I have the following identity:
1 = a + b + c
Supose that I have the expression:
expr = x*(a + b + c)
It can be simplified as x.
Is there a way to declare it to SymPy so it can simplify them? Actually I do the job mannualy:
>>> import sympy
>>> sympy.vars("x a b c")
>>> expr = x*(a + b + c)
>>> expr.subs(a + b + c, 1)
x
The ratsimpmodprime function will work in your case. It simplifies a rational function with respect to some polynomials that are assumed to be equal to zero:
In [13]: a, b, c, x = symbols('a, b, c, x')
In [14]: polys = [a + b + c - 1]
In [15]: basis = groebner(polys).polys
In [16]: ratsimpmodprime(x*(a + b + c), basis)
Out[16]: x
https://docs.sympy.org/latest/modules/simplify/simplify.html#ratsimpmodprime