Setup for parallel construction of braces with SCSCP

constr/README.md

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+Quickstart guide for parallel braces enumeration with SCSCP package
+
+The file `count.g` is the original file containing `AllSkewbraces` 
+function which calculates skew braces enumerating all groups of a 
+given order.
+
+It was extended by `AllSkewbracesByGroupId` function which takes one
+group id `[size,nr]` and produces all skew braces that originate from
+that group id.
+
+Obviously, this can be performed independently, and this is where
+one can use the SCSCP package.
+
+To set up parallel distributed calculation do the following:
+
+1. Edit server configuration file `myserver.g` as needed (e.g. to
+update filenames and paths).
+
+2. Edit part 1 of the `gapd.sh` script to update the way how GAP 
+starts and the location of the server configuration file.
+
+3. Edit `gapfarm.sh` script to specify GAP workers, each listening
+to a specific port. The number of workers depend on the number of
+cores on your computer.
+
+4. Start GAP workers with
+
+    ./gapfarm.sh
+
+5. Start a GAP session and execute the following commands:
+
+Load SCSCP package:
+
+    gap> LoadPackage("scscp");
+
+Inform GAP which server to use (port numbers must be the same
+as in `gapfarm.sh`):
+
+    gap> SCSCPservers:=List([26133..26136], i -> ["localhost",i]);
+    [ [ "localhost", 26133 ], [ "localhost", 26134 ], [ "localhost", 26135 ], [ "localhost", 26136 ] ]
+
+Generate the list of tasks (each task is a group id):
+
+    todo:=List([1..NrSmallGroups(16)],i->[16,i]);
+    [ [ 16, 1 ], [ 16, 2 ], [ 16, 3 ], [ 16, 4 ], [ 16, 5 ], [ 16, 6 ], [ 16, 7 ], [ 16, 8 ], [ 16, 9 ], [ 16, 10 ], [ 16, 11 ], [ 16, 12 ], [ 16, 13 ], [ 16, 14 ] ]
+
+Start parallel computation:
+
+    gap> ParListWithSCSCP(todo,"AllSkewbracesByGroupId");
+    #I  1/14:master --> localhost:26133
+    #I  2/14:master --> localhost:26134
+    #I  3/14:master --> localhost:26135
+    #I  4/14:master --> localhost:26136
+    #I  5/14:master --> localhost:26133
+    #I  6/14:master --> localhost:26133
+    #I  7/14:master --> localhost:26134
+    #I  8/14:master --> localhost:26133
+    #I  9/14:master --> localhost:26134
+    #I  10/14:master --> localhost:26134
+    #I  11/14:master --> localhost:26133
+    #I  12/14:master --> localhost:26135
+    #I  13/14:master --> localhost:26136
+    #I  14/14:master --> localhost:26136
+    [ 8, 83, 191, 190, 66, 66, 80, 144, 80, 161, 227, 118, 152, 39 ]
+
+Each of the workers will produce output files with the name in the 
+format `SBsizeX_Y.dat` in their current directory.

