Python: defining my own operators?

While technically you cannot define new operators in Python, this clever hack works around this limitation. It allows you to define infix operators like this:

# simple multiplication
x=Infix(lambda x,y: x*y)
print 2 |x| 4
# => 8

# class checking
isa=Infix(lambda x,y: x.__class__==y.__class__)
print [1,2,3] |isa| []
print [1,2,3] <<isa>> []
# => True

No, Python comes with a predefined, yet overridable, set of operators.

No, you can't create new operators. However, if you are just evaluating expressions, you could process the string yourself and calculate the results of the new operators.

Sage provides this functionality, essentially using the "clever hack" described by @Ayman Hourieh, but incorporated into a module as a decorator to give a cleaner appearance and additional functionality – you can choose the operator to overload and therefore the order of evaluation.

from sage.misc.decorators import infix_operator

@infix_operator('multiply')
def dot(a,b):
    return a.dot_product(b)
u=vector([1,2,3])
v=vector([5,4,3])
print(u *dot* v)
# => 22

@infix_operator('or')
def plus(x,y):
    return x*y
print(2 |plus| 4)
# => 6

See the Sage documentation and this enhancement tracking ticket for more information.