def test_create_f():
i, j, n, m = symbols('i,j,n,m')
o = Fd(i)
assert isinstance(o, CreateFermion)
o = o.subs(i, j)
assert o.atoms(Symbol) == set([j])
o = Fd(1)
assert o.apply_operator(FKet([n])) == FKet([1,n])
assert o.apply_operator(FKet([n])) ==-FKet([n,1])
o = Fd(n)
assert o.apply_operator(FKet([])) == FKet([n])
vacuum = FKet([],fermi_level=4)
assert vacuum == FKet([],fermi_level=4)
i,j,k,l = symbols('i,j,k,l',below_fermi=True)
a,b,c,d = symbols('a,b,c,d',above_fermi=True)
p,q,r,s = symbols('p,q,r,s')
assert Fd(i).apply_operator(FKet([i,j,k],4)) == FKet([j,k],4)
assert Fd(a).apply_operator(FKet([i,b,k],4)) == FKet([a,i,b,k],4)
def test_create_f():
i, j, n, m = symbols('i,j,n,m')
o = Fd(i)
assert isinstance(o, CreateFermion)
o = o.subs(i, j)
assert o.atoms(Symbol) == {j}
o = Fd(1)
assert o.apply_operator(FKet([n])) == FKet([1, n])
assert o.apply_operator(FKet([n])) == -FKet([n, 1])
o = Fd(n)
assert o.apply_operator(FKet([])) == FKet([n])
vacuum = FKet([], fermi_level=4)
assert vacuum == FKet([], fermi_level=4)
i, j, k, l = symbols('i,j,k,l', below_fermi=True)
a, b, c, d = symbols('a,b,c,d', above_fermi=True)
p, q, r, s = symbols('p,q,r,s')
assert Fd(i).apply_operator(FKet([i, j, k], 4)) == FKet([j, k], 4)
assert Fd(a).apply_operator(FKet([i, b, k], 4)) == FKet([a, i, b, k], 4)
assert Dagger(B(p)).apply_operator(q) == q * CreateBoson(p)
assert repr(Fd(p)) == 'CreateFermion(p)'
assert srepr(Fd(p)) == "CreateFermion(Symbol('p'))"
assert latex(Fd(p)) == r'a^\dagger_{p}'
def test_annihilate_f():
i, j, n, m = symbols('i,j,n,m')
o = F(i)
assert isinstance(o, AnnihilateFermion)
o = o.subs(i, j)
assert o.atoms(Symbol) == {j}
o = F(1)
assert o.apply_operator(FKet([1, n])) == FKet([n])
assert o.apply_operator(FKet([n, 1])) == -FKet([n])
o = F(n)
assert o.apply_operator(FKet([n])) == FKet([])
i, j, k, l = symbols('i,j,k,l', below_fermi=True)
a, b, c, d = symbols('a,b,c,d', above_fermi=True)
p, q, r, s = symbols('p,q,r,s')
assert F(i).apply_operator(FKet([i, j, k], 4)) == 0
assert F(a).apply_operator(FKet([i, b, k], 4)) == 0
assert F(l).apply_operator(FKet([i, j, k], 3)) == 0
assert F(l).apply_operator(FKet([i, j, k], 4)) == FKet([l, i, j, k], 4)
assert str(F(p)) == 'f(p)'
assert repr(F(p)) == 'AnnihilateFermion(p)'
assert srepr(F(p)) == "AnnihilateFermion(Symbol('p'))"
assert latex(F(p)) == 'a_{p}'
def test_annihilate_f():
i, j, n, m = symbols('i j n m')
o = F(i)
assert isinstance(o, AnnihilateFermion)
o = o.subs(i, j)
assert o.atoms(Symbol) == set([j])
o = F(1)
assert o.apply_operator(FKet([1, n])) == FKet([n])
assert o.apply_operator(FKet([n, 1])) == -FKet([n])
o = F(n)
assert o.apply_operator(FKet([n])) == FKet([])
i, j, k, l = symbols('ijkl', below_fermi=True)
a, b, c, d = symbols('abcd', above_fermi=True)
p, q, r, s = symbols('pqrs')
assert F(i).apply_operator(FKet([i, j, k], 4)) == 0
assert F(a).apply_operator(FKet([i, b, k], 4)) == 0
assert F(l).apply_operator(FKet([i, j, k], 3)) == 0
assert F(l).apply_operator(FKet([i, j, k], 4)) == FKet([l, i, j, k], 4)