69.7 ModuleAction

ModuleAction( QUOT )

This function takes as input the output of a CallPCQA function call (see CallPCQA) or an ExtendPCQA function call (see ExtendPCQA). If the quotient G/[N,N] returned by the function call is polycyclic then ModuleAction computes the action of the polycyclic generators corresponding to G/N on the polycyclic generators of N/[N,N]. The result is returned as an array of matrices. Notice that the Smith normal form of G/[N,N] is returned by the function CallPCQA as part of the polycyclic presentation.

gap> ModuleAction(quot);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0 ],
    [ 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0 ],
    [ 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0 ], 
    [ 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0 ], 
    [ 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0 ], 
    [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1 ], 
    [ 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ], 
    [ 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0 ], 
    [ 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0 ], 
    [ 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], 
    [ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0 ] ], 
  [ [ -1, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0 ], 
    [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
    [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
    [ 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1 ], 
    [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
    [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
    [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], 
    [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
    [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
    [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], 
    [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ], 
  [ [ 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], 
    [ 0, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0 ], 
    [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
    [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
    [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], 
    [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], 
    [ 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1 ], 
    [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
    [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
    [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], 
    [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ] ] ]

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