73.102 WhiteheadMonoidTable

WhiteheadMonoidTable( X )

The derivations of X form a monoid with the first derivation as identity. This function applies CompositeDerivation to all pairs of derivations and produces the multiplication table as a list of lists. A field .monoidTable is added to D. In our example there are 9 derivations and the three irregular ones, numbers 7,8,9, are all left zeroes.

    gap> WMT := WhiteheadMonoidTable( XSC );; PrintList(WMT );
    [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ]
    [ 2, 3, 1, 5, 6, 4, 9, 7, 8 ]
    [ 3, 1, 2, 6, 4, 5, 8, 9, 7 ]
    [ 4, 6, 5, 1, 3, 2, 7, 9, 8 ]
    [ 5, 4, 6, 2, 1, 3, 9, 8, 7 ]
    [ 6, 5, 4, 3, 2, 1, 8, 7, 9 ]
    [ 7, 7, 7, 7, 7, 7, 7, 7, 7 ]
    [ 8, 8, 8, 8, 8, 8, 8, 8, 8 ]
    [ 9, 9, 9, 9, 9, 9, 9, 9, 9 ]  

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GAP 3.4.4
April 1997