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Reduction2.i.m
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Reduction2.i.m
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/*
Bocses - A Magma package for computing with bocses.
By
Julian Külshammer ([email protected])
and
Ulrich Thiel ([email protected])
File: Reduction2.i.m
*/
//==========================================================================
intrinsic Reduction(B::BocsType, X::SeqEnum, e::.) -> SeqEnum
{Reduction of box B at edge e with respect to dimension vector X.}
esourcenum := Position(B`VertexLabels, B`EdgeSources[e]);
etailnum := Position(B`VertexLabels, B`EdgeTails[e]);
x := X[esourcenum];
y := X[etailnum];
Bred := Reduction(B, e);
newboxes := [];
for i:=0 to Minimum({x,y}) do
newX := X;
Append(~newX, i);
newX[esourcenum] := x-i;
newX[etailnum] := y-i;
Append(~newboxes, <Bred, newX>);
end for;
return newboxes;
end intrinsic;
//==========================================================================
intrinsic RemoveZeroEntries(B::BocsType, X::SeqEnum) -> Tup
{}
Bnew := CopyBocs(B);
removed := [];
for i:=1 to #X do
if X[i] eq 0 then
RemoveVertex(~Bnew, B`VertexLabels[i]);
Append(~removed, i);
end if;
end for;
X := [ X[i] : i in [1..#X] | i notin removed ];
return <Bnew, X>;
end intrinsic;
//==========================================================================
intrinsic FindReducibleEdge(BocsXList::SeqEnum) -> BoolElt, RngIntElt, .
{}
for i:=1 to #BocsXList do
B := BocsXList[i][1];
X := BocsXList[i][2];
foundreducible, e := FindReducibleEdge(B);
if foundreducible then
return true, i, e;
end if;
end for;
return false,_,_;
end intrinsic;
//==========================================================================
intrinsic Reduction(BocsXList::SeqEnum : Rounds:=0, Debug:=false) -> SeqEnum
{}
for i:=1 to #BocsXList do
B := BocsXList[i][1];
X := BocsXList[i][2];
L := RemoveZeroEntries(B,X);
Bnew := L[1];
Xnew := L[2];
Bnew := RemoveSuperfluous(Bnew);
BocsXList[i][1] := Bnew;
BocsXList[i][2] := Xnew;
end for;
foundreducible, i, e := FindReducibleEdge(BocsXList);
count := 0;
while foundreducible do
count +:= 1;
B := BocsXList[i][1];
X := BocsXList[i][2];
Remove(~BocsXList, i);
BXnewlist := Reduction(B, X, e);
for j:=1 to #BXnewlist do
Bcur := BXnewlist[j][1];
Xcur := BXnewlist[j][2];
L := RemoveZeroEntries(Bcur,Xcur);
Bnew := L[1];
Xnew := L[2];
Bnew := RemoveSuperfluous(Bnew);
BXnewlist[j] := <Bnew, Xnew>;
end for;
BocsXList cat:= BXnewlist;
foundreducible, i, e := FindReducibleEdge(BocsXList);
PrintAndDelete(Sprint(#BocsXList));
if Rounds ne 0 and count eq Rounds then
return BocsXList;
end if;
end while;
return BocsXList;
end intrinsic;
//==========================================================================
intrinsic Reduction(B::BocsType, X::SeqEnum[RngIntElt] : Rounds:=0, Debug:=true) -> SeqEnum
{Reduction of box B for dimension vector X.}
red := Reduction([<B,X>] : Rounds:=Rounds, Debug:=Debug);
return red;
end intrinsic;