On 6/7/07, David Harvey <[EMAIL PROTECTED]> wrote:
> > I agree too, though I think is_prime should remain provably correct.
>
> I disagree. I think is_prime should have the same option available,
> and the default should be probabilistic.
>
> The idea of these probabilistic tests is supposed to be that the
> probability of error is far less than the probability of error in
> your hardware (bounded uniformly, regardless of the input). Whether
> or not you are searching for the *next* prime or testing a *specific*
> value to be prime shouldn't affect your choice of algorithm. In the
> majority of applications the probabilistic test is the one a user
> would want, given the speed difference.
No. Absolutely throughout SAGE I have in every possible case made
the choice proof=True the default, and here the intension for is_prime
is that proof=True be the default. I'm am deeply opposed to
having proof=False the default for any SAGE functions. However,
one of the SAGE Days 4 coding sprint projects is to implement an
easy-to-use global function "proof":
def proof(on=True):
"""
proof(True) -- turns proof on globally by default
proof(False) -- turns proof off globally by default
"""
The real work here is to retrofit every function in sage that has a proof=
option to now say "proof='default'" by default, which will then respect
the choice made by the proof command above. People could put proof(False)
in their init.sage if they are applied mathematicians... If you're claiming
a result for a paper, you definitely remark that you ran the computation
in SAGE after typing "proof(True)".
I am not going to argue with David Harvey and others about specifically
whether the function is_prime should have proof=True or False by default.
I think the decision about the proof parameters for algorithms should
be a global decision -- i.e., have the default always be true or always be
false. In PARI, e.g., the default is always false. In MAGMA it is always
True (at least that's the goal).
This uniformity should be throughout the system and should only be
invalidated when the function name specifically indicates it. E.g,. we should
add
is_probable_prime
and that would always have proof=False (it wouldn't even have a proof
parameter).
William
-- William
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to sage-devel@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/
-~----------~----~----~----~------~----~------~--~---
