `verbose` (boolean):        verbose mode 
         - `output_file` (string):     filename where to write the parameters 
         - `hty_choice` (string):       strategy to select hy in y = y0 + hy*r and ht in t = t0 + ht*r;
@@ -1076,6 +1084,7 @@ class CocksPinchVariantSearch(object):
         self.T_choice = T_choice
         self.hty_choice = hty_choice
         self.l = l
+        self.max_poly_coeff = Integer(max_poly_coeff)
         self.required_cofactor = Integer(required_cofactor)
         self.allowed_cofactor = Integer(allowed_cofactor)
         self.allowed_size_cofactor = Integer(allowed_size_cofactor)
@@ -1922,6 +1931,18 @@ class CocksPinchVariantSearch(object):
                     fail['p milrab'] += 1
                     continue
 
+                if self.max_poly_coeff > 0 :
+                    boo = False
+                    for alpha in range(1, self.max_poly_coeff):
+                        if (x**k - alpha).is_irreducible() :
+                            boo = True
+                            break
+                        if (x**k + alpha).is_irreducible() :
+                            boo = True
+                            break
+                    if not(boo) :
+                        fail['large poly'] += 1
+
                 E = CocksPinchVariantResult(k,fD,T,i,ht=ht,hy=hy,l=self.l)
 
                 if not self.check_automatic_factors(E):