PERFECT: Documentation, test, Access functions for new groups

Basic test of creating new groups (reading files in)

Removed constructing all perfect groups, as this will be longer now

Remove now pointless tests that checked for the discrepancy between claimed list (up
to 10^6) and existing data.

doc/ref/grplib.xml

@@ -297,42 +297,31 @@ It returns <K>fail</K> if no such group exists in the library.
 <Heading>Finite Perfect Groups</Heading>
 
 <Index>perfect groups</Index>
-The &GAP; library of finite  perfect groups provides, up to isomorphism,
-a list of all perfect groups whose sizes are less than  <M>10^6</M>  excluding
-the following sizes:
-<P/>
-<List>
-<Item>
-      For <M>n = 61440</M>, 122880, 172032, 245760, 344064, 491520, 688128, or
-      983040,  the perfect groups  of size  <M>n</M>  have not completely been
-      determined yet.  The library  neither provides  the number of these
-      groups nor the groups themselves.
-</Item>
-<Item>
-      For  <M>n = 86016</M>,  368640,  or  737280,  the library  does not  yet
-      contain  the perfect groups  of size  <M>n</M>,  it  only provides their
-      numbers which are 52, 46, and 54, respectively.
-</Item>
-</List>
-<P/>
-Except for these eleven sizes, the list of altogether 1097 perfect groups
-in the  library is complete.  It relies  on results of  Derek&nbsp;F. Holt and
-Wilhelm Plesken which  are published in their  book    <Q>Perfect Groups</Q>
-<Cite Key="HP89"/>. Moreover,   they     have  supplied us    with    files with
-presentations of 488 of the groups. In terms of  these, the remaining 607
-nontrivial groups in the library can be described as 276 direct products,
-107  central   products, and 224  subdirect  products.  They are computed
-automatically by suitable &GAP; functions whenever they are needed.  Two
-additional groups omitted from the book <Q>Perfect Groups</Q> have also been
-included.
+The &GAP; library of finite  perfect groups provides, up to isomorphism, a
+list of all perfect groups whose sizes are less than  <M>10^6</M>. 
+The groups of most of these orders have been enumerated by
+Derek&nbsp;F. Holt and Wilhelm Plesken and
+published in their  book    <Q>Perfect Groups</Q> <Cite Key="HP89"/>.
+For orders <M>n = 86016</M>,  368640,  or  737280 this work only counted the
+groups (but did not explicitly list them), the groups of orders
+<M>n = 61440</M>, 122880, 172032, 245760, 344064, 491520,
+688128, or 983040 were omitted.
 <P/>
 We are grateful to Derek Holt and Wilhelm Plesken for making their groups
 available to the &GAP; community  by contributing their files. It should
 be noted that  their book contains a  lot of further information for many
 of the library groups.  So we would like  to recommend  it to any  &GAP;
 user who is interested in the groups.
+Two additional groups omitted from the book <Q>Perfect Groups</Q> have also
+been included.
+<P/>
+The library of these has been brought into &GAP; format by Volkmar Felsch.
+<P/>
+The perfect groups of size less than <M>10^6</M>which were missing in the work of Holt
+and Plesken have been enumerated by Alexander
+Hulpke. They are stored directly and provide less construction information
+in their names.
 <P/>
-The library has been brought into &GAP; format by Volkmar Felsch.
 <P/>
 As  all groups are stored  by presentations, a permutation representation
 is obtained by coset enumeration. Note that some of the library groups do
@@ -343,7 +332,6 @@ Computations in these groups may be rather time consuming.
 <#Include Label="PerfectGroup">
 <#Include Label="PerfectIdentification">
 <#Include Label="NumberPerfectGroups">
-<#Include Label="NumberPerfectLibraryGroups">
 <#Include Label="SizeNumbersPerfectGroups">
 <#Include Label="DisplayInformationPerfectGroups">
 
