Hello Aaron, Thanks for your interest. I am giving some examples below:
*1. The following example computes the fourth integral cohomology of the Mathieu group M24:* gap> GroupCohomology(MathieuGroup(24),4); [ 4, 3 ] *2. Similarly the following example computes the second integral homology of the alternative group:* gap>G = AlternatingGroup(5) ; Alt( [ 1 .. 5 ] ) gap> GroupHomology(G,2); [2] *3. The following example print the character table of S_4* gap> g:= SymmetricGroup( 4 ); Sym( [ 1 .. 4 ] ) gap>Charactertable(g); *4. Some of the character table operations offered by GAP are taking direct product of character tables, character table of a quotient, finding scalar product of characters in the same character table etc. *Best, Aniket On Wed, Mar 24, 2021 at 1:18 PM Aaron Meurer <[email protected]> wrote: > Hi. > > Can you show an example of what this sort of thing looks like in GAP, > so we can get an idea of what it might look like in SymPy? > > Aaron Meurer > > On Tue, Mar 23, 2021 at 9:50 PM Aniket Joshi <[email protected]> > wrote: > > > > Hello, > > > > I have several ideas in computational group theory that seem doable. I > am wondering if these have been considered before and if they are in the > scope of GSoC for Sympy. I have worked with GAP and in particular used it > to compute cohomology groups and character tables. In general the goal > could be to implement several algorithms in the chapter of Holt's book on > representation theory, and cohomology groups(chapter 7). Following are some > ideas: > > > > 1. Computing first and second cohomology groups of finitely presented > groups over a finite field or the integers > > 2. Compute character tables of finite groups (using > Burnside-Dixon-Schneider algorithm) > > 3. Test irreducibility of given representation (using Meataxe algorithm) > > 4. Adding classes on finite groups based on the ATLAS database of finite > groups (http://brauer.maths.qmul.ac.uk/Atlas/v3/) > > > > Since any of these ideas don't appear on the GSoC ideas page, please > could you give me some feedback if they would be of general interest and > can be considered as part of a GSoC project. > > > > Best, > > Aniket > > > > -- > > 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 [email protected]. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/dea71c1f-ee84-4792-b00c-7c635c5f33fdn%40googlegroups.com > . > > -- > 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 [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAKgW%3D6KQfBzgQUP3bZw%2BAOaZDhyTaojPaYvsCrVjdbq0Ac4OLg%40mail.gmail.com > . > -- Aniket S Joshi 4th year B.S.-M.S. Physics Dual Degree Roll no. PH11B001 Department of Physics, IIT Madras -- 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CA%2B9_QKx6dCLAd1UWyYf_AMrmtB5UP9w-DbPBgbqMkF6TSpnQBg%40mail.gmail.com.
