Fractional ideal class double exponentiation fails

[jdemeyer]

sage: k.<a> = NumberField(x^2 + 20072); G = k.class_group(); (G.0^2)^2
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/usr/local/src/sage-4.7.alpha4/<ipython console> in <module>()

/usr/local/src/sage-4.7.alpha4/local/lib/python2.6/site-packages/sage/rings/number_field/class_group.pyc in __pow__(self, n)
    302         # we go along; actually computing self.__ideal ** n would
    303         # be disastrous.
--> 304         n = n % self.order()
    305         return MonoidElement.__pow__(self, n)
    306

/usr/local/src/sage-4.7.alpha4/local/lib/python2.6/site-packages/sage/rings/number_field/class_group.pyc in order(self)
    392         """
    393         # an old method with a new docstring
--> 394         return AbelianGroupElement.order(self)
    395
    396     def multiplicative_order(self):

/usr/local/src/sage-4.7.alpha4/local/lib/python2.6/site-packages/sage/groups/abelian_gps/abelian_group_element.pyc in order(self)
    304             return o
    305         L = list(self.list())
--> 306         N = LCM([invs[i]//GCD(invs[i],L[i]) for i in range(len(invs)) if L[i]!=0])
    307         if N == 0:
    308             return infinity

/usr/local/src/sage-4.7.alpha4/local/lib/python2.6/site-packages/sage/rings/integer.so in sage.rings.integer.Integer.__floordiv__ (sage/rings/integer.c:12659)()

/usr/local/src/sage-4.7.alpha4/local/lib/python2.6/site-packages/sage/structure/element.so in sage.structure.element.bin_op (sage/structure/element.c:19135)()

/usr/local/src/sage-4.7.alpha4/local/lib/python2.6/site-packages/sage/structure/element.so in sage.structure.element.bin_op (sage/structure/element.c:19033)()

/usr/local/src/sage-4.7.alpha4/local/lib/python2.6/site-packages/sage/structure/coerce.so in sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/coerce.c:6498)()

/usr/local/src/sage-4.7.alpha4/local/lib/python2.6/site-packages/sage/structure/coerce.so in sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/coerce.c:6436)()

TypeError: unsupported operand type(s) for //: 'sage.libs.pari.gen.gen' and 'sage.libs.pari.gen.gen'

Both patches should be applied.

[fwclarke]

The root cause of this defect is that the coordinates of class group elements were Pari integers. 

The problem wasn't detected before because only generators were tested in the doctests for sage.rings.number_field.class_group.FractionalIdealClass.order .

The attached patch fixes the problem and alters one doctest.

[jdemeyer]

Replying to fwclarke:

The root cause of this defect is that the coordinates of class group elements were Pari integers. 

The problem wasn't detected before because only generators were tested in the doctests for sage.rings.number_field.class_group.FractionalIdealClass.order .

The attached patch fixes the problem and alters one doctest.

Thanks, I will test it. However, you should add a doctest to show that the problem from this ticket is fixed (so needs_work for this reason).

[fwclarke]

Apply both patches

[fwclarke]

Replying to jdemeyer:

you should add a doctest to show that the problem from this ticket is fixed.

Done. All the previous tests only took powers of a generator.

[jdemeyer]

Looks good! Patch makes sense and fixes the problem.

[cremona]

I also tested the patch (after #11230 and on the way to #11130) and everything tested fine.