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13 Interaction with HAP
 13.1 Calling HAP functions

13 Interaction with HAP

This chapter describes functions which allow functions in the package HAP to be called from XMod.

13.1 Calling HAP functions

In HAP a cat^1-group is called a CatOneGroup and the traditional terms source and target are used for the TailMap and HeadMap. A CatOneGroup is a record C with fields C!.sourceMap and C!.targetMap.

13.1-1 SmallCat1Group
‣ SmallCat1Group( n, i, j )( operation )

This operation calls the HAP function SmallCatOneGroup(n,i,j) which returns a CatOneGroup from the HAP database. This is then converted into an XMod cat^1-group. Note that the numbering is not the same as that used by the XMod operation Cat1Select. In the example C12 is the converted form of H12.


gap> H12 := SmallCatOneGroup( 12, 4, 3 );
Cat-1-group with underlying group Group( [ f1, f2, f3 ] ) . 
gap> C12 := SmallCat1Group( 12, 4, 3 );
[Group( [ f1, f2, f3 ] )=>Group( [ f1, f2, <identity> of ... ] )]

13.1-2 CatOneGroupToXMod
‣ CatOneGroupToXMod( C )( operation )
‣ Cat1GroupToHAP( C )( operation )

These two functions convert between the two alternative implementations.


gap> C12 := CatOneGroupToXMod( H12 );    
[Group( [ f1, f2, f3 ] )=>Group( [ f1, f2, <identity> of ... ] )]
gap> C18 := Cat1Select( 18, 4, 3 );
[(C3 x C3) : C2=>Group( [ f1, <identity> of ..., f3 ] )]
gap> H18 := Cat1GroupToHAP( C18 ); 
Cat-1-group with underlying group (C3 x C3) : C2 . 

13.1-3 IdCat1Group
‣ IdCat1Group( C )( operation )

This function calls the HAP function IdCatOneGroup on a cat^1-group C. This returns [n,i,j] if the cat^1-group is the j-th structure on the SmallGroup(n,i).


gap> IdCatOneGroup( H18 ); 
[ 18, 4, 4 ]
gap> IdCat1Group( C18 ); 
[ 18, 4, 4 ]

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