Change StructureDescription for infinite cyclic group

It used to be C0, now we refer to it as Z (as in: the integers), which
should be understood by more people without consulting the manual. Also,
the short name "0" is likewise replace by 0.

This is also consistent with what the RCWA package does in its custom
StructureDescription method.

lib/grpnames.gd

@@ -695,7 +695,8 @@ DeclareGlobalFunction( "LinearGroupParameters" );
 ## <Listing><![CDATA[
 ## StructureDescription(<G>) ::=
 ## 1 ; trivial group 
-## | C<size> ; cyclic group
+## | C<size> ; finite cyclic group
+## | Z ; infinite cyclic group
 ## | A<degree> ; alternating group
 ## | S<degree> ; symmetric group
 ## | D<size> ; dihedral group
@@ -759,7 +760,7 @@ DeclareGlobalFunction( "LinearGroupParameters" );
 ## If <A>G</A> is abelian, then decompose it into cyclic factors
 ## in <Q>elementary divisors style</Q>. For example,
 ## <C>"C2 x C3 x C3"</C> is <C>"C6 x C3"</C>.
-## For infinite abelian groups, <C>"C0"</C> denotes the group of integers.
+## For infinite abelian groups, <C>"Z"</C> denotes the group of integers.
 ## </Item>
 ## <Mark>3.</Mark>
 ## <Item>
@@ -883,9 +884,9 @@ DeclareGlobalFunction( "LinearGroupParameters" );
 ## gap> StructureDescription(SmallGroup(504,7):nice);
 ## "(C7 : Q8) : C9"
 ## gap> StructureDescription(AbelianGroup([0,2,3]));
-## "C0 x C6"
+## "Z x C6"
 ## gap> StructureDescription(AbelianGroup([0,0,0,2,3,6]):short);
-## "0^3x6^2"
+## "Z^3x6^2"
 ## gap> StructureDescription(PSL(4,2));
 ## "A8"
 ## ]]></Example>

lib/grpnames.gi

@@ -490,7 +490,7 @@ local Ns,MinNs,sel,a,sz,j,gs,g,N;
  Add(MinNs,Ns[a]);
  for j in ShallowCopy(sel) do
  if Size(Ns[j])>sz and Size(Ns[j]) mod sz=0 and IsSubset(Ns[j],Ns[a]) then
- RemoveSet(sel,j);
+ RemoveSet(sel,j);
  fi;
  od;
  od;
@@ -1672,23 +1672,35 @@ BindGlobal( "SD_insertsep", # function to join parts of name
  return s;
  end);
 
+BindGlobal( "SD_cyclic",
+ function ( n )
+ if n = 0 or n = infinity then
+ return "Z";
+ fi;
+ return Concatenation("C",String(n));
+ end);
+
 BindGlobal( "SD_cycsaspowers", # function to write C2 x C2 x C2 as 2^3, etc.
  function ( name, cycsizes )
 
- local short, d, k, j, n;
+ local short, g, d, k, j, n;
 
  short := ValueOption("short") = true;
  if not short then return name; fi;
  RemoveCharacters(name," ");
  cycsizes := Collected(cycsizes);
- for n in cycsizes
- do
+ for n in cycsizes do
  d := n[1]; k := n[2];
+ g := SD_cyclic(d);
+ if d = 0 then
+ d := "Z";
+ else
+ d := String(d);
+ fi;
  if k > 1 then
  for j in Reversed([2..k]) do
- name := ReplacedString(name,SD_insertsep(List([1..j],
- i->Concatenation("C",String(d))),"x",""),
- Concatenation(String(d),"^",String(j)));
+ name := ReplacedString(name,SD_insertsep(List([1..j],i->g),"x",""),
+ Concatenation(d,"^",String(j)));
  od;
  fi;
  od;
@@ -1709,8 +1721,7 @@ BindGlobal( "StructureDescriptionForAbelianGroups", # for abelian groups
  cycsizes := AbelianInvariants(G);
  cycsizes := Reversed(ElementaryDivisorsMat(DiagonalMat(cycsizes)));
  cycsizes := Filtered(cycsizes,n->n<>1);
- return SD_cycsaspowers(SD_insertsep(List(cycsizes,
- n->Concatenation("C",String(n))),
+ return SD_cycsaspowers(SD_insertsep(List(cycsizes, SD_cyclic),
  " x ",""), cycsizes);
  end );
 
