On Thu, Mar 19, 2015 at 3:16 AM, Chris Wuthrich
<[email protected]> wrote:
>
>> What about the quadratic case? Would you oppose change the print order
>> just for quadratic number fields (note that we already have a separate class
>> QuadraticNumberField, so the change can easily be made).
>
> And a further subquestion: What about Q[i] ? It seems really strange that
> sage decides to write 3*I + 1. But reverts it for CC(3*I+1).
> No other cas does that, I would think.
Yes, I was also referring specifically to to the special case of QQ[i],
sage: R.<I> = QQ[sqrt(-1)]
sage: 3 + R.gen()
I + 3
sage: CC(3 + R.gen())
3.00000000000000 + 1.00000000000000*I
which Maple and Mathematica handle this case differently (better) than
arbitrary number fields. For numerical complex numbers, Pari also does
sage: pari(CC(1.0, 2.0))
1.00000000000000 + 2.00000000000000*I
and its "number field element" representation of Mod(poly1, poly2)
isn't very compelling.
Broadening the scope it seems more natural for cyclotomic fields and
quadratic fields as well
sage: S = QQ[sqrt(5)]
sage: 2 + S.gen()
sqrt5 + 2
sage: R = CyclotomicField(5)
sage: (R.gen() + 1)^5
5*zeta5^3 + 5*zeta5^2 - 3
I actually don't think it'd be that bad to print out algebraic number
representations in reverse order than polynomials; that's what we do
for power series (for admittedly even more compelling reasons).
But mine is just one of many opinions.
> While I am at it: Can I ask for a pointer to the discussion why I is
> symbolic ?
Probably because that was an upgrade from I being a member of CC
(precision 53) when symbolics were added. If there's a coercion to
ZZ[i] -> SR, I'd be nice to put it there.
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