Hi all,
On 2015-07-13, Nathann Cohen <nathann.co...@gmail.com> wrote:
>> PS Testing over QQbar certainly does give False, as it would for m*sqrt(1/2)
>> and n for any pair of integers (m,n) not (0,0), since sqrt(2) is irrational!
>
> Wouldn't it be better to compare 'exact types' in an exact ring? Here
> we compare two exact types in a non-exact field.
No, in this example we compare one exact type and one non-exact type!
One of the arguments lives in the Symbolic Ring, which is not an exact ring:
sage: SR
Symbolic Ring
sage: SR.is_exact()
False
By coercion, the comparison of the integer m1 with the symbolic
expression m below is done after coercion to the symbolic ring:
sage: cm = get_coercion_model()
sage: m=540579833922455191419978421211010409605356811833049025*sqrt(1/2)
sage: m1=382247666339265723780973363167714496025733124557617743
sage: cm.explain(m.parent(), m1.parent(), operator.eq)
Coercion on right operand via
Conversion map:
From: Integer Ring
To: Symbolic Ring
Arithmetic performed after coercions.
Result lives in Symbolic Ring
Symbolic Ring
So, if there is anything to fix then it is how the symbolic ring deals
with exact algebraic data. Here, there is a natural interpretation of m
as an element of QQbar. So, the symbolic ring *could* compare the
symbolic data after pushing them to QQbar:
sage: QQbar(m) == QQbar(m1)
False
However, I don't know if there is an easy way to teach the symbolic ring
to do so.
In other words: If one *can* avoid symbolic expressions, then one *should*
avoid symbolic expressions.
Best regards,
Simon
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