Changeset 7443:10ffb2e25cf6

Timestamp:

12/01/07 05:09:30 (5 years ago)

Author:

mabshoff@…

Branch:

default

Tags:

2.8.15.alpha0

Message:

fix odd mismerge with the minkowski bound patch (#1107) - very, very odd

File:

• sage/rings/number_field/number_field_base.pyx (modified) (1 diff)

sage/rings/number_field/number_field_base.pyx

@@ -159 +159 @@
             return d * n.factorial() / (n**n)            
         
-    def signature(self):
-        """
-        Return (r1, r2), where r1 and r2 are the number of real embeddings
-        and pairs of complex embeddings of this field, respectively.
-        """
-        raise NotImplementedError
-
-    def degree(self):
-        """
-        Return the degree of this number field.
-        """
-        raise NotImplementedError
-
-    def discriminant(self):
-        """
-        Return the discriminant of this number field.
-        """
-        raise NotImplementedError
-
-    def minkowski_bound(self):
-        r"""
-        Return the Minkowski bound associated to this number field.
-
-        EXAMPLES:
-        The Minkowski bound for $\QQ[i]$ tells us that the class
-        number is 1:
-            sage: K = QQ[I]
-            sage: B = K.minkowski_bound(); B
-            4/pi
-            sage: B.n()
-            1.27323954473516
-
-        We compute the Minkowski bound for $\QQ[\sqrt[3]{2}]$:
-            sage: K = QQ[2^(1/3)]
-            sage: B = K.minkowski_bound(); B
-            16*sqrt(3)/(3*pi)
-            sage: B.n()
-            2.94042077558289
-            sage: int(B)
-            2
-
-        We compute the Minkowski bound for $\QQ[\sqrt{10}]$, which
-        has class number $2$:
-            sage: K = QQ[sqrt(10)]
-            sage: B = K.minkowski_bound(); B
-            sqrt(10)
-            sage: int(B)
-            3
-            sage: K.class_number()
-            2
-
-        The bound of course also works for the rational numbers:
-            sage: QQ.minkowski_bound()
-            1
-        """
-        _, s = self.signature()
-        n = self.degree()
-        d = self.discriminant().abs().sqrt()
-        from sage.functions.constants import pi
-        if s > 0:
-            return d * (4/pi)**s * n.factorial() / (n**n)
-        else:
-            return d * n.factorial() / (n**n)            
-