CODEWITHSUNDEEP
sympyexponentsimplification
Fabrizio
Fabrizio

Reputation: 81

sympy how to simplify expressions with a variable as exponent

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.

Upvotes: 0

Views: 353

Answers (1)

Oscar Benjamin
Oscar Benjamin

Reputation: 14530

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

Upvotes: 1

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