On Mar 10, 2009, at 11:36 AM, Ralf Hemmecke wrote:
> And the reason is...?
Because it's really inconvenient to always have to manually cast to
the same parent. Imagine I have a loop.
while a < 1:
[do stuff to a to make it smaller]
Would this fail if a was not an integer. What if it started out as an
integer but then I divided it by something and it became a rational.
It's much cleaner to write the above than
while a < a.parent()(1):
[...]
There is are natural morphisms (in Sage called coercion morphism) Z -
> Q, Z -> Z[x], and Z -> Z/nZ that are used to equate objects across
parents.
>
> Ralf
>
> On 03/10/2009 07:34 PM, Robert Bradshaw wrote:
>> For the same reason that
>>
>> sage: z = ZZ(2)
>> sage: parent(z)
>> Integer Ring
>> sage: q = QQ(2)
>> sage: parent(q)
>> Rational Field
>> sage: z == q
>> True
>> sage: p = ZZ['x'](2)
>> sage: p == z
>> True
>>
>>
>> On Mar 10, 2009, at 11:23 AM, Ralf Hemmecke wrote:
>>
>>> Can somebody give me a convincing reason why I see True in the
>>> following
>>> session?
>>>
>>> sage: z = ZZ(2)
>>> sage: parent(z)
>>> Integer Ring
>>> sage: q = Mod(2, 7)
>>> sage: parent(q)
>>> Ring of integers modulo 7
>>> sage: z == q
>>> True
>>>
>>> This is related to...
>>> http://sage.math.washington.edu/home/mhansen/sage/devel/sage/doc/
>>> output/html/en/developer/coding_in_python.html#the-hash-special-
>>> method
>>>
>>> Ralf
>>>
>>
>>
>>
>
> >
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