@@ -1168,4 +1156,3 @@ gap> LargestMovedPoint( P2 );
 <!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
 <!-- %% -->
 <!-- %E -->
-

grp/perf.gd

@@ -97,7 +97,7 @@ DeclareAttribute("PerfectIdentification", IsGroup );
 ##  One can iterate over the perfect groups library with:
 ##  <Example><![CDATA[
 ##  gap> for n in SizesPerfectGroups() do
-##  >      for k in [1..NrPerfectLibraryGroups(n)] do
+##  >      for k in [1..NrPerfectGroups(n)] do
 ##  >        pg := PerfectGroup(n,k);
 ##  >      od;
 ##  >    od;
@@ -116,42 +116,31 @@ DeclareGlobalFunction("SizesPerfectGroups");
 ##  <#GAPDoc Label="NumberPerfectGroups">
 ##  <ManSection>
 ##  <Func Name="NumberPerfectGroups" Arg='size'/>
+##  <Func Name="NrPerfectGroups" Arg='size'/>
+##  <Func Name="NumberPerfectLibraryGroups" Arg='size'/>
+##  <Func Name="NrPerfectLibraryGroups" Arg='size'/>
 ##
 ##  <Description>
 ##  returns the number of non-isomorphic perfect groups of size <A>size</A> for
 ##  each positive integer  <A>size</A> up to <M>10^6</M> except for the eight  sizes
 ##  listed at the beginning  of  this section for  which the number is not
 ##  yet known. For these values as well as for any argument out of range it
 ##  returns <K>fail</K>.
+##  <A>NrPerfectGroups</A> is a synonym for <Ref Func="NumberPerfectGroups"/>.
+##  Moreover <A>NumberPerfectLibraryGroups</A> (and its synonym <A>NrPerfectLibraryGroups</A>)
+##  exist for historical reasons, and return 0 instead of fail for arguments
+##  outside the library scope.
 ##  </Description>
 ##  </ManSection>
 ##  <#/GAPDoc>
 ##
 DeclareGlobalFunction("NumberPerfectGroups");
 DeclareSynonym("NrPerfectGroups",NumberPerfectGroups);
-
-
-#############################################################################
-##
-#F  NumberPerfectLibraryGroups( <size> )  . . . . . . . . . . . . . . . . . .
-##
-##  <#GAPDoc Label="NumberPerfectLibraryGroups">
-##  <ManSection>
-##  <Func Name="NumberPerfectLibraryGroups" Arg='size'/>
-##
-##  <Description>
-##  returns the number of perfect groups of size <A>size</A> which are available
-##  in the  library of finite perfect groups. (The purpose  of the function
-##  is  to provide a simple way  to formulate a loop over all library groups
-##  of a given size.)
-##  </Description>
-##  </ManSection>
-##  <#/GAPDoc>
-##
 DeclareGlobalFunction("NumberPerfectLibraryGroups");
 DeclareSynonym("NrPerfectLibraryGroups",NumberPerfectLibraryGroups);
 
 
+
 #############################################################################
 ##
 #F  PerfectGroup( [<filt>, ]<size>[, <n>] )

grp/perf.grp

@@ -86,26 +86,14 @@ InstallGlobalFunction( NumberPerfectGroups, function ( size )
     fi;
 end );
 
+InstallGlobalFunction(NumberPerfectLibraryGroups,function(size)
+local a;
+  a:=NumberPerfectGroups(size);
+  if a=fail then return 0;
+  else return a;fi;
+end);
 
-#############################################################################
-##
-#F  NumberPerfectLibraryGroups( size )
-##
-##  `NumberPerfectLibraryGroups'  returns the number of nonisomorphic perfect
-##  groups of size `size' for 1 <= size <= 1 000 000 which are available in the
-##  perfect groups library.
-##
-InstallGlobalFunction( NumberPerfectLibraryGroups, function ( size )
-local sizenum;
 
-    if size=1 then
-      return 1;
-    elif IsOddInt(size) then return 0;fi;
-    # get the number and return it.
-    sizenum := PerfGrpLoad( size );
-    return PERFRec.number[sizenum];
-
-end );
 
 #############################################################################
 ##
@@ -489,7 +477,7 @@ local size,i,nr,n,leng,sizenum,hpnum,description,centre,orbsize;
   if IsInt(arg[1]) then
     size:=arg[1];
     if Length(arg)=1 then
-      nr:=[1..NumberPerfectLibraryGroups(size)];
+      nr:=[1..NumberPerfectGroups(size)];
     else
       nr:=arg[2];
     fi;
@@ -690,7 +678,7 @@ local s,l;
     Print("#W  No information about size ",s," available\n");
     return fail;
   fi;
-  l:=NumberPerfectLibraryGroups(s);
+  l:=NumberPerfectGroups(s);
   while l>1 do
     if IsomorphismGroups(G,PerfectGroup(IsPermGroup,s,l))<>fail then
       return [s,l];

