Simplify examples

doc/intro.xml

@@ -30,11 +30,10 @@ how to use the main high-level functions provided by &LINS;. <P/>
 We compute all normal subgroups in <M>D_{50}</M>,
 the dihedral group of size <M>50</M>.
 <Example><![CDATA[
-gap> n := 50;;
-gap> G := DihedralGroup(n);
+gap> G := DihedralGroup(50);
 <pc group of size 50 with 3 generators>
 gap> L := LowIndexNormalSubs(G, n);;
-gap> IsoTypes := List(L, H -> StructureDescription(H));
+gap> IsoTypes := List(L, StructureDescription);
 [ "D50", "C25", "C5", "1" ]
 ]]></Example>
 
@@ -46,13 +45,10 @@ gap> IsoTypes := List(L, H -> StructureDescription(H));
 We compute all normal subgroups of index <M>5^2 = 25</M> in <M>C_5^4</M>,
 the direct product of <M>4</M> copies of the cyclic group of order <M>5</M>:
 <Example><![CDATA[
-gap> p := 5;;
-gap> d := 4;;
-gap> C := CyclicGroup(5);;
-gap> G := DirectProduct(ListWithIdenticalEntries(d, C));
+gap> G := ElementaryAbelianGroup(5^4);
 <pc group of size 625 with 4 generators>
 gap> L := LowIndexNormalSubs(G, 5 ^ 2 : allSubgroups := false);;
-gap> IsoTypes := Collected(List(L, H -> StructureDescription(H)));
+gap> IsoTypes := Collected(List(L, StructureDescription));
 [ [ "C5 x C5", 806 ] ]
 ]]></Example>
 
@@ -63,7 +59,7 @@ gap> IsoTypes := Collected(List(L, H -> StructureDescription(H)));
 <Section Label="Main Functions">
 <Heading>Main Functions</Heading>
 
-In this section, we include all the main high-level functions provided to the User.
+In this section, we include all the main high-level functions provided to the user.
 For advanced search methods in the lattice of normal subgroups, take a look at Chapter <Ref Chap="LINS Interface"/>. <P/>
 
 <#Include Label="LowIndexNormalSubs">

doc/lins_interface.xml

@@ -94,8 +94,7 @@ For this we revise the examples from the introduction as well as include new one
 We compute all normal subgroups in <M>D_{50}</M>,
 the dihedral group of size <M>50</M>.
 <Example><![CDATA[
-gap> n := 50;;
-gap> G := DihedralGroup(n);
+gap> G := DihedralGroup(50);
 <pc group of size 50 with 3 generators>
 ]]></Example>
 
@@ -136,10 +135,7 @@ gap> IsoTypes := List(L, node -> StructureDescription(Grp(node)));
 We compute all normal subgroups of index <M>5^2 = 25</M> in <M>C_5^4</M>,
 the direct product of <M>4</M> copies of the cyclic group of order <M>5</M>:
 <Example><![CDATA[
-gap> p := 5;;
-gap> d := 4;;
-gap> C := CyclicGroup(5);;
-gap> G := DirectProduct(ListWithIdenticalEntries(d, C));
+gap> G := ElementaryAbelianGroup(5^4);;
 <pc group of size 625 with 4 generators>
 ]]></Example>
 
@@ -183,9 +179,8 @@ We compute a normal subgroup of index <M>3 \cdot 5 = 15</M> in
 <M>C_3 \times C_3 \times C_4 \times C_5</M>,
 a direct product of cyclic groups:
 <Example><![CDATA[
-gap> pList := [3, 3, 4, 5];;
-gap> G := DirectProduct(List(pList, p -> CyclicGroup(p)));
-<pc group of size 180 with 5 generators>
+gap> G := AbelianGroup([3, 3, 4, 5]);
+<pc group of size 180 with 4 generators>
 gap> gr := LowIndexNormalSubgroupsSearchForIndex(G, 15, 1);
 <lins graph contains 7 normal subgroups up to index 15>
 ]]></Example>