I have an expression like this one: 4^k/(12^k*A+4^k*B)
Python code is:
import sympy as sy
k,A,B=sy.symbols('k A B',real=True)
C=sy.Rational(4)**k/(sy.Rational(12)**k*A+sy.Rational(4)**k*B)
Is there any SymPy function able to simplify the expression? Something like radcan in MAXIMA. I tried sy.simplify(C), sy.factor(C), sy.powsimp(C), sy.radsimp(C), sy.expand(C) without success.
We need to force the factorisation of the integers which we can do with factorint:
In [46]: C
Out[46]:
k
4
────────────
k k
12 ⋅A + 4 ⋅B
In [47]: C.replace(lambda x: x.is_Integer, lambda x: Mul(*factorint(x, multiple=True), evaluate=False))
Out[47]:
k
(2⋅2)
─────────────────────
k k
A⋅(2⋅2⋅3) + B⋅(2⋅2)
In [48]: expand(_)
Out[48]:
2⋅k
2
──────────────────
2⋅k k 2⋅k
2 ⋅3 ⋅A + 2 ⋅B
In [49]: cancel(_)
Out[49]:
1
────────
k
3 ⋅A + B