grp/perf0.grp

@@ -46,11 +46,6 @@
 ##        have  not  yet   been  determined.   It  is  needed  by  subroutine
 ##        NumberPerfectGroups.
 ##
-##     PERFRec.notAvailable
-##        is a list of all sizes less than 10^6  for which the perfect groups
-##        are known, but not yet in the library.  It is needed by subroutines
-##        DisplayInformationPerfectGroups and NumberPerfectLibraryGroups.
-##
 ##     PERFRec.sizeNumberSimpleGroup
 ##        is an ordered list of the  'size numbers'  of all nonabelian simple
 ##        groups which occur as composition factor of any library group.

tst/testinstall/grp/perf.tst

@@ -10,7 +10,7 @@ gap> NumberPerfectGroups(60);
 gap> NumberPerfectGroups(60^6);
 fail
 gap> NumberPerfectLibraryGroups(60^6);
-0
+fail
 
 #
 gap> SizesPerfectGroups();
@@ -49,36 +49,6 @@ gap> SizesPerfectGroups();
   887040, 892800, 900000, 903168, 907200, 912576, 921600, 921984, 929280, 
   933120, 936000, 937500, 943488, 950400, 950520, 960000, 962280, 967680, 
   976500, 979200, 979776, 983040, 987840 ]
-gap> List(SizesPerfectGroups(), NrPerfectLibraryGroups);
-[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 7, 1, 1, 1, 1, 3, 1, 1, 1, 7, 1, 
-  2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 5, 1, 1, 3, 1, 1, 9, 4, 1, 1, 1, 1, 1, 
-  1, 3, 1, 7, 1, 1, 1, 1, 5, 22, 1, 3, 1, 1, 1, 1, 1, 4, 1, 1, 37, 2, 1, 1, 
-  4, 1, 1, 1, 4, 25, 3, 1, 1, 1, 3, 1, 1, 1, 2, 2, 2, 1, 2, 1, 3, 0, 1, 4, 1, 
-  1, 1, 4, 1, 4, 4, 3, 1, 1, 6, 1, 0, 1, 8, 2, 1, 3, 1, 1, 1, 1, 1, 1, 15, 3, 
-  1, 1, 1, 4, 5, 2, 0, 1, 6, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 18, 1, 3, 1, 12, 
-  1, 0, 8, 1, 1, 1, 3, 1, 19, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 26, 3, 3, 
-  1, 17, 5, 1, 1, 2, 0, 1, 1, 4, 3, 2, 7, 1, 1, 2, 1, 3, 2, 3, 1, 3, 18, 1, 
-  27, 1, 1, 0, 3, 1, 1, 1, 6, 1, 1, 3, 3, 0, 1, 1, 11, 1, 1, 2, 2, 1, 1, 4, 
-  3, 1, 1, 1, 1, 3, 1, 2, 1, 1, 3, 8, 1, 1, 25, 4, 3, 18, 1, 4, 17, 6, 1, 0, 
-  1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 19, 1, 1, 7, 1, 1, 2, 3, 1, 4, 1, 12, 1, 2, 
-  41, 1, 1, 1, 3, 2, 1, 0, 23, 3, 2, 1, 1, 1, 1, 2, 3, 2, 1, 1, 3, 0, 1, 13, 
-  2, 5, 3, 16, 2, 2, 1, 3, 2, 3, 3, 2, 1, 2, 1, 1, 3, 1, 7, 6, 4, 1, 23, 8, 
-  2, 21, 3, 8, 1, 2, 1, 12, 1, 20, 1, 1, 4, 0, 1 ]
-gap> List(SizesPerfectGroups(), NrPerfectGroups);
-[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 7, 1, 1, 1, 1, 3, 1, 1, 1, 7, 1, 
-  2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 5, 1, 1, 3, 1, 1, 9, 4, 1, 1, 1, 1, 1, 
-  1, 3, 1, 7, 1, 1, 1, 1, 5, 22, 1, 3, 1, 1, 1, 1, 1, 4, 1, 1, 37, 2, 1, 1, 
-  4, 1, 1, 1, 4, 25, 3, 1, 1, 1, 3, 1, 1, 1, 2, 2, 2, 1, 2, 1, 3, fail, 1, 4, 
-  1, 1, 1, 4, 1, 4, 4, 3, 1, 1, 6, 1, 52, 1, 8, 2, 1, 3, 1, 1, 1, 1, 1, 1, 
-  15, 3, 1, 1, 1, 4, 5, 2, fail, 1, 6, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 18, 1, 
-  3, 1, 12, 1, fail, 8, 1, 1, 1, 3, 1, 19, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 
-  1, 26, 3, 3, 1, 17, 5, 1, 1, 2, fail, 1, 1, 4, 3, 2, 7, 1, 1, 2, 1, 3, 2, 
-  3, 1, 3, 18, 1, 27, 1, 1, fail, 3, 1, 1, 1, 6, 1, 1, 3, 3, 46, 1, 1, 11, 1, 
-  1, 2, 2, 1, 1, 4, 3, 1, 1, 1, 1, 3, 1, 2, 1, 1, 3, 8, 1, 1, 25, 4, 3, 18, 
-  1, 4, 17, 6, 1, fail, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 19, 1, 1, 7, 1, 1, 2, 
-  3, 1, 4, 1, 12, 1, 2, 41, 1, 1, 1, 3, 2, 1, fail, 23, 3, 2, 1, 1, 1, 1, 2, 
-  3, 2, 1, 1, 3, 54, 1, 13, 2, 5, 3, 16, 2, 2, 1, 3, 2, 3, 3, 2, 1, 2, 1, 1, 
-  3, 1, 7, 6, 4, 1, 23, 8, 2, 21, 3, 8, 1, 2, 1, 12, 1, 20, 1, 1, 4, fail, 1 ]
 
