Thanks. If anyone else is interested, this is what worked for me: sage:gap_console() gap>G:=SL(3,Integers); gap>GeneratorsOfGroup(G); [[0,1,0],[0,0,1][1,0,0]],[[0,1,0],[-1,0,0][0,0,1]],[[1,1,0],[0,1,0], [0,0,1]] %these can now be referred to as G.1, G.2, G.3 respectively gap>epi:=EpimorphismFromFreeGroup(G); [x1,x2,x3] -->[G.1,G.2,G.3] gap>PreImagesRepresentative(epi,[[0,-1,0],[-1,0,0],[0,0,-1]]); x1^2*x2*x1^2*x2^2
-Becky On Apr 9, 12:33 pm, "David Joyner" <[EMAIL PROTECTED]> wrote: > On Wed, Apr 9, 2008 at 12:08 PM, Becky <[EMAIL PROTECTED]> wrote: > > > Yes, I am looking for a finite presentation for SL_3(Z). I was able > > to get three generators from SAGE: > > sage: G=SL(3,ZZ) > > sage: G.gens() > > [ > > [0 1 0] > > [0 0 1] > > [1 0 0], > > [0 1 0] > > [-1 0 0] > > [0 0 1], > > [1 1 0] > > [0 1 0] > > [0 0 1]] > > > I have what I think is a different set of matrix generators, and I'd > > like to be able to write mine in terms of these. For example, what is > > the matrix > > [[0 -1 0][-1 0 0][0 0 -1]] in terms of the above? > > The work problem is in general unsolvable for infinite > groups,http://en.wikipedia.org/wiki/Word_problem_for_groups > No solution algorithm has been implemented in SAGE, except for > finite permutation groups. > Of course, there exist infinite groups with a solvable word problem > and GAP (included with SAGE) might have an algorithm for some of them. > (For example, possibly for polycyclic groups). Here's a link to the GAP > manual which might be a > start:http://www.gap-system.org/Manuals/doc/htm/ref/CHAP037.htm#I2 > > > > > Ideally, I'm looking for the analogue of SL_2(Z)=<S, T | S^4=1, > > (ST)^6=1> where S =[[0 -1][1 0]] and T=[[1 1][0 1]], but for SL_3(Z). > > Any help you can give me would be greatly appreciated. Thanks. > > -Becky > > > On Apr 7, 6:22 pm, "Mike Hansen" <[EMAIL PROTECTED]> wrote: > > > Hi Becky, > > > > Did you have a particular group in mind? > > > > --Mike > > > > On Mon, Apr 7, 2008 at 3:19 PM, Becky <[EMAIL PROTECTED]> wrote: > > > > > Is there a command for SAGE to write an element of a group in terms of > > > > the group's generators? > > > > -Becky- Hide quoted text - > > > > - Show quoted text -- Hide quoted text - > > - Show quoted text -- Hide quoted text - > > - Show quoted text - --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
