42.3 Defining a Pcgs Yourself

constructs a pcgs for the elements family fam from the elements in the list pcs. The elements must lie in the family fam. PcgsByPcSequence(NC) will always create a new pcgs which is not induced by any other pcgs.

gap> fam := FamilyObj( (1,2) );; # the family of permutations
gap> p := PcgsByPcSequence( fam, [(1,2),(1,2,3)] );
[ (1,2), (1,2,3) ]
gap> RelativeOrders(p);
[ 2, 3 ]
gap> ExponentsOfPcElement( p, (1,3,2) );
[ 0, 2 ]

Note that the elementary operations for such a pcgs might be rather inefficient, since GAP has to use generic methods in this case. It might be helpful to supply the relative orders of the self-defined pcgs as well by SetRelativeOrders( pcgs, orders ). See also IsPrimeOrdersPcgs.

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