Re: Computing Galois groups

Hi Daniel,

thank you for your feedback.

Are you suggesting that I try those steps by myself or that I post the 
code with a quick explanation?

Because I already tried them: I went through the code and I already 
traced progress.

I know were (I think) it doesn't work and I also have examples of cases 
where it doesn't work. And cases where it works.

Fabio

Il 07/05/22 16:42, Daniel Herring ha scritto:
> Hi Fabio,
>
> I don't have the time or energy to do a proper review for you.
>
> That said, trying to explain an algorithm can be an effective way of 
> finding the flaws in it.  Start with the code and derive the purpose. 
> This often reveals an inconsistency with the original high-level 
> algorithm.
>
> Unfortunately, other bugs come from an incorrect understanding of the 
> tool you are trying to use, in this case Axiom.  These can require an 
> experienced developer to find, as you see what you expect, and they 
> see what the computer actually does.  Sometimes you can reduce this 
> issue by replacing binary operators with named functions (less parsing 
> mistakes). Other times you can do "the same thing" with a different 
> choice of functions or operators, and compare results.
>
> Do you have a simple example of when the algorithm does not work? 
> Tracing its progress step by step can help spot the bug.  This 
> approach doesn't prove the overall algorithm, but it does eliminate 
> one defect.
>
> Best wishes!
>
> -- Daniel
>
>
> On Sat, 7 May 2022, Fabio Stumbo wrote:
>
>> Hi,
>>
>> I am trying to compute some Galois groups with Axiom.
>>
>> A way is to go after the example given in section 8.13 of the manual 
>> which follows closely and implements the original definition by 
>> Galois of the Galois group.
>>
>> I am trying a different way: I would like to exploit a theorem by 
>> Kronecker which provides an easy algorithm to compute the Galois 
>> group of a given polynomial.
>>
>> I wrote the function which implements the algorithm and it works... 
>> sometimes. :(
>>
>> Which means that I have some problems.
>>
>> My question is: is there anybody that is willing to help me to fix it 
>> if I post the code?
>>
>> The code is not very long (about 40-50 lines) but it needs to be 
>> explained, so I am asking before to make the effort.
>>
>> TIA
>>
>> Fabio
>>
>>
>>