2008/6/27 William Stein <[EMAIL PROTECTED]>:
>
> On Tue, Jun 24, 2008 at 10:31 PM, Nick Alexander <[EMAIL PROTECTED]> wrote:
>>
>> Could someone who knows orders in number fields verify that they are
>> not at the moment unique parents and, if that is the desired
>> behaviour, explain why?
>
> I do not like the current behavior. I would be very with you changing
> it so orders are unique.
Agreed. Why not be more restrictive and insist that the number of
gens passed is equal to the field degree and that the elements are
linearly independent? Then the constructor should check that the
Z-module they span is closed under multiplication and contains 1, else
raise an error.
John
>
>> I have a coercion error in ell_number_field
>> based on this.
>
>
>
>> {{{
>> sage: K.<a> = NumberField(x^2 + 1, 'a')
>> sage: O1 = K.order([a, 1])
>> sage: O2 = K.order([a, 1, 1])
>> sage: O1 == O2
>> True
>> sage: O1 is O2
>> False
>> sage: O1.gens()
>> (1, a)
>> sage: O2.gens()
>> (1, a)
>> }}}
>>
>> Nick
>>
>> >
>>
>
>
>
> --
> William Stein
> Associate Professor of Mathematics
> University of Washington
> http://wstein.org
>
> >
>
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