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We present a reduction method for Wilson Dirac fermions with non-zerochemical potential which generates a dimensionally reduced fermion matrix. Thesize of the reduced fermion matrix is independent of the temporal latticeextent and the dependence on the chemical potential is factored out. As aconsequence the reduced matrix allows a simple evaluation of the Wilson fermiondeterminant for any value of the chemical potential and hence the exactprojection to the canonical partition functions.

QCD at non-zero density and canonical partition functions with Wilson fermions