Re: [sympy] Introduction + Galois Theory

[Aaron Meurer]

On Sat, Mar 3, 2018 at 12:56 PM, Alice Liu  wrote:

> Hi thank you for your reply! Yes this is for GSoC.
>
> There are general steps for calculating the Galois Group (I am using
> "Galois Theory" by Ian Stewart as my reference), involving the tower law
> and working out the the Q-automorphisms of K (K being the splitting field
> for the given polynomial). I am not too sure about that precise algorithms.
>
> For the tower law, I am not too sure if field extensions and its
> degree are implemented in SymPy? I am aware there is a algebraic field
> class in the polys module, that gives you Q(α) from Q. But is it worth
> implementing field extension Q(α)(β):Q(α) for example. Also I might need
> a bit of help with understanding the code (what is dtype?).
>
> And for example:
>
>> def from_QQ_gmpy(K1, a, K0):
>
> """Convert a GMPY ``mpq`` object to ``dtype``. """
>
> return K1(K1.dom.convert(a, K0))
>
> I don't quite understand this - it seems to do with rational fields.
>

The polys code is organized in layers. The bottommost layer, which you are
looking at, deals directly with the coefficient data types (called dtypes,
from numpy parlance). Here the function works specifically on gmpy data. If
gmpy is not installed, a different function (most likely from_QQ_python)
would be used. In these low level functions, K refers to the domain (the
ring). Here (as I understand it), a is an element of K0, and it is
converted to K1. K0 might be something like QQ and K1 something like QQ[x].

These low level functions are generally only where the polynomial
algorithms are written, because that is the fastest way. For the Galois
group project, I would focus on higher levels, working directly with the
Poly() or ring() objects. This is what is documented at
http://docs.sympy.org/latest/modules/polys/index.html.


> In GAP you mentioned, fields are generated as follows
>
> 58.1-3 Field
>> ‣ Field( z, ... )
>
> ( function )
>
> ‣ Field( [F, ]list )
>
> ( function )
>
> Field returns the smallest field K that contains all the elements z, ...,
> or the smallest field K that contains all elements in the list list. If
> no subfield F is given, K is constructed as a field over itself, i.e. the
> left acting domain of K is K. Called with a field F and a list list, Field 
> constructs
> the field generated by F and the elements in list, as a vector space over
> F.
>
> I am wondering if you could do similar thing in SymPy? Again I might need
> help understanding the field class in the polys module.
>

Look at the field() and ring() functions.


> 58.3-1 GaloisGroup
>> ‣ GaloisGroup( F )
>
> ( attribute )
>
> The *Galois group* of a field F is the group of all field automorphisms
> of F that fix the subfield K =LeftActingDomain( F ) pointwise.
> Note that the field extension F > K need *not* be a Galois extension.
> gap> g:= GaloisGroup( AsField( GF(2^2), GF(2^12) ) );;
> gap> Size( g ); IsCyclic( g );
> 6
> true
> gap> h:= GaloisGroup( CF(60) );;
> gap> Size( h ); IsAbelian( h );
> 16
> true
>
> Then they used this for the Galois group, not sure if it can tell you the
> abstract structure of the whole group, or just test for properties. (and I
> am not sure I understand how to tell what K is in this context?)
>
> Also I am not too sure if automorphisms are implemented in SymPy? (I am
> aware that group isomorphism is yet to be implemented in SymPy?)
>
> The correspondence is between the subgroups of the Galois Group and the
> intermediate fields of K:L, so if you draw a lattice diagram the diagram
> looks the same. I think this might be too difficult to implement.
>

I don't know the answers to the group theory module questions. Someone else
will need to comment. I recommend going to
https://gitter.im/sympy/GroupTheory, which is the gitter group for last
year's group theory GSoC project, and asking there. It may also be helpful
to look at the report for that project (
https://github.com/sympy/sympy/wiki/GSoC-2017-Report-Valeriia-Gladkova:-Group-Theory)
to get an idea of the current state of the group theory module.

Aaron Meurer


>
> Thank you!
>
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Re: [sympy] GSOC Continuum mechanics 2D beam solving system

[Jason Moore]

Subash,

These all sound like great ideas! Looking forward to the proposal.

Jason

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On Thu, Mar 8, 2018 at 6:34 AM, SUBHASH SAURABH  wrote:

> I have gone through the current continuum mechanics package and I think
> the following can be implemented in this summer.
>
> 1. Improve the beam module so that it can solve for indeterminate beams.
> 2. Implement plotting of shear_force, bending_moment, slope and deflection.
> 3. Implement CrossSection class that can calculate second moment using the
> given cross-section.
> 4. Implement a JointBeam class that can join multiple beams and then the
> entire system can be solved.
> 5. Implement a function that gives the stress and strain at any given
> location (in 2D).
> 6. Implement a 3DBeam class that can solve a beam in 3D and can give the
> stress and strain any arbitrary point.
>
> I will start working on the formal proposal from Monday.
> Jason it will be great if you can suggest some other features that I have
> missed.
>
>
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Re: [sympy] GSoC 2018

