[with negative review] QuadraticFields and ClassGroups

[sagetrac-ljpk]

SAGE can compute the class group of a quadratic field, but it has issues with computing the order of elements within that class group:

QF.<x>=QuadraticField(-39)
CF=QF.class_group()
CF(QF.ideal(1+x)).order()

gives

NotImplementedErrorTraceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/server2/sage_notebook/worksheets/ljpk/0/code/6.py", line 6, in <module>
    CF(QF.ideal(Integer(1)+x)).order()
  File "/home/sage10/", line 1, in <module>
    
  File "element.pyx", line 1190, in sage.structure.element.MultiplicativeGroupElement.order
  File "element.pyx", line 1130, in sage.structure.element.MonoidElement.multiplicative_order
NotImplementedError

Component: number theory

Keywords: editor_craigcitro

Issue created by migration from https://trac.sagemath.org/ticket/1400

[aghitza]

Attachment: 1400-quadratic_field_order.patch.gz

[aghitza]

comment:2

The attached patch adds this functionality for fractional ideals and for their representatives in class groups.

[ncalexan]

comment:3

This uses an O(n) algorithm to compute orders. Don't we have generic BSGS O(sqrt(n)) that would be better here?

[craigcitro]

Changed keywords from none to editor_craigcitro

[sagetrac-mabshoff]

comment:5

Fixed via #3913.

Cheers,

Michael