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Change StructureDescription for infinite cyclic group
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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.
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@fingolfin
fingolfin committed Feb 6, 2019
1 parent b9c057f commit 9520869
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Showing 3 changed files with 40 additions and 21 deletions.
9 changes: 5 additions & 4 deletions lib/grpnames.gd
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Original file line number Diff line number Diff line change
Expand Up @@ -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
Expand Down Expand Up @@ -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>
Expand Down Expand Up @@ -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>
Expand Down
32 changes: 21 additions & 11 deletions lib/grpnames.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -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;
Expand Down Expand Up @@ -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;
Expand All @@ -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 );

Expand Down Expand Up @@ -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);
Expand Down
20 changes: 14 additions & 6 deletions tst/testinstall/opers/StructureDescription.tst
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Original file line number Diff line number Diff line change
Expand Up @@ -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"

Expand All @@ -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"
Expand Down Expand Up @@ -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:
Expand All @@ -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);

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