Change Set(Factors(n)) to PrimeDivisors(n)

benchmark/transgrp/examine4

@@ -2902,7 +2902,7 @@ local b,w,a,fno,cnt,normalsyl,tf,nt,tno,ntno,i,j,k,com,hom,cs,ker,nf;
   fno:=PreImage(sys.blockhom,fno); # factor normalizer
 
   # are we effectively working modulo a prime?
-  normalsyl:=Filtered(Set(Factors(Size(fno))),p->
+  normalsyl:=Filtered(PrimeDivisors(Size(fno)),p->
     (not IsInt(Index(w,b)/p)) and
     IsNormal(fno,SylowSubgroup(b,p)) );
 
@@ -3559,7 +3559,7 @@ local bls, # block size
     else
       # see, whether it's worth to use subgroups of minops
       p:=List(minops,i->Factors(Size(i)));
-      c:=Set(Factors(Size(i)));
+      c:=PrimeDivisors(Size(i));
       c:=List(p,i->Filtered(i,j->not j in c));
       p:=Minimum(List(c,Product));
       if p>1 and bla>5 and bls*bla>23 then

doc/ref/intrfc.xml

@@ -335,8 +335,7 @@ operation:
 InstallMethod(PrimesDividingSize,"for finite groups",
   [IsGroup and IsFinite],
 function(G)
-  if Size(G)=1 then return [];
-  else return Set(Factors(Size(G)));fi;
+  return PrimeDivisors(Size(G));
 end);
 ]]></Log>
 <P/>

grp/simple.gi

@@ -412,7 +412,7 @@ local brg,str,p,a,param,g,s,small,plus,sets;
 	SetIsSimpleGroup(g,true);
 	return g;
       elif Length(param)=1 and param[1]>7 and
-        Set(Factors(param[1]))=[2] and IsOddInt(LogInt(param[1],2)) then
+        PrimeDivisors(param[1])=[2] and IsOddInt(LogInt(param[1],2)) then
 	g:=SuzukiGroup(IsPermGroup,param[1]);
 	SetName(g,Concatenation("Sz(",String(param),")"));
 	SetIsSimpleGroup(g,true);
@@ -422,7 +422,7 @@ local brg,str,p,a,param,g,s,small,plus,sets;
       fi;
     elif str="R" or str="REE" or str="2G" then
       if Length(param)=1 and param[1]>26 and
-        Set(Factors(param[1]))=[3] and IsOddInt(LogInt(param[1],3)) then
+        PrimeDivisors(param[1])=[3] and IsOddInt(LogInt(param[1],3)) then
 	g:=ReeGroup(IsMatrixGroup,param[1]);
 	SetName(g,Concatenation("Ree(",String(param[1]),")"));
 	SetIsSimpleGroup(g,true);

hpcgap/lib/polyconw.gi

@@ -105,7 +105,7 @@ BindGlobal( "IsConsistentPolynomial", function( pol )
   local n, p, ps, x, null, f;
   n := DegreeOfLaurentPolynomial(pol);
   p := Characteristic(pol);
-  ps := Set(FactorsInt(n));
+  ps := PrimeDivisors(n);
   x := IndeterminateOfLaurentPolynomial(pol);
   null := 0*pol;
   f := function(k)
@@ -187,7 +187,7 @@ end);
 ##  all proper subfields.
 BindGlobal("NrCompatiblePolynomials", function(p, n)
   local ps, lcm;
-  ps := Set(Factors(n));
+  ps := PrimeDivisors(n);
   lcm := Lcm(List(ps, r-> p^(n/r)-1));
   return (p^n-1)/lcm;
 end);
@@ -320,7 +320,7 @@ InstallGlobalFunction( ConwayPol, function( p, n )
       if n > 1 then
 
