I have two questions:
1. Given elements g1,...,gm in the symmetric group Sn on n letters,
let G:=Group(g1,...,gm). Can one use GRAPE to construct the Cayley
graph for G relative to the g1,...,gm? (Ie, the vertices are labeled
by the elements of G and two vertices are connected by an edge (I
don't care about directions) if and only if one is g.i times the
other for some 1 <= i <= m.)
2. I have tried using the share package AbStab.g to ``solve'' the
masterball, a Rubik's cube-like puzzle. (AbStab.g is a GAP share
package.) I've implemented the masterball in MAPLE for the
purpose of testing out moves, etc. The problem is that sometimes
the AbStab.g ``solution'' works in MAPLE and sometimes it doesn't.
My question: Has anyone tested AbStab.g out on the Rubik's cube
and checked their result on the cube or a computer simulation of the
cube? Basically, I'm wondering if the problem is with me, GAP, or MAPLE.
Also, I'm interested in the mathematics behind the AbStab.g
package, so any references would be appreciated.
- David Joyner, email@example.com