General Functions

Some of the functions provided by &HAPprime; are not specifically aimed at homological algebra or extending the &HAP; package. The functions in this chapter, which are used internally by &HAPprime; extend some of the standard &GAP; functions and datatypes.

Matrices

For details of the standard &GAP; vector and matrix functions, see and in the &GAP; tutorial and reference manuals. &HAPprime; provides improved versions of a couple of standard matrix operations, and two small helper functions.

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Example: matrices and vector spaces

&GAP; uses rows of a matrix to represent basis vectors for a vector space. In this example we have two matrics U and V that we suspect represent the same subspace. Using we can see that V lies in U, but shows that they are the same subspace, as is confirmed by having identical sums and intersections. gap> U := [[1,2,3],[4,5,6]];; gap> V := [[3,3,3],[5,7,9]];; gap> SolutionMat(U, V); [ [ -1, 1 ], [ 1, 1 ] ] gap> IsSameSubspace(U, V); true gap> SumIntersectionMatDestructive(U, V); [ [ [ 1, 2, 3 ], [ 0, 1, 2 ] ], [ [ 0, 1, 2 ], [ 1, 0, -1 ] ] ] gap> IsSameSubspace(last[1], last[2]); true gap> PrintDimensionsMat(V); "2x3"
Groups

Small groups in &GAP; can be indexed by their small groups library number . An alternative indexing scheme, the Hall-Senior number, is used by Jon Carlson to publish his cohomology ring calculations at http://www.math.uga.edu/~lvalero/cohointro.html. To allow comparison with these results, we provide a function that converts from the &GAP; small groups library numbers to Hall-Senior number for the groups of order 8, 16, 32 and 64.

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