[Jason Moore]

Rohit,

You can get started here:
https://github.com/sympy/sympy/wiki/GSoC-2018-Student-Instructions

Jason

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On Tue, Mar 6, 2018 at 6:44 AM, ROHIT SHARMA 
wrote:

> Hi,
>
> My name is Rohit Sharma. I am a student of Computer Science and
> Engineering at IIT Gandhinagar
>
> I am willing to join GSoC 2018 program and interested in SymPy
> organization.
>
> I know Python programming language and Git & GitHub.I am interested in the
> field of mathematics, especially in combinatorics, probability and number
> theory.
>
> I am want to contribute to open source. Can you please tell me How to get
> started?
>
> Thanks.
>
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Re: [sympy] GSoC 2018 - introduction

[Jason Moore]

Tabichou,

Welcome. You should get started here:
https://github.com/sympy/sympy/wiki/GSoC-2018-Student-Instructions.

Jason

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On Tue, Mar 6, 2018 at 10:06 PM, tabichou brian 
wrote:

> Hello,
>
>
> My name is Tabicho Affangha Brian. I am a  second year student of Computer
> Engineering in the  faculty of engineering and Technology, university of
> Buea, Cameroon.
>
>
> I am interested in partaking in GSoC 2018 and enthusiastic about the SymPy
> project.
>
> I know the basics of python 3 and have  worked  with PyQt5 to carry out a
> few personal projects.I got to know of the SymPy organization from the GSoC
> program and  I am still trying to understand  SymPy itself.
>
> I have a great passion for mathematics and have taken courses in Iinear
> Algebra and mathematical analysis.
> I am relatively new to open source and working with github but want to
> contribute to it. How to get started?
>
>
> Thanks.
>
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Re: [sympy] Re: Regarding Pull Request

[Jason Moore]

Yes, you should make a pull request from your repository to sympy's
repository.

moorepants.info
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On Wed, Mar 7, 2018 at 5:21 AM,  wrote:

> Firstly i tried to push directly to sympy, then i understood about
> permission and then I pushed to my account and created a pull request, now
> would it have been a pull request on sympy repository?
>
>
> On Sunday, March 4, 2018 at 12:09:29 AM UTC+5:30, Amit Kumar wrote:
>>
>> What's the error message you're getting and where?
>>
>> -
>> Amit
>>
>> On Saturday, March 3, 2018 at 5:32:30 AM UTC, aaris...@iiitd.ac.in wrote:
>>>
>>> I am unable to make a pull request for an issue to which already a pull
>>> request has been made by someone else.What could be the issue?Waiting for
>>> an early reply.
>>>
>> --
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Re: [sympy] GSOC 2018 - Intro

[Jason Moore]

Koneru,

Welcome, you can get started here:
https://github.com/sympy/sympy/wiki/GSoC-2018-Student-Instructions

Jason

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On Wed, Mar 7, 2018 at 11:51 AM, koneru nikhil 
wrote:

> Hi everyone, Myself K.Nkhil.I am studying Computer Science and Engineering
> at Sathyabama University, Chennai.I know Python programming from past 2
> years and I developed 6 projects in python which includes machine learning,
> offline web apps, few games.I would like to contribute to SymPy with my
> skills.
>
>
> Thank You
>
>
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Re: [sympy] GSOC 2018 Introduction.

[Jason Moore]

Udit,

Welcome, you can find out how to get started here:
https://github.com/sympy/sympy/wiki/GSoC-2018-Student-Instructions

Jason

moorepants.info
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On Wed, Mar 7, 2018 at 5:35 AM, udit gera  wrote:

> Greetings,
>
> My name is Udit and i am a junior at Indraprastha University, Delhi.
>
> I am interested in contributing to the "Lcapy Project" of the SymPy
> organisation. I have past experience of internships, hackathons and some
> projects.
>
> I do not have any past experience of contribution to open source
> organisations, but i want to be a part of this project and contribute
> specifically to the "Lcapy Projrect".
>
> Thank You.
>
> Regards,
>
> Udit Gera.
>
>
>
>
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Re: [sympy] GSOC Continuum mechanics 2D beam solving system

[SUBHASH SAURABH]

I have gone through the current continuum mechanics package and I think the 
following can be implemented in this summer.

1. Improve the beam module so that it can solve for indeterminate beams.
2. Implement plotting of shear_force, bending_moment, slope and deflection.
3. Implement CrossSection class that can calculate second moment using the 
given cross-section.
4. Implement a JointBeam class that can join multiple beams and then the 
entire system can be solved.
5. Implement a function that gives the stress and strain at any given 
location (in 2D).
6. Implement a 3DBeam class that can solve a beam in 3D and can give the 
stress and strain any arbitrary point.

I will start working on the formal proposal from Monday. 
Jason it will be great if you can suggest some other features that I have 
missed.


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