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25. Miscellaneous

### 25. 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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