 #
 gap> DisplayInformationPerfectGroups(1);
@@ -106,10 +76,6 @@ gap> DisplayInformationPerfectGroups([3840,2]);
 #I Perfect group 3840:  A5 ( 2^4 E 2^1 A ) C 2^1 II
 #I   centre = 4  size = 2^8*3*5  orbit size = 64
 #I   Holt-Plesken class 1 (6,2)
-gap> DisplayInformationPerfectGroups(61440);
-#I  no information known about size 61440
-gap> DisplayInformationPerfectGroups(86016);
-#I  no information available about size 86016
 gap> DisplayInformationPerfectGroups(967680,4);
 #I Perfect group 
 967680:  quasisimple group  L3(4) 3^1 x ( 2^1 A 2^1 ) x ( 2^1 A 2^1 )
@@ -163,16 +129,6 @@ A5
 gap> IsFpGroup(g);
 true
 
-#
-# construct all perfect groups, to verify this works
-# TODO: slow (takes a few seconds), move to teststandard?
-#
-gap> for n in SizesPerfectGroups() do
->   for i in [1..NumberPerfectLibraryGroups(n)] do
->     PerfectGroup(n, i);
->   od;
-> od;
-
 #
 # test PerfGrpConst directly for some corner cases
 #
@@ -192,10 +148,6 @@ gap> PerfectGroup(1,2);
 Error, PerfectGroup(1,2) does not exist !
 gap> PerfectGroup(30,1);
 Error, PerfectGroup(30,1) does not exist !
-gap> PerfectGroup(61440, 1);
-Error, Perfect groups of size 61440 not known
-gap> PerfectGroup(86016, 1);
-Error, Perfect groups of size 86016 not available
 
 #
 gap> STOP_TEST("perfectgroups.tst", 1);

tst/teststandard/opers/PerfectGroups.tst

@@ -0,0 +1,20 @@
+gap> START_TEST("PerfectGroups.tst");
+
+#
+gap> Sum(SizesPerfectGroups(),NrPerfectGroups);
+6002
+gap> l:=[61440, 86016, 122880, 172032, 245760, 344064, 368640, 491520,
+> 688128, 737280, 983040 ];;
+gap> List(l,NrPerfectGroups);
+[ 98, 52, 258, 154, 582, 291, 46, 975, 508, 54, 1881 ]
+gap> gp:=List(l,x->PerfectGroup(IsPermGroup,x,30));;
+gap> gp:=List(gp,x->Group(GeneratorsOfGroup(x)));;
+gap> List(gp,Size)=l;
+true
+gap> ForAll(gp,IsPerfect);
+true
+gap> List(gp,NrMovedPoints);
+[ 240, 28, 768, 128, 400, 224, 116, 80, 308, 1024, 360 ]
+
+#
+gap> STOP_TEST("PerfectGroups.tst",1);