64.4 IsFiniteDeterministic for integer matrix groups

IsFiniteDeterministic( G )

The integer matrix group G is tested for finiteness, using a deterministic algorithm. In most cases, this seems to be less efficient than the Las Vegas IsFinite. However, the number of arithmetic steps of this algorithm does not depend on the size of the entries of G, which is not true of the Las Vegas version.

If G is finite, then a G-invariant positive definite quadratic form is stored in G.quadraticForm.

gap> a := [[1,1],[0,-1]];
[ [ 1, 1 ], [ 0, -1 ] ]
gap> G := Group(a);;
gap> IsFiniteDeterministic(G);
true
gap> B := G.quadraticForm;;
gap> B;
[ [ 1, 1/2 ], [ 1/2, 3/2 ] ]
gap> TransposedMat(a)*B*a;
[ [ 1, 1/2 ], [ 1/2, 3/2 ] ]

See also (IsFinite for rational matrix groups). Previous Up Top
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