op_with_no_indices = 1*C^+() + 1*C() + -1*C^+()C()
op_with_many_indices = 1*C^+(3,15,b,0,-5) + 1*C(1,2,a,1,-2)

Anticommutators:
{1*C^+(1), 1*C(1)} = 1
{1*C^+(1), 1*C(2)} = 0
{1*C^+(1), 1*C(3)} = 0
{1*C^+(2), 1*C(1)} = 0
{1*C^+(2), 1*C(2)} = 1
{1*C^+(2), 1*C(3)} = 0
{1*C^+(3), 1*C(1)} = 0
{1*C^+(3), 1*C(2)} = 0
{1*C^+(3), 1*C(3)} = 1

Commutators:
[1*C^+(1), 1*C(1)] = -1 + 2*C^+(1)C(1)
[1*C^+(1), 1*C(2)] = 2*C^+(1)C(2)
[1*C^+(1), 1*C(3)] = 2*C^+(1)C(3)
[1*C^+(2), 1*C(1)] = 2*C^+(2)C(1)
[1*C^+(2), 1*C(2)] = -1 + 2*C^+(2)C(2)
[1*C^+(2), 1*C(3)] = 2*C^+(2)C(3)
[1*C^+(3), 1*C(1)] = 2*C^+(3)C(1)
[1*C^+(3), 1*C(2)] = 2*C^+(3)C(2)
[1*C^+(3), 1*C(3)] = -1 + 2*C^+(3)C(3)

Algebra:
x = 1*C(0)
y = 1*C^+(1)
-x = -1*C(0)
x + 2.0 = 2 + 1*C(0)
2.0 + x = 2 + 1*C(0)
x - 2.0 = -2 + 1*C(0)
2.0 - x = 2 + -1*C(0)
3.0*y = 3*C^+(1)
y*3.0 = 3*C^+(1)
x + y = 1*C^+(1) + 1*C(0)
x - y = -1*C^+(1) + 1*C(0)
(x + y)*(x - y) = 2*C^+(1)C(0)

N^3:
N = 1*C^+(dn)C(dn) + 1*C^+(up)C(up)
N^3 = 1*C^+(dn)C(dn) + 1*C^+(up)C(up) + 6*C^+(dn)C^+(up)C(up)C(dn)
New N^3 = 1*C^+(dn)C(dn) + 1*C^+(up)C(up) + 6*C^+(dn)C^+(up)C(up)C(dn)
X = -1*C^+(1)C^+(2)C(4)C(3)
dagger(X) = -1*C^+(3)C^+(4)C(2)C(1)