Dear Piyush, Am 07.06.2011 um 02:56 schrieb Piyush garg:
> Dear GAP Forum, [...] > I have two more doubts : > ## How to get the matrices from the output generated by GeneratorsOfGroup > for the Special Linear Group; like for SL(2,17) : > s:=SL(2,17); > gens:=GeneratorsOfGroup(s); > [ [ [ Z(17), 0*Z(17)], [ 0*Z(17), Z(17)^15 ] ], > [ [ Z(17)^8, Z(17)^0], [Z(17)^8, 0*Z(17)] ] ] > > this is the output we are getting, now hwo to get the matrices from it which > can generate the whole set of SL(2,17) ?? (with the elements' values from 0 > to 16.) Note the output already does consist of two matrices which generate SL(2,17). However, based on what you say last, it seems you want matrices in a special presentation, identifying the field F_17 with certain residues in Z/17Z. A very simple way to do this is to use Display: gap> Display(gens[1]); 3 . . 6 gap> Display(gens[2]); 16 1 16 . But you seem to need a bit more: > > ## How can we store this output of matrices in a file and make use of > them in Matlab program ?? > like storing the matrices now generated in a 3d-array and then later using > them in Matlab. I don't know matlab very well, so I can't say what format for matrices it expects, but I can tell you how to convert eh list of matrices GAP gives you into a list of *integer* matrices, which, viewed modulo 17, generate SL(2,17). For a single element, the Int() function does the job: gap> Int(Z(17)); 3 To apply it to all coefficients of each generator you computed above, you could use for example this: gap> List(gens,g->List(g,row->List(row,Int))); [ [ [ 3, 0 ], [ 0, 6 ] ], [ [ 16, 1 ], [ 16, 0 ] ] ] This program iterates over all elements g in gens; for each of the g, it iterates over all rows; and for each element of a row, it calls the "Int" function. You could also write this with a loop, of course, and then adapt the output as you need. Finally, you can store things into a file in GAP by using the PrintTo and AppendTo functions. I suggest you look them up in the GAP reference manual. Cheers, Max _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
