On Fri, Feb 16, 2018 at 9:08 AM, Alice Liu <[email protected]> wrote:
> Hi my name is Alice Liu, I am a third year Maths student at UCL.
>
> I am interested in implementing computation of Galois groups for a given
> polynomial, I am wondering if this is enough material for a stand-alone
> project?
>
I'm not familiar with the algorithms required for this, but I think it
should be enough material (you didn't mention it but I'm assuming this is
for GSoC).
Do you know what references you would use to implement this? If you don't
know yet, I would start by looking at what algorithms GAP uses.
>
> Also is the desired computation just for the Galois group of the splitting
> field of the given polynomial over [image: \mathbb {Q}]; or a more
> abstract and more general approach should be taken? Also do I need to aim
> for writing codes for the Galois correspondence of associated intermediate
> fields?
>
I would definitely just focus on Q for starters, but it would be nice to
design the API of the module so that it could be generalized if desired.
SymPy already has a delineation of different fields in the polys module, so
this shouldn't be hard. Although if a given algorithm extends nicely to
other fields it would make sense to support them all from the start.
Regarding the correspondence, I don't know. I suppose it depends if that
falls out nicely from the algorithm or not. Another question: does the
correspondence help to compute the roots in closed form, for the instances
where the Galois group is solvable? I was never clear if knowing the Galois
group helps you here or not.
>
> Also shall I aim to write a patch for the Combinatorics module or any
> patch I write would suffice?
>
Technically the rules require any patch anywhere, but I would recommend
making a patch to the code that you would be modifying for the project if
you can. This is better because
1. a more technically complicated patch will shine better on you than a
simple one, and
2. if you are accepted, it is code you would be modifying anyway. So it's
good to get a head start on modifying that code.
With that being said, don't be afraid to start somewhere simpler if you
still need to get your feet wet.
Aaron Meurer
> Thank you!
>
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