         # Compute the list of all `n / l' for `l' a prime divisor of `n'
-        nfacs:= List( Set( Factors( n ) ), d -> n / d );
+        nfacs:= List( PrimeDivisors( n ), d -> n / d );
 
         if nfacs = [ 1 ] then
 
@@ -343,7 +343,7 @@ InstallGlobalFunction( ConwayPol, function( p, n )
 
         quots:= List( nfacs, x -> pp / ( p^x -1 ) );
         lencpols:= Length( cpols );
-        ppmin:= List( Set( Factors( pp ) ), d -> pp/d );
+        ppmin:= List( PrimeDivisors( pp ), d -> pp/d );
 
         found:= false;
         onelist:= [ one ];
@@ -557,7 +557,7 @@ InstallGlobalFunction( RandomPrimitivePolynomial, function(F, n, varnum...)
   FF := AlgebraicExtension(F, pol);
   one := One(FF);
   zero := Zero(FF);
-  fac:=List(Set(Factors(Size(FF)-1)), p-> (Size(FF)-1)/p);
+  fac:=List(PrimeDivisors(Size(FF)-1), p-> (Size(FF)-1)/p);
   repeat
     a := Random(FF);
   until a <> zero and ForAll(fac, d-> a^d <> one);

lib/autsr.gi

@@ -254,7 +254,7 @@ local ff,r,d,ser,u,v,i,j,k,p,bd,e,gens,lhom,M,N,hom,Q,Mim,q,ocr,split,MPcgs,
 	d:=RefinedSubnormalSeries(d,i);
       od;
     fi;
-    for i in Set(Factors(Size(r))) do
+    for i in PrimeDivisors(Size(r)) do
       u:=PCore(r,i);
       if Size(u)>1 then
 	d:=RefinedSubnormalSeries(d,u);
@@ -288,7 +288,7 @@ local ff,r,d,ser,u,v,i,j,k,p,bd,e,gens,lhom,M,N,hom,Q,Mim,q,ocr,split,MPcgs,
   ser:=[TrivialSubgroup(G)];
   for i in d{[2..Length(d)]} do
     u:=ser[Length(ser)];
-    for p in Set(Factors(Size(i)/Size(u))) do
+    for p in PrimeDivisors(Size(i)/Size(u)) do
       bd:=PValuation(Size(i)/Size(u),p); # max p-exponent
       u:=ClosureSubgroup(u,SylowSubgroup(i,p));
       v:=ser[Length(ser)];

lib/clas.gi

@@ -725,7 +725,7 @@ InstallGlobalFunction( RationalClassesTry, function(  G, classes, elm  )
         Add( classes, C );
 
         # try the powers of this element that reduce the order
-        for i  in Set(FactorsInt(Order(elm)))  do
+        for i in PrimeDivisors(Order(elm)) do
             RationalClassesTry( G, classes, elm ^ i );
         od;
 

lib/ctbl.gi

@@ -353,7 +353,7 @@ InstallGlobalFunction( CompatibleConjugacyClassesDefault,
     fi;
 
     # Use power maps.
-    primes:= Set( Factors( Size( tbl ) ) );
+    primes:= PrimeDivisors( Size( tbl ) );
 
     # store power maps of the group, in order to identify the class
     # of the power only once.
@@ -1130,7 +1130,7 @@ InstallMethod( AbelianInvariants,
 
       # For all prime divisors $p$ of the size,
       # compute the element of maximal $p$ power order.
-      primes:= Set( FactorsInt( Size( tbl ) ) );
+      primes:= PrimeDivisors( Size( tbl ) );
       max:= List( primes, x -> 1 );
       pos:= [];
       orders:= OrdersClassRepresentatives( tbl );
@@ -1618,7 +1618,7 @@ InstallMethod( OrdersClassRepresentatives,
 
     # If these maps do not suffice, compute the missing power maps
     # and then try again.
-    for p in Set( Factors( Size( tbl ) ) ) do
+    for p in PrimeDivisors( Size( tbl ) ) do
       PowerMap( tbl, p );
     od;
     ord:= ElementOrdersPowerMap( ComputedPowerMaps( tbl ) );
@@ -2659,7 +2659,7 @@ InstallMethod( ClassRoots,
     orders := OrdersClassRepresentatives( tbl );
     root   := List([1..nccl], x->[]);
 