constr/count.g

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+ConstructBrace := function(hol, subgroup)
+  local ab, p, f, g, a, b;
+
+  ab := Image(Embedding(hol, 2));
+
+  p := [];
+  f := IsomorphismPermGroup(ab);
+  g := IsomorphismPermGroup(subgroup);
+
+  for a in ab do
+    if Number(subgroup, x->x*a in Image(Embedding(hol, 1))) <> 1 then
+      return fail;
+    else
+      Add(p, [Image(f,a), Image(g, First(subgroup, x->x*a in Image(Embedding(hol, 1))))]);
+    fi;
+  od;
+
+  return p;
+end;
+
+Brace := function(p)
+  local ab, gr;
+
+  ab := Group(List(p, x->x[1]));
+  gr := Group(List(p, x->x[2]));
+
+  return rec(
+    size := Size(ab),
+    ab := ab,
+    gr := gr, 
+    p := MappingByFunction(ab, gr, x->First(p, y->IsOne(y[1]*Inverse(x)))[2]),
+  );
+end;
+
+BracesWithAdditiveGroup:= function(ab)
+  local aut, hol, c, s , p, l, f, used, m, max;
+
+  aut := AutomorphismGroup(ab);
+  hol := SemidirectProduct(aut, ab);
+
+  l := [];
+  used := [];
+
+  for c in ConjugacyClassesSubgroups(hol) do
+
+    if Size(Representative(c)) <> Size(ab) then
+      continue;
+    fi;
+
+    p := ConstructBrace(hol, Representative(c));
+
+    if not p = fail then
+      Add(l, p);
+    fi;
+  od;
+
+  return l;
+end;
+
+BracesWithAbelianGroupMAXIMAL:= function(ab)
+  local aut, hol, c, s, p, l, f, used, m, max;
+
+  aut := AutomorphismGroup(ab);
+  hol := SemidirectProduct(aut, ab);
+
+  l := [];
+  used := [];
+
+  max := ConjugacyClassesMaximalSubgroups(hol);
+  Print("There are ", Size(max), " conjugacy classes of maximal subgroups\n");
+
+  for m in max do 
+    Print("Checking maximal: ", Position(max, m), " of size ", Size(Representative(m)));
+
+    if Size(Representative(m)) mod Size(ab) <> 0 or IsSolvable(Representative(m)) = false then
+      Print(" - Skipped!\n");
+      continue;
+    else
+      Print("\n");
+    fi;
+
+    f := Filtered(ConjugacyClassesSubgroups(Representative(m)), x->Size(Representative(x)) = Size(ab));
+    for c in f do 
+    for s in c do
+
+      if ForAny(used, x->IsConjugate(Image(Embedding(hol, 1)), s, x)) then
+        continue;
+      fi;
+
+      Add(used, s);
+      p := ConstructBrace(hol, s);
+
+      if not p = fail then
+        Add(l, p);
+      fi;
+    od;
+  od;
+od;
+Print("--\n");
+  return l;
+end;
+
+BracesWithAbelianGroup2 := function(ab)
+  local gr, aut, hol, c, s, p, l, f, used;
+
+  aut := AutomorphismGroup(ab);
+  hol := SemidirectProduct(aut, ab);
+
+  l := [];
+  used := [];
+
+  for gr in AllGroups(Size, Size(ab), IsSolvable, true) do
+    f := List(IsomorphicSubgroups(hol, gr), x->Image(x));
+
+    for s in f do
+
+      if ForAny(used, x->IsConjugate(Image(Embedding(hol, 1)), s, x)) then
+        continue;
+      fi;
+
+      Add(used, s);
+      p := ConstructBrace(hol, s);
+
+      if not p = fail then
+        Add(l, p);
+      fi;
+    od;
+  od;
+  return l;
+end;
+
+MakeList := function(n, l)
+  local k, x;
+
+  Print("## size ", n, "\n");
+  Print("BRACES[", n, "] := rec( total := -1, implemented := ", -1, ", size := ", n, ", brace := [] );\n");
+  for k in [1..Size(l)] do
+    Print("BRACES[", n, "].brace[", k, "] := rec ( size := ", n, ", perms :=\n", l[k] );
+    Print("\n);\n\n");
+  od;
+  return Size(l);
+end;
+
+AllSkewbraces := function(size)
+  local t, x, l, k, ad;
+
+  k := 1;
+  t := 0;
+
+  for ad in AllGroups(Size, size) do
+    Print("id: ", IdGroup(ad), "\n");
+    l := BracesWithAdditiveGroup(Image(IsomorphismPermGroup(ad)));
+    for x in l do
+      LogTo();
+      LogTo(Concatenation("SBsize", String(size), "_", String(k), ".dat"));
+      MakeList(size, l);
+      LogTo();
+      Print("found ", Size(l), "\n");
+      t := t+1;
+    od;
+    k := k+1;
+  od;
+  return t;
+end;
+
+AllSkewbracesByGroupId := function( id )
+  local t, x, l, ad, size, nr;
+
+  size := id[1];
+  nr := id[2];
+  t := 0;
+
+    ad :=SmallGroup( id );
+    Print("id: ", IdGroup(ad), "\n");
+    l := BracesWithAdditiveGroup(Image(IsomorphismPermGroup(ad)));
+    for x in l do
+      LogTo();
+      LogTo(Concatenation("SBsize", String(size), "_", String(nr), ".dat"));
+      MakeList(size, l);
+      LogTo();
+      Print("found ", Size(l), "\n");
+      t := t+1;
+    od;
+
+  return t;
+end;
+
+
+AllBraces := function(size)
+  local x, l, ab;
+
+  l := [];
+
+  for ab in AllGroups(Size, size, IsAbelian, true) do
+    Print("id: ", IdGroup(ab), "\n");
+    for x in BracesWithAdditiveGroup(Image(IsomorphismPermGroup(ab))) do
+      Add(l, x);
+    od;
+  od;
+
+  return l;
+end;
+
+#IsYB := function(group)
+#  local f, s, ab, hol, aut, used;
+#  
+#  if not IsSolvable(group) then
+#    return false;
+#  fi;
+#
+#  for ab in AllGroups(Size, Size(group), IsAbelian, true) do
+#
+#    aut := AutomorphismGroup(ab);
+#    hol := SemidirectProduct(aut, ab);
+#
+#    used := [];
+#
+#    f := IsomorphicSubgroups(hol, group);
+#
+#    if f <> [] then
+#      for s in List(f, x->Image(x)) do
+#
+#        if ForAny(used, x->IsConjugate(Image(Embedding(hol, 1)), s, x)) then
+#          continue;
+#        fi;
+#     
+#        Add(used, s);
+#
+#        if ForAll(Image(Embedding(hol, 2)), a->Number(s, x->x*a in Image(Embedding(hol, 1)))=1) then
+#          return true;
+#        fi;
+#      od;
+#    fi;
+#  od;
+#  return false;
+#end;