#############################################################################
####
##
#W anupqxdesc.gi ANUPQ package Werner Nickel
#W Greg Gamble
##
## Installs functions to do recursive development of a descendants tree.
## If ANUPQ is loaded from XGAP the development is seen graphically.
##
#Y Copyright (C) 2001 Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany
##
#############################################################################
##
#F PqDescendantsTreeCoclassOne([<i>]) . . . generate a coclass one des. tree
##
## for the <i>th or default interactive {\ANUPQ} process, generates a
## descendant tree for the group of the process (which must be a pc
## $p$-group) consisting of descendants of $p$-coclass 1 and extending to
## the class determined by the option `TreeDepth' (or 6 if the option is
## omitted). In an {\XGAP} session, a graphical representation of the
## descendants tree appears in a separate window. Subsequent calls to
## `PqDescendantsTreeCoclassOne' for the same process may be used to extend
## the descendant tree from the last descendant computed that itself has
## more than one descendant. `PqDescendantsTreeCoclassOne' also accepts the
## options `CapableDescendants' (or `AllDescendants') and any options
## accepted by the interactive `PqDescendants' function
## (see~"PqDescendants!interactive").
##
## *Notes*
##
## `PqDescendantsTreeCoclassOne' first calls `PqDescendants'. If
## `PqDescendants' has already been called for the process, the previous
## value computed is used and a warning is `Info'-ed at `InfoANUPQ" level 1.
##
## As each descendant is processed its unique label defined by the `pq'
## program and number of descendants is `Info'-ed at `InfoANUPQ' level 1.
##
## `PqDescendantsTreeCoclassOne' is an ``experimental'' function that is
## included to demonstrate the sort of things that are possible with the
## $p$-group generation machinery.
##
InstallGlobalFunction( PqDescendantsTreeCoclassOne, function( arg )
local datarec, title, des, node;
datarec := ANUPQ_ARG_CHK("PqDescendantsTreeCoclassOne", arg);
if datarec.procId = 0 then
Error("non-interactive `PqDescendantsTreeCoclassOne' is not ",
"currently supported\n");
fi;
if IsBound(datarec.treepos) then
PQX_RECURSE_DESCENDANTS( datarec,
datarec.treepos.class,
datarec.treepos.node,
datarec.treepos.ndes );
return;
fi;
des := PqDescendants( datarec.procId : StepSize := 1 );
if IsPackageMarkedForLoading("xgap","") then
title := Concatenation( "Descendants Tree, p=",
String( PrimePGroup(datarec.group) ),
", order: ",
String( Size(datarec.group) ),
", class <= ",
String( VALUE_PQ_OPTION("TreeDepth", 6, datarec) ) );
if VALUE_PQ_OPTION("CapableDescendants",
not VALUE_PQ_OPTION("AllDescendants", true, datarec),
datarec) then
Append( title, ", capable descendants" );
else
Append( title, ", all descendants" );
fi;
datarec.xgapsheet := GraphicSheet( title, 800, 700 );
datarec.nextX := [0, 0];
node := PQX_PLACE_NEXT_NODE( datarec, 1 );
else
node := 0;
fi;
PQX_RECURSE_DESCENDANTS( datarec, 2, node, Length(des) );
if datarec.calltype = "non-interactive" then
PQ_COMPLETE_NONINTERACTIVE_FUNC_CALL(datarec);
if IsBound( datarec.setupfile ) then
return true;
fi;
fi;
end);
#############################################################################
##
#F PQX_PLACE_NEXT_NODE( <datarec>, <class> ) . place a node on an XGAP sheet
##
## places a node for the current descendant of class <class> on the {\XGAP}
## sheet `<datarec>.xgapsheet'.
##
InstallGlobalFunction( PQX_PLACE_NEXT_NODE, function( datarec, class )
local y, x;
y := 40 * class;
datarec.nextX[class] := datarec.nextX[class] + 16;
x := datarec.nextX[class];
Disc( datarec.xgapsheet, x, y, 6 );
return [x,y];
end);
#############################################################################
##
#F PQX_MAKE_CONNECTION( <datarec>, <a>, <b> ) . . join two XGAP sheet nodes
##
## joins the nodes <a> and <b> on the {\XGAP} sheet `<datarec>.xgapsheet'
## with a straight line, where <a> and <b> are each `[<x>, <y>]' coordinate
## pairs (lists) of integers.
##
InstallGlobalFunction( PQX_MAKE_CONNECTION, function( datarec, a, b )
Line( datarec.xgapsheet, a[1], a[2], b[1]-a[1], b[2]-a[2] );
end);
#############################################################################
##
#F PQX_RECURSE_DESCENDANTS(<datarec>,<class>,<parent>,<n>) extend des. tree
##
## extends a descendant tree of coclass 1 descendants from the current `pq'
## descendant that has <n> descendants from class <class> to class
## determined by the option `TreeDepth' (or 6, by default) from the node
## <parent> which is an `[<x>, <y>]' coordinate pair (list) of integers.
##
InstallGlobalFunction( PQX_RECURSE_DESCENDANTS,
function( datarec, class, parent, n)
local i, node, nr;
if class > VALUE_PQ_OPTION("TreeDepth", 6, datarec) then
datarec.treepos := rec(class:=class, node:=parent, ndes:=n);
return;
fi;
if parent <> 0 then
datarec.nextX[class] := datarec.nextX[class] + 14;
fi;
for i in [1..n] do
PQ_PG_RESTORE_GROUP( datarec, class, i );
PQ_PG_EXTEND_AUTOMORPHISMS( datarec );
nr := PqPGConstructDescendants( datarec.procId : StepSize := 1 );
if parent <> 0 and (not datarec.CapableDescendants or nr > 0) then
# Place a node on the Graphic Sheet and connect it with its
# parent node.
node := PQX_PLACE_NEXT_NODE( datarec, class );
PQX_MAKE_CONNECTION( datarec, node, parent );
else
node := 0;
fi;
Info(InfoANUPQ, 1, "Number of descendants of group ", datarec.gpnum,
" to class ", class, ": ", nr);
if nr > 0 then
if IsBound(datarec.nextX) and
not IsBound(datarec.nextX[class + 1]) then
datarec.nextX[class + 1] := 0;
fi;
PQX_RECURSE_DESCENDANTS( datarec, class+1, node, nr );
fi;
od;
return;
end);
#E anupqxdesc.gi . . . . . . . . . . . . . . . . . . . . . . . . . ends here
