On 28/03/18 10:33, Ralf Stephan wrote:
Ask yourself, are these arguments you give for current is_prime(x)
behaviour not just the inertia of your thinking.
Wolfram tells me plainly "1/3 (2^23 + 1) is a prime number"---no
ambiguity, no attempt to show a glimpse of algebraic truth.
Pari gives
? isprime((2^23+1)/3)
%1 = 1
Giac:
>> is_prime((2^23+1)/3)
1
SymPy however:
In [7]: isprime((2**23+1)/3)
Out[7]: False
But then it's clear that the value is not integer:
In [8]: (2**23+1)/3
Out[8]: 2796203.0
Why not improve mathematics? Why not define the primality term you apply
in the element is_prime() as having a different name than "prime"? Why
not introduce 123/1 as notation to avoid ambiguities in mathematics? I'm
quite astonished that mathematicians allow these fuzziness in their
language, it is unusual.
The documentation of RingElement.is_prime [1], which most people will
never read, does give the example of fields, where an element is never
prime.
I am not sure what will be the impact of changing the global is_prime
function (I used it for rings other than ZZ), but updating its
documentation [2] not to say "Return True if n is a prime *number*", and
saying something about rings which are not the integers, is surely
better than the current situation.
Regarding SymPy, I think this is something more general to Python. Even
unrelated to mathematics, if one wants for example to iterate over the
first half of some list, they might use range(n/2) where n is an integer
which raises:
TypeError: range() integer end argument expected, got float.
In such scenarios, the programmer will soon learn about floor division.
The difference with is_prime is that a non-integer is expected...
Regards,
TB
[1]
https://doc.sagemath.org/html/en/reference/structure/sage/structure/element.html#sage.structure.element.RingElement.is_prime
[2]
https://doc.sagemath.org/html/en/reference/rings_standard/sage/arith/misc.html#sage.arith.misc.is_prime
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