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##
## Takes an Majorana representation <rep> and an integer <index> that corresponds to
## an orbit of algebra products (given by rep.setup.pairreps[ index ])
##
InstallGlobalFunction(MAJORANA_NClosedSetUp,
function(rep, index)
local unknowns, dim, new_dim, x, elts, k, i, j, ev, gens, pos, sign, new;
dim := Size(rep.setup.coords);
# Add all products that are in the chosen orbit
for i in [1..dim] do
for j in [i..dim] do
if rep.setup.pairorbit[i, j] in [index, -index] then
Add(rep.setup.coords, [i,j]);
rep.setup.coordmap[[i,j]] := Size(rep.setup.coords);
fi;
od;
od;
# Extend all permutations that are stored in the setup record
for x in rep.setup.pairconjelts do MAJORANA_ExtendPerm(x, rep); od;
for x in rep.setup.conjelts do MAJORANA_ExtendPerm(x, rep); od;
for x in rep.generators do MAJORANA_ExtendPerm(x, rep); od;
new_dim := Size(rep.setup.coords);
# Extend the matrices of pairorbit and pairconj
for i in [1..dim] do
Append(rep.setup.pairorbit[i], [dim + 1 .. new_dim]*0);
Append(rep.setup.pairconj[i], [dim + 1 .. new_dim]*0);
od;
Append(rep.setup.pairorbit, NullMat(new_dim - dim, new_dim));
Append(rep.setup.pairconj, NullMat(new_dim - dim, new_dim));
# Calculate the new orbital
MAJORANA_Orbitals(rep.generators, dim, rep.setup);
# Add the new algebra product for the chosen orbit
pos := rep.setup.coordmap[rep.setup.pairreps[index]];
rep.algebraproducts[index] := SparseMatrix(1, new_dim, [[pos]], [[1]], Rationals);
# Adjust the existing algebra products and eigenvectors
for i in [1..Size(rep.algebraproducts)] do
if not rep.algebraproducts[i] in [false, fail] then
rep.algebraproducts[i]!.ncols := new_dim;
fi;
od;
for i in [Size(rep.algebraproducts) + 1 .. Size(rep.setup.pairreps)] do
rep.algebraproducts[i] := false;
if IsBound(rep.innerproducts) then rep.innerproducts[i] := false; fi;
od;
for i in rep.setup.orbitreps do
for ev in RecNames(rep.evecs[i]) do
rep.evecs[i].(ev)!.ncols := new_dim;
od;
od;
MAJORANA_NClosedNullspace(rep);
end );
##
## Takes the last linear system outputted by the main algorithm and uses it
## to create new nullspace vectors
##
InstallGlobalFunction( MAJORANA_NClosedNullspace,
function(rep)
local i, j, v, x, pos;
# Adjust the matrices of the system to the new spanning set
rep.system.vec!.ncols := Size(rep.setup.coords);
rep.setup.nullspace.vectors!.ncols := Size(rep.setup.coords);
for i in [1..Nrows(rep.system.mat)] do
# If the row of the matrix involves only products that are in the new spanning set
if ForAll(rep.system.mat!.indices[i], x -> rep.system.unknowns[x] in rep.setup.coords) then
# The vector <v> will be the new nullspace vector
v := CertainRows(rep.system.vec, [i]);
for j in [1..Size(rep.system.mat!.indices[i])] do
# Add any coefficients coming from the matrix of the system
x := rep.system.mat!.indices[i, j];
pos := Position(rep.setup.coords, rep.system.unknowns[x]);
SetEntry(v, 1, pos, -rep.system.mat!.entries[i, j]);
rep.setup.nullspace.vectors := MAJORANA_UnionOfRows(rep.setup.nullspace.vectors, v);
od;
fi;
od;
rep.setup.nullspace := ReversedEchelonMatDestructive(rep.setup.nullspace.vectors);
end );
InstallGlobalFunction( NClosedMajoranaRepresentation,
function(rep)
local products, unknowns;
# Find the positions of the unknown algebra products
products := Positions(rep.algebraproducts, false);
if products = [] then return; fi;
# Added the first of these products to the spanning set of the algebra
MAJORANA_NClosedSetUp(rep, products[1]);
while true do
unknowns := Positions(rep.algebraproducts, false);
MAJORANA_MainLoop(rep);
Info(InfoMajorana, 20, STRINGIFY( "There are ", Size(Positions(rep.algebraproducts, false)), " unknown algebra products ") );
if IsBound(rep.innerproducts) then
Info(InfoMajorana, 20, STRINGIFY( "There are ", Size(Positions(rep.innerproducts, false)), " unknown inner products ") );
fi;
if not false in rep.algebraproducts then
Info( InfoMajorana, 10, "Success" );
return;
fi;
# If no more algebra products have been found then add the next unknown product to the
# spanning set of the algebra and run the algorithm again. If all products have been
# used then quit with a fail.
if ForAll(rep.algebraproducts{unknowns}, x -> x = false) then
products := Filtered(products, x -> rep.algebraproducts[x] = false);
if products = [] then
Info( InfoMajorana, 10, "Fail" );
return;
else
MAJORANA_NClosedSetUp(rep, products[1]);
fi;
fi;
od;
end );
[ Dauer der Verarbeitung: 0.31 Sekunden
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