How to simplify set expressions with union, intersection, and negation, in python
Question:
Is there any in-built python library that can be used to generate simplified set expressions?
For examples, let’s say, we have a set expression (A∩B)U(A∩C). This can be simplified as A∩(BUC).
Similarly (A∩B)U(A∩!B) can be simplified as A.
I am looking to implement this logic in python. I found that sympy can be used to simplify algebraic expressions like x**2 + 2*x + 1 but I am not sure it handles set expressions.
Answers:
Yes. Set expressions are equivalent to boolean expressions, and sympy can simplify those.
Your examples:
(A∩B)U(A∩C) is equivalent to (a & b) | (a & c),(A∩B)U(A∩!B) is equivalent to (a & b) | (a & ~b),
from sympy import *
a, b, c = symbols('a, b, c')
expr = (a & b) | (a & c)
simplify_logic(expr) # produces: a∧(b∨c)
expr = (a & b) | (a & ~b)
simplify_logic(expr) # produces: a
Some other examples can be found here.
Is there any in-built python library that can be used to generate simplified set expressions?
For examples, let’s say, we have a set expression (A∩B)U(A∩C). This can be simplified as A∩(BUC).
Similarly (A∩B)U(A∩!B) can be simplified as A.
I am looking to implement this logic in python. I found that sympy can be used to simplify algebraic expressions like x**2 + 2*x + 1 but I am not sure it handles set expressions.
Yes. Set expressions are equivalent to boolean expressions, and sympy can simplify those.
Your examples:
(A∩B)U(A∩C)is equivalent to(a & b) | (a & c),(A∩B)U(A∩!B)is equivalent to(a & b) | (a & ~b),
from sympy import *
a, b, c = symbols('a, b, c')
expr = (a & b) | (a & c)
simplify_logic(expr) # produces: a∧(b∨c)
expr = (a & b) | (a & ~b)
simplify_logic(expr) # produces: a
Some other examples can be found here.