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### 29 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. Classify(L,Inv) Inputs a list of objects L and a function Inv which computes an invariant of each object. It returns a list of lists which classifies the objects of L according to the invariant.. RefineClassification(C,Inv) Inputs a list C:=Classify(L,OldInv) and returns a refined classification according to the invariant Inv. 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(,) .) LinearHomomorphismsPersistenceMat(L) Inputs a composable sequence L of vector space homomorphisms. It returns an integer matrix containing the dimensions of the images of the various composites. The sequence L is determined up to isomorphism by this matrix. NormalSeriesToQuotientHomomorphisms(L) Inputs an (increasing or decreasing) chain L of normal subgroups in some group G. This G is the largest group in the chain. It returns the sequence of composable group homomorphisms G/L[i] -> G/L[i+/-1]. TestHap() This runs a representative sample of HAP functions and checks to see that they produce the correct output.

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