125 lines
3.1 KiB
Plaintext
125 lines
3.1 KiB
Plaintext
Symmetrise := function(elts)
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return Unique(Concatenation(elts, List(elts, Inverse)));
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end;
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MYAllProducts := function(elts1, elts2)
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local products, elt;
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products := [];
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for elt in elts1 do
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products := Concatenation(products, elt*elts2);
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od;
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return products;
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end;
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Products := function(elts, n)
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local products, i;
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if n<=0 then
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return [ ];
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elif n = 1 then
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return elts;
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else
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products := elts;
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for i in [2..n] do
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products := MYAllProducts(elts, products);
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od;
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return products;
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fi;
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end;
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IsSupportedOn := function(basis, elt)
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local elt_supp, x;
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elt_supp := Support(elt);
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for x in elt_supp do
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if not x in basis then
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return false;
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fi;
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od;
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return true;
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end;
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Laplacian := function(G, generating_set)
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local QG, emb, result, S, g, elt;
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QG := GroupRing(Rationals, G);;
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emb := Embedding(G,QG);;
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S := generating_set;
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result := Length(S)*One(QG);
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for g in S do
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result := result - g^emb;
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od;
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return result;
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end;
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Vectorise := function(elt, basis)
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local result, l, i, g, coeff, axis;
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Assert(0, IsSupportedOn(basis, elt),
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"AssertionError: Element of interest is not supported on the basis!");
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result := List(0*[1..Length(basis)]);
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l := CoefficientsAndMagmaElements(elt);
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for i in [1..Length(l)/2] do
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g := l[2*i-1];
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coeff := l[2*i];
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axis := Position(basis, g);
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result[axis] := result[axis] + coeff;
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od;
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return result;
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end;
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Constraints := function(basis)
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local result, i, j, pos;
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result := [];
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for i in [1..Length(basis)] do
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Add(result,[]);
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od;
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for i in [1..Length(basis)] do
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for j in [1..Length(basis)] do
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pos := Position(basis, Inverse(basis[i])*basis[j]);
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if not pos = fail then
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Add(result[pos], [i,j]);
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fi;
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od;
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od;
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return result;
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end;
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SDPGenerateAll := function(G, S, basis, name)
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local QG, emb, delta, delta_sq, delta_vec, delta_sq_vec, product_constr;
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Print("Initializing GroupAlgebra");
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QG := GroupRing(Rationals, G);;
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Print(".");
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emb := Embedding(G,QG);;
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Print("\n");
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Print("Initializing GroupAlgebra elements: ");
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delta := Laplacian(G, S);;
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Print("delta! ");
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delta_sq := delta^2;;
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Print("delta_sq! ");
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Print("\n");
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Print("Check if delta_sq is supported on the given basis: ");
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if not IsSupportedOn(basis, delta_sq) then
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Print("delta_sq is not supported on basis\n");
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return fail;
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else
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Print("it is!\n");
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PrintTo(Concatenation("./basis.", name), basis);
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Print("Written basis to ", Concatenation("./basis.", name), "\n");
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delta_vec := Vectorise(delta, basis);;
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PrintTo(Concatenation("./delta.", name), delta_vec);
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Print("Written delta to ", Concatenation("./delta.", name), "\n");
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delta_sq_vec := Vectorise(delta_sq, basis);;
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PrintTo(Concatenation("./delta_sq.", name), delta_sq_vec);
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Print("Written delta_sq to ", Concatenation("./delta_sq.", name), "\n");
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product_constr := Constraints(basis);;
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PrintTo(Concatenation("./constraints.", name), product_constr);
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Print("Written Matrix Constraints to ", Concatenation("./Constraints.", name), "\n");
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return "Done!";
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fi;
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end;;
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