Changeset 7442:f3627c90367a

Timestamp:

12/01/07 03:39:38 (5 years ago)

Author:

mabshoff@…

Branch:

default

Parents:

7440:3e6bbc9928b6 (diff), 7441:5b6d6e2e4a87 (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent.

Message:

merge

Files:

• sage/rings/number_field/number_field.py (modified) (1 diff)
• sage/rings/number_field/number_field.py (modified) (5 diffs)

sage/rings/number_field/number_field.py

@@ -4627 +4627 @@
         parts = -b/(2*a), (Dpoly/D).sqrt()/(2*a)
         self._NumberField_generic__gen = self._element_class(self, parts)
+
+
+    def coerce_map_from_impl(self, S):
+        """
+        EXAMPLES:
+            sage: K.<a> = QuadraticField(-3)
+            sage: f = K.coerce_map_from(QQ); f
+            Natural morphism:
+              From: Rational Field
+              To:   Number Field in a with defining polynomial x^2 + 3
+            sage: f(3/5)
+            3/5
+            sage: parent(f(3/5)) is K
+            True
+        """
+        if S is QQ:
+            return number_field_element_quadratic.Q_to_quadratic_field_element(self)
+        else:
+            return NumberField_absolute.coerce_map_from_impl(self, S)
+
+
         
     def discriminant(self, v=None):

sage/rings/number_field/number_field.py

@@ -170 +170 @@
 def NumberField(polynomial, name=None, check=True, names=None, cache=True):
     r"""
-    Return {\em the} number field defined by the given irreducible
+    Return \emph{the} number field defined by the given irreducible
     polynomial and with variable with the given name.  If check is
     True (the default), also verify that the defining polynomial is
@@ -471 +471 @@
 def is_QuadraticField(x):
     r"""
-    Return True if x is of the quadratic {\em number} field type.
+    Return True if x is of the quadratic \emph{number} field type.
 
     EXAMPLES:
@@ -1266 +1266 @@
                 gens = I.gens()
         return sage.rings.ring.Ring.ideal(self, gens, **kwds)
+
+    def ideals_of_bdd_norm(self, bound):
+        """
+        All integral ideals of bounded norm.
+
+        INPUT:
+            bound -- a positive integer
+
+        OUTPUT:
+            A dict of all integral ideals I such that Norm(I) <= bound,
+            keyed by norm.
+
+        EXAMPLE:
+            sage: K.<a> = NumberField(x^2 + 23)
+            sage: d = K.ideals_of_bdd_norm(10)
+            sage: for n in d:
+            ...       print n
+            ...       for I in d[n]:
+            ...           print I
+            1
+            Fractional ideal (1)
+            2
+            Fractional ideal (2, 1/2*a - 1/2)
+            Fractional ideal (2, 1/2*a + 1/2)
+            3
+            Fractional ideal (3, -1/2*a + 1/2)
+            Fractional ideal (3, -1/2*a - 1/2)
+            4
+            Fractional ideal (4, 1/2*a + 3/2)
+            Fractional ideal (2)
+            Fractional ideal (4, 1/2*a + 5/2)
+            5
+            6
+            Fractional ideal (-1/2*a + 1/2)
+            Fractional ideal (6, 1/2*a + 5/2)
+            Fractional ideal (6, 1/2*a + 7/2)
+            Fractional ideal (1/2*a + 1/2)
+            7
+            8
+            Fractional ideal (-1/2*a - 3/2)
+            Fractional ideal (4, a - 1)
+            Fractional ideal (4, a + 1)
+            Fractional ideal (1/2*a - 3/2)
+            9
+            Fractional ideal (9, 1/2*a + 11/2)
+            Fractional ideal (3)
+            Fractional ideal (9, 1/2*a + 7/2)
+            10
+
+        """
+        from sage.rings.number_field.number_field_ideal import convert_from_zk_basis
+        hnf_ideals = pari('ideallist(%s, %d)'%(self.pari_nf(),bound))
+        d = {}
+        for i in xrange(bound):
+            d[i+1] = [self.ideal([ self(generator) for generator in convert_from_zk_basis(self, hnf_I) ]) for hnf_I in hnf_ideals[i]]
+        return d
 
     def _is_valid_homomorphism_(self, codomain, im_gens):
@@ -2053 +2109 @@
         """
         return infinity.infinity
-        
+
     def polynomial_ntl(self):
         """
@@ -3623 +3679 @@
         return K
 
+    def absolute_polynomial_ntl(self):
+        """
+        Return defining polynomial of this number field
+        as a pair, an ntl polynomial and a denominator.
+
+        This is used mainly to implement some internal arithmetic.
+
+        EXAMPLES:
+            sage: NumberField(x^2 + (2/3)*x - 9/17,'a').polynomial_ntl()
+            ([-27 34 51], 51)
+        """
+        try:
+            return (self.__abs_polynomial_ntl, self.__abs_denominator_ntl)
+        except AttributeError:
+            self.__abs_denominator_ntl = ntl.ZZ()
+            den = self.absolute_polynomial().denominator()
+            self.__abs_denominator_ntl.set_from_sage_int(ZZ(den))
+            self.__abs_polynomial_ntl = ntl.ZZX((self.absolute_polynomial()*den).list())
+        return (self.__abs_polynomial_ntl, self.__abs_denominator_ntl)
+
     def absolute_polynomial(self):
         r"""