Marshall Hampton wrote:
>> I too have founds bugs by reading code that I've written - usually,
>> very
>> early on in the development process.  Note that I'm talking in the
>> context
>> of result verification, however.  That is, when I publish a paper
>> that
>> depends on computations, it is incumbent upon me to verify those
>> computations.  I'm saying that I don't think that reading source code
>> at that point is particularly necessary or useful.
>>
>> Mark
> 
> Really?  I find that very surprising.  While it was not the primary
> reason that I became interested in Sage, the ability to examine the
> source code for verification purposes was a major attraction.


But reading the source still doesn't get around bugs in a compiler, bugs 
in supporting libraries, etc.  Mark, if I understand you correctly, you 
are saying that a person:

1. uses software to generate a list of results, and then
2. checks these results by hand or in some way that doesn't use a computer.

Step 2 is to avoid (or at least drastically cut down the chance of) 
errors due to any issues with a particular computation system.  I agree 
that this should be done for published results to the extent possible 
(or reasonable), and that results that only rely on computational 
results (without independent verification) should be flagged as such.  I 
also agree that being able to read the source code for doing step 2 is 
not necessary, *unless* your method of verification is to trace through 
the program by hand.

Of course, I'm sure there are many results in many fields that would be 
practically impossible to independently verify in any reasonable amount 
of time.  I suppose those people at least verify that they get the same 
results with completely different systems (e.g., Sage and Mathematica 
and Magma).  Of course, since Sage interfaces with a number of different 
systems, it can help with this.

Jason


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