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### 12 Interaction with HAP

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

#### 12.1 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.

##### 12.1-1 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 ... ] )]



##### 12.1-2 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 .



##### 12.1-3 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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