# Changeset 7443:10ffb2e25cf6

Ignore:
Timestamp:
12/01/07 05:09:30 (5 years ago)
Branch:
default
Tags:
2.8.15.alpha0
Message:

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

File:
1 edited

### Legend:

Unmodified
 r7437 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)