I want to create a 2-D matrix of binary variables x. For now I do it like this: x = IndexedBase('x', shape=(imax,jmax), integer=True)

For a binary variable, the following identity holds: x_i**n == x_i for n>0, and I want to make use of this identity for simplifying my expressions later on. Therefore, the 'integer' assumption should be replaced with a "stronger" 'binary' assumption.

Creating a single binary variable works (Ref: ):

from sympy import *

class Binary(Symbol):
    def _eval_power(self, other):
        return self

x0 = Binary('x0')
x0**2 == x0

Output: True

What I'm struggling with right now is creating an IndexedBase object where its entries are instances of my Binary class rather than of Symbol. Looking at .html#sympy.tensor.indexed.IndexedBase I saw that assumptions can be inherited if a Symbol is used to initialize the IndexedBase, which led me to unsuccessfully try the following:

x = symbols('x', cls=Binary)
x = IndexedBase(x)

x[0,0]**2 == x[0,0]

Output: False (expected True)

Is there another way to get IndexedBase to use my custom Binary class?

Many thanks in advance!

I want to create a 2-D matrix of binary variables x. For now I do it like this: x = IndexedBase('x', shape=(imax,jmax), integer=True)

For a binary variable, the following identity holds: x_i**n == x_i for n>0, and I want to make use of this identity for simplifying my expressions later on. Therefore, the 'integer' assumption should be replaced with a "stronger" 'binary' assumption.

Creating a single binary variable works (Ref: https://stackoverflow.com/a/73953040/7740977):

from sympy import *

class Binary(Symbol):
    def _eval_power(self, other):
        return self

x0 = Binary('x0')
x0**2 == x0

Output: True

What I'm struggling with right now is creating an IndexedBase object where its entries are instances of my Binary class rather than of Symbol. Looking at https://docs.sympy.org/latest/modules/tensor/indexed.html#sympy.tensor.indexed.IndexedBase I saw that assumptions can be inherited if a Symbol is used to initialize the IndexedBase, which led me to unsuccessfully try the following:

x = symbols('x', cls=Binary)
x = IndexedBase(x)

x[0,0]**2 == x[0,0]

Output: False (expected True)

Is there another way to get IndexedBase to use my custom Binary class?

Many thanks in advance!

• python
• binary
• sympy
• symbolic-math

1 Answer 1

It's a different strategy, but instead of defining custom Symbol properties, you may be able to .replace() away exponentiation instead

• custom Symbol can be simplified
• define Wilds which are broad enough, but won't match nested instances

class Binary(Symbol):
    pass

a = Wild("a", properties=[lambda a: isinstance(a, Indexed) and a.atoms(Binary)])
b = Wild("b", properties=[lambda b: isinstance(b, Number)])

Now set up the problem and use .replace()

>>> x = Binary("x")
>>> A = IndexedBase(x)
>>> expr = A[0,0]
>>> expr
x[0, 0]
>>> expr = expr**2
>>> expr
x[0, 0]**2
>>> srepr(expr)  # NOTE the Indexed wrapper
"Pow(Indexed(IndexedBase(Binary('x')), Integer(0), Integer(0)), Integer(2))"
>>> expr.replace(Pow(a, b), lambda a, b: a)
x[0, 0]

If you're passing this on to someone else, consider a custom function to make it look cleaner and a docstring, but .replace() + Wild are surprisingly powerful and can reach into all sorts of expressions

>>> expr = Integral(5*A[0,0]**2 + sin(A[0,1]**3), x)  # not meaningful
>>> expr  
Integral(sin(x[0, 1]**3) + 5*x[0, 0]**2, x)
>>> expr.replace(Pow(a, b), lambda a, b: a)
Integral(sin(x[0, 1]) + 5*x[0, 0], x)