-    for p in Set( Factors( Size( tbl ) ) ) do
+    for p in PrimeDivisors( Size( tbl ) ) do
        pmap:= PowerMap( tbl, p );
        for i in [1..nccl] do
           if i <> pmap[i] and orders[i] <> orders[pmap[i]] then
@@ -3495,7 +3495,7 @@ InstallMethod( IsInternallyConsistent,
       # If the power maps of all prime divisors of the order are stored,
       # check if they are consistent with the representative orders.
       if     IsBound( orders )
-         and ForAll( Set( FactorsInt( order ) ), x -> IsBound(powermap[x]) )
+         and ForAll( PrimeDivisors( order ), x -> IsBound(powermap[x]) )
          and orders <> ElementOrdersPowerMap( powermap ) then
         Info( InfoWarning, 1,
               "IsInternallyConsistent(", tbl, "):\n",
@@ -3656,7 +3656,7 @@ InstallMethod( IsInternallyConsistent,
       # If the power maps of all prime divisors of the order are stored,
       # check if they are consistent with the representative orders.
       if     IsBound( orders )
-         and ForAll( Set( FactorsInt( order ) ), x -> IsBound(powermap[x]) )
+         and ForAll( PrimeDivisors( order ), x -> IsBound(powermap[x]) )
          and orders <> ElementOrdersPowerMap( powermap ) then
         flag:= false;
         Info( InfoWarning, 1,
@@ -3775,7 +3775,7 @@ InstallMethod( IsPSolvableCharacterTableOp,
       # \ldots and its size.
       nextsize:= Sum( classes{ nsg[i] }, 0 );
 
-      facts:= Set( FactorsInt( nextsize / size ) );
+      facts:= PrimeDivisors( nextsize / size );
       if 1 < Length( facts ) and ( p = 0 or p in facts ) then
 
         # The chief factor `nsg[i] / n' is not a prime power,
@@ -4820,7 +4820,7 @@ BindGlobal( "CharacterTableDisplayDefault", function( tbl, options )
       tbl_centralizers:= SizesCentralizers( tbl );
     elif centralizers = true then
       tbl_centralizers:= SizesCentralizers( tbl );
-      primes:= Set( FactorsInt( Size( tbl ) ) );
+      primes:= PrimeDivisors( Size( tbl ) );
       cen:= [];
       for prime in primes do
         cen[ prime ]:= [];
@@ -5650,7 +5650,7 @@ InstallMethod( CharacterTableFactorGroup,
     # Transfer necessary power maps of `tbl' to `F'.
     inverse:= ProjectionMap( factorfusion );
     maps:= ComputedPowerMaps( F );
-    for p in Set( Factors( Size( F ) ) ) do
+    for p in PrimeDivisors( Size( F ) ) do
       if not IsBound( maps[p] ) then
         maps[p]:= factorfusion{ PowerMap( tbl, p ){ inverse } };
       fi;
@@ -5923,7 +5923,7 @@ InstallOtherMethod( CharacterTableIsoclinic,
     invfusion:= InverseMap( factorfusion );
 
     # Adjust the power maps.
-    for p in Set( Factors( size ) ) do
+    for p in PrimeDivisors( size ) do
 
       map:= ShallowCopy( PowerMap( tbl, p ) );
 

lib/ctblauto.gi

@@ -596,7 +596,7 @@ InstallMethod( TableAutomorphisms,
     nccl:= NrConjugacyClasses( tbl );
 
     # Check whether all generators commute with all power maps.
-    powermap:= List( Set( Factors( Size( tbl ) ) ),
+    powermap:= List( PrimeDivisors( Size( tbl ) ),
                      p -> PowerMap( tbl, p ) );
     admissible:= Filtered( gens, 
                            perm -> ForAll( powermap, 
@@ -1011,7 +1011,7 @@ InstallMethod( TransformingPermutationsCharacterTables,
     # - If the group orders differ then return `fail'.
     # - If irreducibles are stored in the two tables and coincide,
     #   and if the power maps are known and equal then return the identity.
-    primes:= Set( Factors( Size( tbl1 ) ) );
+    primes:= PrimeDivisors( Size( tbl1 ) );
     if Size( tbl1 ) <> Size( tbl2 ) then
       return fail;
     elif HasIrr( tbl1 ) and HasIrr( tbl2 ) and Irr( tbl1 ) = Irr( tbl2 )

lib/ctblfuns.gi

@@ -4323,7 +4323,7 @@ InstallGlobalFunction( ReductionToFiniteField, function( value, p )
 
     if k <> 1 then
 
-      primes:= Set( Factors( m ) );
+      primes:= PrimeDivisors( m );
       sol:= fail;
 
       while not IsEmpty( primes ) do

lib/ctblmono.gi

@@ -1105,7 +1105,7 @@ InstallMethod( TestMonomialQuick,
     # This follows from Theorem~(2D) in~\cite{Fon62}.
     if IsSolvableGroup( G ) then
 
