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InstallGlobalFunction(TensorProductOfChainComplexes,
function(arg)
local TensorProductOfTwoChainComplexes,
i,LR,R;
TensorProductOfTwoChainComplexes := function(R,S)
local
rdim,rbound,sdim,sbound,N,
Dimen,Bound,count,n,k,M,i,j,ii,jj,x,Rew,beg1,beg2,LH,LV,
dim,SearchPosition,dhr,dvs,
Dimension,Boundary;
########################## Modified by Graham
rdim := function(n);
if n<0 or n> Length(R) then return 0; fi;
return R!.dimension(n);
end;
##########################
rbound := R!.boundary;
########################## Modified by Graham
sdim := function(n);
if n<0 or n> Length(S) then return 0; fi;
return S!.dimension(n);
end;
##########################
sbound := S!.boundary;
#N := Minimum(EvaluateProperty(R,"length"),EvaluateProperty(S,"length")); #CHANGED BY GRAHAM
N := 1+EvaluateProperty(R,"length")+EvaluateProperty(S,"length");
##############################################
dim := function(i,j)
if i<0 or j <0 then
return 0;
fi;
return rdim(i)*sdim(j);
end;
###############################################
Dimen := [];
for n in [0..N] do
count := 0;
for j in [0..n] do;
count := count+dim(n-j,j);
od;
Dimen[n+1] := count;
od;
######################################################
Dimension := function(n)
return Dimen[n+1];
end;
###################################################
###################################################
SearchPosition := function(n,k)
local count,ord,j,b,x,ii,jj;
if k>Dimension(n) then
return fail;
fi;
count := 0;
for j in [0..n] do
ord := k-count;
count := count+dim(n-j,j);
if k <=count then
b := sdim(j);
x := Int((ord-1)/b);
ii := x+1;
jj := ord-x*b;
return [n-j,j,ii,jj];
break;
fi;
od;
end;
########################################################
########################################################
dhr := function(i,j,ii,jj)
local a,b,L,x,LR;
if i=0 then
return [];
fi;
a := rdim(i-1);
b := sdim(j);
L := List([1..a*b],x->0);
LR := rbound(i,ii);
for x in [1..a] do
L[(x-1)*b+jj] := LR[x];
od;
return L;
end;
########################################################
dvs := function(i,j,ii,jj)
local a,b,L,x,LS,sign;
if j =0 then
return [];
fi;
if (i mod 2)=0 then
sign := 1;
else
sign := -1;
fi;
a := rdim(i);
b := sdim(j-1);
L := List([1..a*b],x->0);
LS := sbound(j,jj);
for x in [1..b] do
L[(ii-1)*b+x] := sign*LS[x];
od;
return L;
end;
##########################################################
Bound := List([0..N],x->[]);
Bound[1][1] := [0];
for n in [1..N] do
for k in [1..Dimension(n)] do
M := SearchPosition(n,k);
i := M[1];
j := M[2];
ii := M[3];
jj := M[4];
Rew := List([1..Dimension(n-1)],x->0);
beg1 := 0;
for x in [0..(j-2)] do
beg1 := beg1+ dim((n-1)-x,x);
od;
beg2 := beg1+ dim(i,j-1);
LV := dvs(i,j,ii,jj);
LH := dhr(i,j,ii,jj);
for x in [1..dim(i,j-1)]do
Rew[beg1+x] := LV[x];
od;
for x in [1..dim(i-1,j)] do
Rew[beg2+x] := LH[x];
od;
Bound[n+1][k] := Rew;
od;
od;
################################################################
Boundary := function(n,k)
return Bound[n+1][k];
end;
################################################################
return Objectify( HapChainComplex, rec(
boundary := Boundary,
dimension := Dimension,
properties := [ [ "length",N-1],
[ "type", "chainComplex" ],
[ "characteristic",0 ] ] ) );
end;
################################################################
if Length(arg)=1 then
LR := arg[1];
if IsList(LR) then
R := LR[1];
for i in [2..Length(LR)] do
R := TensorProductOfTwoChainComplexes(R,LR[i]);
od;
return R;
else
return LR;
fi;
else
R := arg[1];
for i in [2..Length(arg)] do
R := TensorProductOfTwoChainComplexes(R,arg[i]);
od;
return R;
fi;
end);
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