def test_sorting():
i, j = symbols("i,j", below_fermi=True)
a, b = symbols("a,b", above_fermi=True)
p, q = symbols("p,q")
# p, q
assert _sort_anticommuting_fermions([Fd(p), F(q)]) == ([Fd(p), F(q)], 0)
assert _sort_anticommuting_fermions([F(p), Fd(q)]) == ([Fd(q), F(p)], 1)
# i, p
assert _sort_anticommuting_fermions([F(p), Fd(i)]) == ([F(p), Fd(i)], 0)
assert _sort_anticommuting_fermions([Fd(i), F(p)]) == ([F(p), Fd(i)], 1)
assert _sort_anticommuting_fermions([Fd(p), Fd(i)]) == ([Fd(p), Fd(i)], 0)
assert _sort_anticommuting_fermions([Fd(i), Fd(p)]) == ([Fd(p), Fd(i)], 1)
assert _sort_anticommuting_fermions([F(p), F(i)]) == ([F(i), F(p)], 1)
assert _sort_anticommuting_fermions([F(i), F(p)]) == ([F(i), F(p)], 0)
assert _sort_anticommuting_fermions([Fd(p), F(i)]) == ([F(i), Fd(p)], 1)
assert _sort_anticommuting_fermions([F(i), Fd(p)]) == ([F(i), Fd(p)], 0)
# a, p
assert _sort_anticommuting_fermions([F(p), Fd(a)]) == ([Fd(a), F(p)], 1)
assert _sort_anticommuting_fermions([Fd(a), F(p)]) == ([Fd(a), F(p)], 0)
assert _sort_anticommuting_fermions([Fd(p), Fd(a)]) == ([Fd(a), Fd(p)], 1)
assert _sort_anticommuting_fermions([Fd(a), Fd(p)]) == ([Fd(a), Fd(p)], 0)
assert _sort_anticommuting_fermions([F(p), F(a)]) == ([F(p), F(a)], 0)
assert _sort_anticommuting_fermions([F(a), F(p)]) == ([F(p), F(a)], 1)
assert _sort_anticommuting_fermions([Fd(p), F(a)]) == ([Fd(p), F(a)], 0)
assert _sort_anticommuting_fermions([F(a), Fd(p)]) == ([Fd(p), F(a)], 1)
# i, a
assert _sort_anticommuting_fermions([F(i), Fd(j)]) == ([F(i), Fd(j)], 0)
assert _sort_anticommuting_fermions([Fd(j), F(i)]) == ([F(i), Fd(j)], 1)
assert _sort_anticommuting_fermions([Fd(a), Fd(i)]) == ([Fd(a), Fd(i)], 0)
assert _sort_anticommuting_fermions([Fd(i), Fd(a)]) == ([Fd(a), Fd(i)], 1)
assert _sort_anticommuting_fermions([F(a), F(i)]) == ([F(i), F(a)], 1)
assert _sort_anticommuting_fermions([F(i), F(a)]) == ([F(i), F(a)], 0)
def test_sorting():
i, j = symbols('i,j', below_fermi=True)
a, b = symbols('a,b', above_fermi=True)
p, q = symbols('p,q')
# p, q
assert _sort_anticommuting_fermions([Fd(p), F(q)]) == ([Fd(p), F(q)], 0)
assert _sort_anticommuting_fermions([F(p), Fd(q)]) == ([Fd(q), F(p)], 1)
# i, p
assert _sort_anticommuting_fermions([F(p), Fd(i)]) == ([F(p), Fd(i)], 0)
assert _sort_anticommuting_fermions([Fd(i), F(p)]) == ([F(p), Fd(i)], 1)
assert _sort_anticommuting_fermions([Fd(p), Fd(i)]) == ([Fd(p), Fd(i)], 0)
assert _sort_anticommuting_fermions([Fd(i), Fd(p)]) == ([Fd(p), Fd(i)], 1)
assert _sort_anticommuting_fermions([F(p), F(i)]) == ([F(i), F(p)], 1)
assert _sort_anticommuting_fermions([F(i), F(p)]) == ([F(i), F(p)], 0)
assert _sort_anticommuting_fermions([Fd(p), F(i)]) == ([F(i), Fd(p)], 1)
assert _sort_anticommuting_fermions([F(i), Fd(p)]) == ([F(i), Fd(p)], 0)
# a, p
assert _sort_anticommuting_fermions([F(p), Fd(a)]) == ([Fd(a), F(p)], 1)
assert _sort_anticommuting_fermions([Fd(a), F(p)]) == ([Fd(a), F(p)], 0)
assert _sort_anticommuting_fermions([Fd(p), Fd(a)]) == ([Fd(a), Fd(p)], 1)
assert _sort_anticommuting_fermions([Fd(a), Fd(p)]) == ([Fd(a), Fd(p)], 0)
assert _sort_anticommuting_fermions([F(p), F(a)]) == ([F(p), F(a)], 0)
assert _sort_anticommuting_fermions([F(a), F(p)]) == ([F(p), F(a)], 1)
assert _sort_anticommuting_fermions([Fd(p), F(a)]) == ([Fd(p), F(a)], 0)
assert _sort_anticommuting_fermions([F(a), Fd(p)]) == ([Fd(p), F(a)], 1)
# i, a
assert _sort_anticommuting_fermions([F(i), Fd(j)]) == ([F(i), Fd(j)], 0)
assert _sort_anticommuting_fermions([Fd(j), F(i)]) == ([F(i), Fd(j)], 1)
assert _sort_anticommuting_fermions([Fd(a), Fd(i)]) == ([Fd(a), Fd(i)], 0)
assert _sort_anticommuting_fermions([Fd(i), Fd(a)]) == ([Fd(a), Fd(i)], 1)
assert _sort_anticommuting_fermions([F(a), F(i)]) == ([F(i), F(a)], 1)
assert _sort_anticommuting_fermions([F(i), F(a)]) == ([F(i), F(a)], 0)
