Re: too many special linear matrices

*To*: mathgroup at smc.vnet.net*Subject*: [mg68830] Re: too many special linear matrices*From*: Roger Bagula <rlbagula at sbcglobal.net>*Date*: Sun, 20 Aug 2006 04:43:52 -0400 (EDT)*References*: <200608160736.DAA06175@smc.vnet.net> <CE14B3F1-9562-4363-9D03-D37E82CF28FB@mimuw.edu.pl> <ec1amo$os1$1@smc.vnet.net> <200608180712.DAA02032@smc.vnet.net> <ec64qm$1bp$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Andrzej Kozlowski wrote: >On 18 Aug 2006, at 09:12, Roger Bagula wrote: > > > >>Andrzej Kozlowski wrote: >> >> >> >>>The code below will produce the list of elements of SL[n,p] (as long >>>as n and p are not too large): >>> >>>SL[n_, p_] := Module[{vars = >>> Table[Unique[ >>> a], {n^2}], iters, mat}, iters = Map[{#, 0, p - 1} &, vars]; >>>mat = >>> Partition[vars, n]; Reap[ >>> Do[If[Det[mat, >>> Modulus -> p] == 1, Sow[mat], Continue[]], Evaluate[Sequence @@ >>> iters]]][[2, 1]]] >>> >>> >>>For n=2 it gives the lengths: >>> >>> >>>Table[Length[SL[2,Prime[i]]],{i,1,7}] >>> >>> >>>{6,24,120,336,1320,2184,4896} >>> >>>which agree with the formula I sent earlier: >>> >>>In[16]:= >>>Table[f[2,Prime[i]],{i,1,7}] >>> >>>Out[16]= >>>{6,24,120,336,1320,2184,4896} >>> >>>Andrzej Kozlowski >>> >>> >>> >>> >>> >>> >>Andrzej Kozlowski, >>You give the correct anwers in this post, but >>your code doesn't run in my 5.1 version. >>Roger Bagula >> >> >> > >If really so, then it is very strange because my version is: > > >$Version > >5.1 for Mac OS X (October 25, 2004) > > >and in my case the code does run, .e.g. > > >SL[2,2] > > >{{{0, 1}, {1, 0}}, {{0, 1}, {1, 1}}, {{1, 0}, {0, 1}}, > {{1, 0}, {1, 1}}, {{1, 1}, {0, 1}}, {{1, 1}, {1, 0}}} > > >Length[%] > >6 > >Andrzej Kozlowski > > > Maybe if you sent me the working notebook by email?

**References**:**too many special linear matrices***From:*Roger Bagula <rlbagula@sbcglobal.net>

**Re: too many special linear matrices***From:*Roger Bagula <rlbagula@sbcglobal.net>