64.3 InvariantLattice for rational matrix groups

InvariantLattice( G )

This function returns a lattice L (given by a basis) which is G-invariant. That is, for any A in G, L A L^{-1} is an integer matrix.

L is also stored in G.invariantLattice, and the conjugate group L <G> L^{-1} is stored in G.integerMatrixGroup.

This function finds an L unless G contains elements of non-integer trace (in which case no such L exists, and false is returned).

gap> a := [[1,1/2],[0,-1]];; G := Group(a);;
gap> L := InvariantLattice(G);;
gap> L*a*L^(-1);
[ [ 1, 1 ], [ 0, -1 ] ]

This function is Las Vegas: it is randomized, but the randomization only affects the running time, not the correctness of the output. Previous Up Top Next
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