Importing variables non-deterministic?

[Antoon Pardon]

Op 20-08-13 07:48, Steven D'Aprano schreef:
> On Mon, 19 Aug 2013 22:34:00 +0200, Antoon Pardon wrote:
> 
>> Op 19-08-13 19:05, Steven D'Aprano schreef:
>>
>>
>>> I wish Python had stronger support for enforcing constantness, to whit,
>>> some way to say "you can't rebind or delete this name once it is
>>> bound". You can do it with attributes, by use of property, or in C
>>> extensions, but you cannot do it with top-level name bindings. It makes
>>> me terribly sad that you can do this:
>>>
>>> import math
>>> math.pi = 3.0
>>>
>>>
>>> although I can't decide whether I am less sad or more sad to see that
>>> the behaviour of math.sin and friends doesn't depend on math.pi.
>>
>> Why should you expect math.sin and friends be dependant on math.pi?
>> AfAIR the numerical algorithms for calulating sin and friends don't
>> depend on (the value of) pi. So there is no reason to suspect that
>> altering math.pi would have any effect on the results of these
>> functions.
> 
> 
> Of course they depend on pi. Or rather, they depend on the geometric 
> properties of circles, which are related to pi. If the ratio of the 
> circumference of a circle to its diameter was exactly 3, instead of 
> 3.1415..., then sine and cosine functions would be periodic with period 6 
> rather than τ = 2π.

Which is beside the point. The fact that nπ are the zeropoints of the
sin function doesn't imply in any way that you somehow need to work with
the value of π in order to calculate any result of the function.

Just as the function x^2 - 2 has -√2 and √2 as zeropoints, yet when
given a numerical value, you dont need (the value of) √2 in order to
get the result. So setting a variable like sqrt2 to whatever value
shouldn't lead us to suspect it would influence the zeropoints of
that function. Likewise with π and the calculation of sin.


> If you consider the implementation of sin and cos functions, they usually 
> reduce the argument modulo π to something in the first quadrant, and then 
> use symmetry to adjust the value. So changing the value of pi could, in 
> principle, change the implementation of sin, cos and tan.

Yes there is this aspect, which is a fair point.

-- 
Antoon Pardon