On 23 October 2016 at 08:05, Ralf Stephan <[email protected]> wrote:
> On Saturday, October 22, 2016 at 6:28:58 PM UTC+2, vdelecroix wrote:
>>
>> ... The behavior of any operation in Sage is that
>> the parent of op(a, b) should only depend on the operator op,
>> parent(a) and parent(b). Powers are a bit special but not enough to
>> use conversion instead of coercion.
>
>
> Reference, please? This seems quite important but I cannot find
> it in the developer manual.

http://doc.sagemath.org/html/en/reference/coercion/index.html

But as Jeroen said, powers are not part of the coercion model since
when you do pow(a, b) you do not want a and b to have the same parent
in general. However the following situations involve coercions

sage: 2 ** 3.4
10.5560632861832
sage: 2.3 ** 3
12.1670000000000
sage: R = RealField(256)
sage: R(1) ** 2.3
1.000000000000000000000000000000000000000000000000000000000000000000000000000
sage: 1 ** R(2.3)
1.000000000000000000000000000000000000000000000000000000000000000000000000000

In general, pow(a, b) should only depend on parent(a) and parent(b)
and not the actual values of a and b. This is how behave all
arithmetic operations.

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