On Sun, Mar 24, 2013 at 5:36 PM, Alan Bromborsky <abro...@verizon.net>wrote:
> On 03/24/2013 06:57 AM, David Joyner wrote: > >> On Sun, Mar 24, 2013 at 5:43 AM, Tarang Patel <tarangro...@gmail.com> >> wrote: >> >>> Hello, >>> I want to work for the idea of Group theory as a part of my >>> GSoC >>> 2013 project. I also satisfy the patch requirement for GSoC >>> https://github.com/sympy/**sympy/pull/1843<https://github.com/sympy/sympy/pull/1843> >>> I have gone through the combinatorics module containing some of the >>> implementations of group theory. The already implemented works of group >>> theory are symmetric groups, >>> alternating groups, dihedral groups, rubik cube, direct product of >>> groups, >>> abelian groups, permutation groups, polyhedron group. >>> >>> But still there are things that need to be implemented in >>> discrete >>> group and lie groups.I think it would be nice to have a module on Young >>> tableaux, >>> representations of the symmetric group,and their relation to irreducible >>> tensors in sympy. I want to implement it as a part of my GSoC project. I >>> >> >> Can you give more details on this idea? >> > Regarding the implementation of Young Tableaux module, I think we can implement things like : Given 'k' number of partitions. >>> k=4 >>> Y=YoungTableaux.young_partition(k) >>> Y >>> [[4],[3,1],[2,2],[2,1,1],[1,1,1,1]] >>> Yt=YoungTableaux.young_transpose([3,1]) >>> Yt >>> [2,1,1] >>> d=YoungTableaux.dimension([2,1,1]) >>> 3 Similarly, for a given k-box young diagram with given partition p, we can represent corresponding standard Young Tableaux by YoungTableaux(p). It will be somewhat difficult to implement. Also, Young Tableaux are useful for labeling irreps of various groups. (1) The k-box Young diagrams label all irreps of the corresponding symmetric group Sk. (2) The standard tableaux of k-box Young diagrams with no more than n rows label the irreps of GL(n). (3) The standard tableaux of k-box Young diagrams with no more than n - 1 rows label the irreps of SL(n). This is how I am thinking of implementing the module on Young Tableaux. Any suggestion or help would be really helpful. I know it seems somewhat vague at this stage but I will make it clear and concrete soon. >> >> have done a course on Group theory in my last semester. >>> I think this would be helpful for me to implement a module on Young >>> Tableaux and orthogonal groups. >>> ( >>> http://www.cns.gatech.edu/**GroupTheory/chapters/draft.pdf<http://www.cns.gatech.edu/GroupTheory/chapters/draft.pdf>). >>> >>> Also I think, I can implement things like Orthogonal groups, >>> Normal >>> subgroup, homomorphisms of groups, isomorphisms of groups in group >>> theory. >>> I want to know that are there any other things that needs to be >>> implemented >>> in group theory so that I start working on it ? >>> >>> Thanks, >>> Tarang Patel >>> >>> -- >>> You received this message because you are subscribed to the Google Groups >>> "sympy" group. >>> To unsubscribe from this group and stop receiving emails from it, send an >>> email to >>> sympy+unsubscribe@**googlegroups.com<sympy%2bunsubscr...@googlegroups.com> >>> . >>> To post to this group, send email to sympy@googlegroups.com. >>> Visit this group at >>> http://groups.google.com/**group/sympy?hl=en-US<http://groups.google.com/group/sympy?hl=en-US> >>> . >>> For more options, visit >>> https://groups.google.com/**groups/opt_out<https://groups.google.com/groups/opt_out> >>> . >>> >>> >>> You might find the attached paper of interest > > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to > sympy+unsubscribe@**googlegroups.com<sympy%2bunsubscr...@googlegroups.com> > . > To post to this group, send email to sympy@googlegroups.com. > Visit this group at > http://groups.google.com/**group/sympy?hl=en-US<http://groups.google.com/group/sympy?hl=en-US> > . > For more options, visit > https://groups.google.com/**groups/opt_out<https://groups.google.com/groups/opt_out> > . > > > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at http://groups.google.com/group/sympy?hl=en-US. For more options, visit https://groups.google.com/groups/opt_out.