@@ -1886,8 +1897,7 @@ BindGlobal( "StructureDescriptionForFiniteGroups", # for finite groups
  if cyclics <> [] then
  cycsizes := ElementaryDivisorsMat(DiagonalMat(List(cyclics,Size)));
  cycsizes := Filtered(cycsizes,n->n<>1);
- cycname := SD_cycsaspowers(SD_insertsep(List(cycsizes,
- n->Concatenation("C",String(n))),
+ cycname := SD_cycsaspowers(SD_insertsep(List(cycsizes, SD_cyclic),
  " x ",":."), cycsizes);
  else cycname := ""; fi;
  noncyclics := Difference(Gs,cyclics);

tst/testinstall/opers/StructureDescription.tst

@@ -15,9 +15,9 @@ gap> StructureDescription(SmallGroup(504,7));
 gap> StructureDescription(SmallGroup(504,7):nice);
 "(C7 : Q8) : C9"
 gap> StructureDescription(AbelianGroup([0,2,3]));
-"C0 x C6"
+"Z x C6"
 gap> StructureDescription(AbelianGroup([0,0,0,2,3,6]):short);
-"0^3x6^2"
+"Z^3x6^2"
 gap> StructureDescription(PSL(4,2));
 "A8"
 
@@ -34,7 +34,7 @@ gap> List(AllPrimitiveGroups(DegreeAction, 8), StructureDescription);
 [ "(C2 x C2 x C2) : C7", "(C2 x C2 x C2) : (C7 : C3)", 
  "(C2 x C2 x C2) : PSL(3,2)", "PSL(3,2)", "PSL(3,2) : C2", "A8", "S8" ]
 gap> StructureDescription(AbelianGroup([0,0,0,2,3,6]):short);
-"0^3x6^2"
+"Z^3x6^2"
 gap> G := Group([ (4,8)(6,10), (4,6,10,8,12), (2,4,12)(6,10,8), (3,9)(4,6,10,8,12)(7,11), (3,5)(4,6,10,8,12)(9,11), (1,3,11,9,5)(4,6,10,8,12) ]);;
 gap> StructureDescription(G);
 "A5 x A5"
@@ -87,9 +87,9 @@ true
 gap> StructureDescriptionForFiniteSimpleGroups(Ree(27));
 "Ree(27)"
 gap> StructureDescription(AbelianGroup([0,0,0,2,3,4,5,6,7,8,9,10]));
-"C0 x C0 x C0 x C2520 x C60 x C6 x C2 x C2"
+"Z x Z x Z x C2520 x C60 x C6 x C2 x C2"
 gap> StructureDescription(AbelianGroup([0,0,0,2,3,4,5,6,7,8,9,10]):short);
-"0^3x2520x60x6x2^2"
+"Z^3x2520x60x6x2^2"
 gap> infolevel:=InfoLevel(InfoWarning);; SetInfoLevel(InfoWarning,2);
 gap> StructureDescription(SmallGroup(48,16):recompute,nice);
 #I Warning! Non-unique semidirect product:
@@ -104,7 +104,15 @@ gap> F := FreeGroup("r", "s");; r := F.1;; s := F.2;;
 gap> G := F/[s^2, r^3, s*r*s*r];;
 gap> StructureDescription(G);
 "S3"
+
+# some infinite groups
 gap> G := F/[s*r*s^(-1)*r^(-1)];;
 gap> StructureDescription(G);
-"C0 x C0"
+"Z x Z"
+gap> StructureDescription(CyclicGroup(infinity));
+"Z"
+gap> StructureDescription(AbelianGroup([0,2,0]));
+"Z x Z x C2"
+
+#
 gap> STOP_TEST("StructureDescription.tst", 1);