  
  [1X28. Miscellaneous[0X
  
      | [10X BigStepLCS(G,n) [0X 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.                                                                                                                         | 
      | [10X Classify(L,Inv) [0X 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..                                                                                                          | 
      | [10X RefineClassification(C,Inv) [0X Inputs a list C:=Classify(L,OldInv) and returns a refined classification according to the invariant Inv.                                                                                                                                                                         | 
      | [10X Compose(f,g) [0X 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.                                                                                                         | 
      | [10X HAPcopyright() [0X This function provides details of HAP'S GNU public copyright licence.                                                                                                                                                                                                                         | 
      | [10X IsLieAlgebraHomomorphism(f) [0X Inputs an object f and returns true if f is a homomorphism f:A --> B of Lie algebras (preserving the Lie bracket).                                                                                                                                                               | 
      | [10X IsSuperperfect(G) [0X Inputs a group G and returns "true" if both the first and second integral homology of G is trivial. Otherwise, it returns "false".                                                                                                                                                         | 
      | [10XMakeHAPManual()[0X This function creates the manual for HAP from an XML file.                                                                                                                                                                                                                                     | 
      | [10X PermToMatrixGroup(G,n) [0X Inputs a permutation group G and its degree n. Returns a bijective homomorphism f:G --> M where M is a group of permutation matrices.                                                                                                                                                 | 
      | [10X SolutionsMatDestructive(M,B) [0X 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>) .) | 
      | [10X LinearHomomorphismsPersistenceMat(L) [0X 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.                                            | 
      | [10X NormalSeriesToQuotientHomomorphisms(L) [0X 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].                                                           | 
      | [10X TestHap() [0X This runs a representative sample of HAP functions and checks to see that they produce the correct output.                                                                                                                                                                                         | 
  
