On Sat, Dec 4, 2010 at 1:59 AM, Simon King <[email protected]> wrote:
> Hi John,
>
> On 4 Dez., 00:52, John H Palmieri <[email protected]> wrote:
>> I accidentally just typed this:
>>
>> sage: R = QQ['y', 'y']
>>
>> Should this perhaps raise an error?
>
> I strongly agree.
I very strongly disagree. What's wrong with making a polynomial ring
with two distinct variables whose *print* names you happen to set to
be the same? The variables are different. It's just that they
print in the same way. Magma also allows this, by the way.
sage: R = PolynomialRing(QQ, names=('y','y'))
sage: R
Multivariate Polynomial Ring in y, y over Rational Field
sage: R.0
y
sage: R.1
y
sage: R.0 == R.1
False
sage: R.0 + R.1
y + y
sage: !magma
Magma V2.15-11 Sat Dec 4 2010 13:25:15 on deep [Seed = 3070315377]
Type ? for help. Type <Ctrl>-D to quit.
> R<y,y> := PolynomialRing(RationalField(),2);
> R.1 + R.2;
y + y
> I also think this should raise an error:
> sage: R.<x> = QQ[]
> sage: S.<y> = R[]
> sage: T.<x> = S[]
I also disagree. This definitely should not raise an error.
William
>
> Generally, I think that
>
> Cheers,
> Simon
>
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--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org
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