simplifying ( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4) [closed]

epimetheus
31 ●3 ●6 ●11

the sage command

var('x alpha beta Lambda mu')
f(x) = ( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4)
f(x).simplify()

does not give the correct answer g(x)

alpha_x = ((x*f.diff(x)/f).simplify_full()).factor()
g(x) = x^alpha_x

does anyone know why ?

thank you

Philippe

Comments

Coud you please tell us which answer would you expect ?

tmonteil ( 2016-11-27 15:24:07 +0100 )edit

This is what I would expect :

x^(-(Lambda*beta - alpha*mu + 2*alpha - 2*beta - 4*mu + 8)/(mu - 2))

instead of

x^(alpha - beta + 4)/(x^beta)^((Lambda - mu)/(mu - 2))

Thank you

Philippe

epimetheus ( 2016-11-27 17:32:16 +0100 )edit

This is what I would expect :

x^(-(Lambda*beta - alpha*mu + 2*alpha - 2*beta - 4*mu + 8)/(mu - 2))

instead of

x^(alpha - beta + 4)/(x^beta)^((Lambda - mu)/(mu - 2))

Thank you

Philippe

epimetheus ( 2016-11-27 17:33:16 +0100 )edit