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 ]
GAP 3.4.4