How can I simplify sqrt((n*n-19)*(x**3+x**2*y**5))/sqrt(x**3+x**2*y**5) ?

[hogehoge]

I would like to reduction to common denominator in following case.

sqrt((n*n-19)*(x**3+x**2*y**5))/sqrt(x**3+x**2*y**5) ---> sqrt( n*n - 19 )

 

In [4]: sqrt((n*n-19)*(x**3+x**2*y**5))/sqrt(x**3+x**2*y**5)

Out[4]: 

   ________________________

  ╱ ⎛ 2     ⎞ ⎛ 3    2  5⎞ 

╲╱  ⎝n  - 19⎠⋅⎝x  + x ⋅y ⎠ 

───────────────────────────

         ____________      

        ╱  3    2  5       

      ╲╱  x  + x ⋅y        

In [5]: ratsimp(Out[4])

Out[5]: 

   _____________________________________

  ╱  2  3    2  2  5       3       2  5 

╲╱  n ⋅x  + n ⋅x ⋅y  - 19⋅x  - 19⋅x ⋅y  

────────────────────────────────────────

               ____________             

              ╱  3    2  5              

            ╲╱  x  + x ⋅y       

How can I simplify Out[4]?

In [8]: simplify(Out[4]*Out[4])

Out[8]: 

 2     

n  - 19

But I don't know How to reduction to common denominator in Out[4].

Could you tell me how to reduce to common denominator in Out[4]?

[Aaron Meurer]

SymPy isn't simplifying is because sqrt(x*y) isn't equal to
sqrt(x)*sqrt(y) in general (e.g., if x and y are negative).

You can force this simplification use expand_power_base(force=True):

In [12]: expand_power_base(sqrt((n*n-19)*(x**3+x**2*y**5))/sqrt(x**3+x**2*y**5),
force=True)
Out[12]:
_________
╱ 2
╲╱ n - 19

Aaron Meurer

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[hogehoge]

Thank you very much for your help!

2016年8月1日月曜日 6時14分38秒 UTC+9 Aaron Meurer: