Given a NumberField, is there a way to check if its ring of integers is a PID? This could be with a built in method, analogous to is_noetherian(), but if there's a more complicated way to do it that's good too.
The method class_number gives you the answer, there is no need for further methods
sage: QuadraticField(2).class_number()
1
sage: QuadraticField(-5).class_number()
2
For a number field K, the fractional ideals form a group under multiplication. The class number of K is the number of elements in the quotient of this ring by the principal ideals. In particular, the class number is 1 if and only if the ring of integers of K is a PID.
see also: http://en.wikipedia.org/wiki/Ideal_cl...
Asked: 2012-06-06 19:28:05 +0200
Seen: 662 times
Last updated: Jul 21 '12
Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.