-      pi   := Set( FactorsInt( codegree ) );
+      pi   := PrimeDivisors( codegree );
       hall := Product( Filtered( FactorsInt( factsize ), x -> x in pi ), 1 );
 
       if factsize / hall = chi[1] then
@@ -1245,7 +1245,7 @@ InstallOtherMethod( TestMonomialQuick,
         test:= rec( isMonomial := true,
                     comment    := "abelian by supersolvable group" );
 
-      elif ForAll( Set( FactorsInt( Size( ssr ) ) ),
+      elif ForAll( PrimeDivisors( Size( ssr ) ),
                    x -> IsAbelian( SylowSubgroup( ssr, x ) ) ) then
 
         # Sylow abelian by supersolvable groups are monomial.

lib/ctblpope.gi

@@ -77,7 +77,7 @@ InstallGlobalFunction( TestPerm2, function(tbl, char)
    od;
 
    # TEST 5:
-   subfak:= Set(Factors(subord));
+   subfak:= PrimeDivisors(subord);
    for prime in subfak do
       if subord mod prime^2 <> 0 then
 
@@ -205,7 +205,7 @@ InstallGlobalFunction( TestPerm4, function( tbl, chars )
     size:= Size( tbl );
     orders:= OrdersClassRepresentatives( tbl );
 
-    for p in Set( Factors( Size( tbl ) ) ) do
+    for p in PrimeDivisors( Size( tbl ) ) do
 
       # Compute the distribution of characters to blocks.
       bl:= PrimeBlocks( tbl, p );

lib/ctblsymm.gi

@@ -1185,7 +1185,7 @@ InstallGlobalFunction( CharacterTableWreathSymmetric, function( sub, n )
     # \ldots, `ComputedPowerMaps', \ldots
     tbl.ComputedPowerMaps:= [];
     powermap:= tbl.ComputedPowerMaps;
-    for prime in Set( Factors( tbl.Size ) ) do
+    for prime in PrimeDivisors( tbl.Size ) do
        spm:= PowerMap( sub, prime );
        powermap[prime]:= List( [ 1 .. nccl ],
            i -> Position(parts, PowerWreath(spm, parts[i], prime)) );
@@ -1250,7 +1250,7 @@ InstallMethod( Irr,
     # Compute and store the power maps.
     pow:= ComputedPowerMaps( cG );
     fun:= gentbl.powermap[1];
-    for p in Set( Factors( Size( G ) ) ) do
+    for p in PrimeDivisors( Size( G ) ) do
       if not IsBound( pow[p] ) then
         pow[p]:= List( cp, x -> Position( cp, fun( deg, x[2], p ) ) );
       fi;

lib/cyclotom.gi

@@ -231,7 +231,7 @@ InstallGlobalFunction( CoeffsCyc, function( z, N )
         #   and $n / s$, and hence remain in the reduced expression,
         # - all primes but the squarefree part of the rest.
 
-        factors:= Set( FactorsInt( s ) );
+        factors:= PrimeDivisors( s );
         second:= 1;
         for p in factors do
           if s mod p <> 0 or ( n / s ) mod p <> 0 then
@@ -301,7 +301,7 @@ InstallGlobalFunction( CoeffsCyc, function( z, N )
     # `E(n)^k' by $ - \sum_{j=1}^{p-1} `E(n*p)^(p*k+j*n)'$.
     if quo <> 1 then
 
