rrop.py

import sympy as sp
from sympy.core.expr import Expr

class TP(Expr):
    __slots__ = ['is_commutative']

    def __new__(cls, l, r):
        l = sp.sympify(l)
        r = sp.sympify(r)
        obj = Expr.__new__(cls, l, r)
        obj.is_commutative = False
        return obj

    def __neg__(self):
        return self

    def __mul__(self, other):
        if isinstance(other, TP):
            return TP(self.args[0] * other.args[0], other.args[1] * self.args[1])
        elif other.is_number:
            if other % 2 == 0:
                return 0
            else:
                return self
        else:
            return sp.Mul(self, other)


x, y = sp.symbols('x, y', commutative=False)

Ym = TP(y, 1) - TP(1, y)
Yp = TP(y, 1) + TP(1, y)
Xm = TP(x, 1) - TP(1, x)

d1 = Ym * Yp + Xm * 0
print(d1)
print(sp.expand(d1))

d2 = Xm * Ym
print(d2)
print(sp.expand(d2))