On Sep 3, 12:36 am, William Stein <wst...@gmail.com> wrote:
>
> Sage has the Gaussian integers, and I'm sure the basic arithmetic and
> functionality is as good or better than Mathematica already.
>
> sage: R.<I> = ZZ[sqrt(-1)]; R
> Order in Number Field in I with defining polynomial x^2 + 1

Okay, this looks like a bug to me:

----------------------------------------------------------------------
| Sage Version 4.1.1, Release Date: 2009-08-14                       |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
sage: I
I
sage: R.<I> = ZZ[sqrt(-1)]
sage: I
1
sage: I^2
1

Why is I equal to 1 all of a sudden?  Same problem here:

sage: reset()
sage: R.<a> = ZZ[sqrt(-5)]
sage: a
1
sage: R.1
a
sage: R.1 == a
False
sage: (R.1)^2
-5
sage: R.inject_variables()
Defining a
sage: a
1


Ouch.
--
John

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