-      for p in Set( FactorsInt( quo ) ) do
+      for p in PrimeDivisors( quo ) do
         if p <> 2 and n mod p <> 0 then
           nn  := n * p;
           quo := quo / p;
@@ -634,7 +634,7 @@ InstallGlobalFunction( NK, function( n, k, deriv )
       od;
     elif k in [ 3, 5, 7 ] then   # for odd primes
       if ( n mod ( k*k ) <> 0 ) and
-         ForAll( Set( FactorsInt( n ) ), p -> (p-1) mod k <> 0 ) then
+         ForAll( PrimeDivisors( n ), p -> (p-1) mod k <> 0 ) then
         return fail;
       fi;
       while true do
@@ -666,7 +666,7 @@ InstallGlobalFunction( NK, function( n, k, deriv )
     elif k = 4 then
       # An automorphism of order 4 exists if 4 divides $p-1$ for an odd
       # prime divisor $p$ of `n', or if 16 divides `n'.
-      if ForAll( Set( FactorsInt( n ) ), p -> (p-1) mod k <> 0 )
+      if ForAll( PrimeDivisors( n ), p -> (p-1) mod k <> 0 )
          and n mod 16 <> 0 then
         return fail;
       fi;
@@ -691,7 +691,7 @@ InstallGlobalFunction( NK, function( n, k, deriv )
       # An automorphism of order 6 exists if automorphisms of the orders
       # 2 and 3 exist; the former is always true.
       if ( n mod 9 <> 0 ) and
-         ForAll( Set( FactorsInt( n ) ), p -> (p-1) mod 3 <> 0 ) then
+         ForAll( PrimeDivisors( n ), p -> (p-1) mod 3 <> 0 ) then
         return fail;
       fi;
       while true do
@@ -721,7 +721,7 @@ InstallGlobalFunction( NK, function( n, k, deriv )
     elif k = 8 then
       # An automorphism of order 8 exists if 8 divides $p-1$ for an odd
       # prime divisor $p$ of `n', or if 32 divides `n'.
-      if ForAll( Set( FactorsInt( n ) ), p -> (p-1) mod k <> 0 )
+      if ForAll( PrimeDivisors( n ), p -> (p-1) mod k <> 0 )
          and n mod 32 <> 0 then
         return fail;
       fi;

lib/fitfree.gi

@@ -887,7 +887,7 @@ local o,C;
     Append(o,List(Orbits(C,MovedPoints(G)),Length));
   fi;
   o:=Lcm(o);
-  if Set(Factors(Size(G)))=Set(Factors(o)) then
+  if PrimeDivisors(Size(G))=PrimeDivisors(o) then
     # all primes in -- useless
     return G;
   fi;
@@ -898,7 +898,7 @@ end);
 BindGlobal("Halleen",function(arg)
 local G,gp,p,r,s,c,i,a,pp,prime,sy,k,b,dc,H,e,j,forbid;
   G:=arg[1];
-  gp:=Set(Factors(Size(G)));
+  gp:=PrimeDivisors(Size(G));
   if Length(arg)>1 then
     r:=arg[2];
     forbid:=Difference(gp,r);
@@ -1012,7 +1012,7 @@ local s,d,c,act,o,i,j,h,p,hf,img,n,prd,k,nk,map,ns,all,hl,hcomp,
     return [TrivialSubgroup(G)];
   elif false and Length(pi)=1 then
     return [SylowSubgroup(G,pi[1])];
-  elif pi=Set(Factors(Size(G))) then
+  elif pi=PrimeDivisors(Size(G)) then
     return [G];
   fi;
 

lib/gaussian.gi

@@ -279,7 +279,7 @@ InstallMethod( Factors,
 
     # loop over all factors of the norm of x
     facs := [];
-    for prm in Set( FactorsInt( EuclideanDegree( GaussianIntegers, x ) ) ) do
+    for prm in PrimeDivisors( EuclideanDegree( GaussianIntegers, x ) ) do
 
         # $p = 2$ and primes $p = 1$ mod 4 split according to $p = x^2 + y^2$
         if prm = 2  or prm mod 4 = 1  then

lib/gpprmsya.gi

@@ -1187,7 +1187,7 @@ syll, act, typ, sel, bas, wdom, comp, lperm, other, away, i, j,b0,opg,bp;
   Info(InfoGroup,1,"SymmAlt normalizer: orbits ",List(o,Length));
 
   if Length(o)=1 and IsAbelian(u) then
-    b:=List(Set(Factors(Size(u))),p->Omega(SylowSubgroup(u,p),p,1));
+    b:=List(PrimeDivisors(Size(u)),p->Omega(SylowSubgroup(u,p),p,1));
     if Length(b)=1 and IsTransitive(b[1],dom) then
       # elementary abelian, regular -- construct the correct AGL
       b:=b[1];