@Miguel Thanks for replying
I guess you have done plenty of good work in group theory,So can you
suggest any good project for me in fields like Linear Algebra,Abstract
Algebra,Differential Equation,Real Analysis,Optimization.
On Saturday, March 1, 2014 1:50:15 AM UTC+5:30, Vishnu Agarwal wrote:
>
> Hi,
> I am a student of Third year in IIT Roorkee currently pursuing
> Integrated MSc. in Applied Mathematics.I want to add my idea that is not
> listed in your idea list but still want to discuss.I want to build "Group
> theory Module "for Sage as a part of Google Summer of Code 2014.
>
> *My inputs for this idea are:-*
>
> Finite groups can be handled using array, it can be implemented in such a
> way that it supports abstract initialization and binary operator abstract
> initialization. For example it should understand set theoretic notation.
>
> A=\{ x:x\in \mathbb{N},1 \leq x \leq 502\} (latex format )
>
> a.b=ab\hspace{1 mm}mod \hspace{1 mm} n\hspace{1 mm} \forall a,b\in A
>
>
> The elements of a finite group are elements of an array.
>
> Handling special cases of infinite groups.
>
> Defining group by generator:- let M be a set of all elements present in
> generator group,update the set M:=M\cup_{a\in M}(Ma \cup aM) stop when
> there is no change in M.But it is exponential in time so not feasible for
> large finite groups.
>
>
> And these are my more inputs in this idea
>
> Declaration of groups (. binary operator assignment) in abstract way i.e
> using symbols isgroup() function will return 1 if that set is a group under
> that specific operator.
>
> Isabelian () function will return 1 if group is abelian 0
> otherwise.Location of subgroups of a given order especially finding out Sylow
> subgroups,and from Cayley's theorem every finite group is isomorphic to a
> subgroup of permutation group so return_perm_iso function will return
> the subgroup of perm group isomorphic to the given group.This will useful
> for construction of Sylow subgroups. Inverse(element ) function will return
> the inverse of that element.,isNormal() subgroup will tell whether the
> subgroup is normal or not.
>
> Is_ Simple(group) will tell whether the group is simple or not.
>
>
> *Some functions relating to library*
>
> Commutative subgroup
>
> Center of a group
>
> left cosets and right cosets
>
> Product of two subgroups
>
> Intersection ,Union of two subgroups
>
>
> I am looking forward to work with your organization and very interested in
> this project.My knowledge in coureses like Abstract Algebra,Linear
> Algebra,Partial Differential Equation,Real Analysis will enhance energy in
> this project.
>
>
> @Prospective Mentor:-Please reply to this post so that I can discuss
> further regarding the topic.
>
> Regards
>
> Vishnu Agarwal
>
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