Fractional ideals for $\mathbb{Z}$

asked 2015-05-22 06:54:38 +0200

Oderyn gravatar image

Why isn't it possible to construct fractional ideals for the integers $\mathbb{Z}$?

sage: ZZ.fractional_ideal(3/5)
AttributeError: 'sage.rings.integer_ring.IntegerRing_class' object has no attribute 'fractional_ideal'

sage: II = ZZ.ideal(5)
sage: II^(-1)
TypeError: bad operand type for unary ~: 'Ideal_pid'

But absurdly this works:

sage: JJ = NumberField(x-7,"a").ring_of_integers().fractional_ideal(3/5)
sage: JJ^(-1)
Fractional ideal (5/3)

What should I do? Use this crude workaround?

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kcrisman gravatar imagekcrisman ( 2015-05-23 20:48:38 +0200 )edit
kcrisman gravatar imagekcrisman ( 2015-05-26 18:07:05 +0200 )edit