22. Miscellaneous

BigStepLCS(G,n)

Inputs a group G and a positive integer n. It returns a subseries G=L_1>L_2>... L_k=1 of the lower central series of G such that L_i/L_i+1 has order greater than n.

Compose(f,g)

Inputs two FpG-module homomorphisms f:M --> N and g:L --> M with Source(f)=Target(g) . It returns the composite homomorphism fg:L --> N .

This also applies to group homomorphisms f,g.

HAPcopyright()

This function provides details of HAP'S GNU public copyright licence.

IsLieAlgebraHomomorphism(f)

Inputs an object f and returns true if f is a homomorphism f:A --> B of Lie algebras (preserving the Lie bracket).

IsSuperperfect(G)

Inputs a group G and returns "true" if both the first and second integral homology of G is trivial. Otherwise, it returns "false".

MakeHAPManual()

This function creates the manual for HAP from an XML file.

PermToMatrixGroup(G,n)

Inputs a permutation group G and its degree n. Returns a bijective homomorphism f:G --> M where M is a group of permutation matrices.

SolutionsMatDestructive(M,B)

Inputs an m×n matrix M and a k×n matrix B over a field. It returns a k×m matrix S satisfying SM=B.

The function will leave matrix M unchanged but will probably change matrix B.

(This is a trivial rewrite of the standard GAP function SolutionMatDestructive(<mat>,<vec>) .)

TestHap()

This runs a representative sample of HAP functions and checks to see that they produce the correct output.


 





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