[Python-ideas] Add the imath module

[Chris Angelico]

On Fri, Jul 13, 2018 at 2:58 PM, Tim Peters <tim.peters at gmail.com> wrote:
> [Chris Angelico, on "probable prime" testers]
>>
>> You can say that about algorithms easily enough. My point is that this
>> ought to be a constraint on the function - implementations may choose
>> other algorithms, but they MUST follow one pattern or the other,
>> meaning that a Python script can depend on it without knowing the
>> implementation. Like guaranteeing that list.sort() is stable without
>> stipulating the actual sort algo used.
>
>
> I agree!  Don't worry about it - if this module gets added, I'll make sure
> of it.  My own "probable prime" function starts like so:
>
> def pp(n, k=10):
>     """
>     Return True iff n is a probable prime, using k Miller-Rabin tests.
>
>     When False, n is definitely composite.
>     """
>
> In the context of algorithmic number theory, "no false negatives" is implied
> by that context, but it should be spelled out anyway.  A "probable prime",
> by definition, is an integer that satisfies some property that _all_ primes
> satisfy, but that some composites may satisfy too.  The variation among
> probable prime algorithms is in which specific property(ies) they test for.
>
> For example:
>
> def pp1(n):
>     return True
>
> meets the promise, but is useless ;-)
>
> def pp2(n):
>     return  n % 3 != 0 or n == 3
>
> is slightly less useless.
>
> But
>
> def pp3(n):
>     return n % 3 != 0
>
> would be incorrect, because pp3(3) returns False - `n % 3 != 0` is not a
> property that all primes satisfy.
>

Thank you. Great explanation. Much appreciated!

ChrisA