<Chapter><Heading> Miscellaneous</Heading> <Table Align="|l|" > <Row> <Item> <Index> BigStepLCS </Index> <C> BigStepLCS(G,n) </C> <P/> Inputs a group <M>G</M> and a positive integer <M>n</M>. It returns a subseries <M>G=L_1</M>&tgt;<M>L_2</M>&tgt;<M> \ldots L_k=1</M> of the lower central series of <M>G</M> such that <M>L_i/L_{i+1}</M> has order greater than <M>n</M>. </Item> </Row> <Row> <Item> <Index> Classify </Index> <C> Classify(L,Inv) </C> <P/> Inputs a list of objects <M>L</M> and a function <M>Inv</M> which computes an invariant of each object. It returns a list of lists which classifies the objects of <M>L</M> according to the invariant.. </Item> </Row> <Row> <Item> <Index> RefineClassification </Index> <C> RefineClassification(C,Inv) </C> <P/> Inputs a list <M>C:=Classify(L,OldInv)</M> and returns a refined classification according to the invariant <M>Inv</M>. </Item> </Row> <Row> <Item> <Index> Compose(f,g)</Index> <C> Compose(f,g) </C> <P/> Inputs two <M>FpG</M>-module homomorphisms <M> f:M \longrightarrow N</M> and <M>g:L \longrightarrow M</M> with <M>Source(f)=Target(g)</M> . It returns the composite homomorphism <M>fg:L \longrightarrow N</M> . <P/> This also applies to group homomorphisms <M>f,g</M>. </Item> </Row> <Row> <Item> <Index> HAPcopyright</Index> <C> HAPcopyright() </C> <P/> This function provides details of HAP'S GNU public copyright licence. </Item> </Row> <Row> <Item> <Index> IsLieAlgebraHomomorphism</Index> <C> IsLieAlgebraHomomorphism(f) </C> <P/> Inputs an object <M>f</M> and returns true if <M>f</M> is a homomorphism <M>f:A \longrightarrow B</M> of Lie algebras (preserving the Lie bracket). </Item> </Row> <Row> <Item> <Index> IsSuperperfect</Index> <C> IsSuperperfect(G) </C> <P/> Inputs a group <M>G</M> and returns "true" if both the first and second integral homology of <M>G</M> is trivial. Otherwise, it returns "false". </Item> </Row> <Row> <Item> <Index>MakeHAPManual</Index> <C>MakeHAPManual()</C> <P/> This function creates the manual for HAP from an XML file. </Item> </Row> <Row> <Item> <Index> PermToMatrixGroup </Index> <C> PermToMatrixGroup(G,n) </C> <P/> Inputs a permutation group <M>G</M> and its degree <M>n</M>. Returns a bijective homomorphism <M>f:G \longrightarrow M</M> where <M>M</M> is a group of permutation matrices. </Item> </Row> <Row> <Item> <Index> SolutionsMatDestructive</Index> <C> SolutionsMatDestructive(M,B) </C> <P/> Inputs an <M>m×n</M> matrix <M>M</M> and a <M>k×n</M> matrix <M>B</M> over a field. It returns a k×m matrix <M>S</M> satisfying <M>SM=B</M>. <P/> The function will leave matrix <M>M</M> unchanged but will probably change matrix <M>B</M>. <P/> (This is a trivial rewrite of the standard GAP function <M>SolutionMatDestructive(</M>&tlt;<M>mat</M>&tgt;,&tlt;<M>vec</M>&tgt;) .) </Item> </Row> <Row> <Item> <Index> TestHap</Index> <C> TestHap() </C> <P/> This runs a representative sample of HAP functions and checks to see that they produce the correct output. </Item> </Row> </Table> </Chapter>