Revision history [back]
 | 1 | initial version |
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, the fractional ideals form a group under multiplication. The class number is the number of elements in the quotient of this ring by the principal ideals. Hence, the class number is 1 if and only if the number field is a PID.
see also: http://en.wikipedia.org/wiki/Ideal_class_group
| | 2 | No.2 Revision |
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, 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. Hence, In particular, the class number is 1 if and only if the number field ring of integers of K is a PID.
see also: http://en.wikipedia.org/wiki/Ideal_class_group
