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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