73.89 RegularDerivations

RegularDerivations( X [,"back" rm or "cat1"] )

By default, this function uses a backtrack search to find all the regular derivations of {cal X}. The result is stored in a derivations record. The alternative strategy, for which "cat1" option should be specified is to calculate the regular sections of the associated cat1-group first, and convert these to derivations.

    gap> regXSC := RegularDerivations( XSC );
    RegularDerivations record for crossed module [c3->s3],
    : 6 regular derivations, others not found.
    gap> PrintList( regXSC.genimageList );
    [ (), () ]
    [ (), ( 1, 2, 3)( 4, 6, 5) ]
    [ (), ( 1, 3, 2)( 4, 5, 6) ]
    [ ( 1, 3, 2)( 4, 5, 6), () ]
    [ ( 1, 3, 2)( 4, 5, 6), ( 1, 2, 3)( 4, 6, 5) ]
    [ ( 1, 3, 2)( 4, 5, 6), ( 1, 3, 2)( 4, 5, 6) ]
    gap> RecFields( regXSC );
    [ "areDerivations", "isReg", "isAll", "genimageList", "operations",
      "xmod", "generators", "regular" ]  

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