TableOfMarks( str )
If the argument str given to TableOfMarks
is a string then
The Library of Tables of Marks) for a table with name str. If such a
table is found then TableOfMarks
will return a copy of that table.
Otherwise TableOfMarks
will return false
.
gap> a5 := TableOfMarks( "A5" ); rec( derivedSubgroup := 9, normalizer := [ 9, 4, 6, 8, 7, 6, 7, 8, 9 ], nrSubs := [ [ 1 ], [ 1, 1 ], [ 1, 1 ], [ 1, 3, 1 ], [ 1, 1 ], [ 1, 3, 1, 1 ], [ 1, 5, 1, 1 ], [ 1, 3, 4, 1, 1 ], [ 1, 15, 10, 5, 6, 10, 6, 5, 1 ] ], order := [ 1, 2, 3, 4, 5, 6, 10, 12, 60 ], subs := [ [ 1 ], [ 1, 2 ], [ 1, 3 ], [ 1, 2, 4 ], [ 1, 5 ], [ 1, 2, 3, 6 ], [ 1, 2, 5, 7 ], [ 1, 2, 3, 4, 8 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ] ], length := [ 1, 15, 10, 5, 6, 10, 6, 5, 1 ] ) gap> TableOfMarks( "A10" ); #W TableOfMarks: no table of marks A10 found. false
TableOfMarks( grp )
If TableOfMarks
is called with a group grp as its argument then the
table of marks of that group will be computed and returned in the
compressed format. The computation of the table of marks requires the
knowledge of the complete subgroup lattice of the group grp. If the
lattice is not yet known then it will be constructed (see Lattice).
This may take a while if the group grp is large.
Moreover, as the Lattice
command is involved the applicability of
TableOfMarks
underlies the same restrictions with respect to the
soluble residuum of grp as described in section Lattice. The result
of TableOfMarks
is assigned to the component tableOfMarks
of the
group record grp, so that the next call to TableOfMarks
with the same
argument can just return this component tableOfMarks
.
Warning: Note that TableOfMarks
has changed with the release
GAP 3.2. It now returns the table of marks in compressed form.
However, you can apply the MatTom
command (see MatTom) to convert it
into the square matrix which was returned by TableOfMarks
in GAP
version 3.1.
gap> alt5 := AlternatingPermGroup( 5 );; gap> TableOfMarks( alt5 ); rec( subs := [ [ 1 ], [ 1, 2 ], [ 1, 3 ], [ 1, 2, 4 ], [ 1, 5 ], [ 1, 2, 3, 6 ], [ 1, 2, 5, 7 ], [ 1, 2, 3, 4, 8 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ] ], marks := [ [ 60 ], [ 30, 2 ], [ 20, 2 ], [ 15, 3, 3 ], [ 12, 2 ], [ 10, 2, 1, 1 ], [ 6, 2, 1, 1 ], [ 5, 1, 2, 1, 1 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ] ) gap> last = alt5.tableOfMarks; true
For a pretty print display of a table of marks see DisplayTom.
GAP 3.4.4