othergroups.ijs

NB. Permutation representations of various
NB. groups including the Quaternion group.
NB. @author Jon Hough
NB. @since 14 July 2014



NB. Construction is 8x8 array of permutations
NB. Q8 =: 8 8 $ 0 1 2 3 4 5 6 7 
NB. 	      1 0 3 2 5 4 7 6 
NB. 	      2 3 1 0 6 7 5 4 
NB. 	      3 2 0 1 7 6 4 5 
NB. 	      4 5 7 6 1 0 2 3
NB. 	      5 4 6 7 0 1 3 2
NB.             6 7 4 5 3 2 1 0
NB.             7 6 5 4 2 3 0 1
Q8 =: 8 8 $ 0 1 2 3 4 5 6 7 1 0 3 2 5 4 7 6 2 3 1 0 6 7 5 4 3 2 0 1 7 6 4 5 4 5 7 6 1 0 2 3 5 4 6 7 0 1 3 2 6 7 4 5 3 2 1 0 7 6 5 4 2 3 0 1


NB. Klein 4 group V4, isomorphic to C2xC2
NB. Group can also be constructed by calling
NB. derived_subgroup Alt 4
NB. V4 = 
NB. 0 1 2 3
NB. 3 2 1 0
NB. 1 0 3 2
NB. 2 3 0 1
V4 =: 4 4 $ 0 1 2 3, 3 2 1 0, 1 0 3 2, 2 3 0 1

NB. Returns true if the set of permutations
NB. is isomorphic to the group V4 (=C2xC2)
IsV4Isomorphic =: monad define
grp =: y
if. 4 = # grp do.
-. 4 e. order grp
else. 0 end. 
)