How to simplify x^a/x into x^(a-1) OR how to solve...?

asked 2013-07-17 11:05:49 +0100

Qiang
11 ●2

Can any body show me which function simplifies x^a/x into x^(a-1)? A related question is how to solve x^a == 2*x to have x = 2^(1/(a-1))? Mathematica works out these questions well, but I'm a huge fan of Sage/Maxima, and eager to get an answer using Sage. Thanks!

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answered 2013-07-17 12:28:20 +0100

tmonteil
27423 ●31 ●204 ●517 http://wiki.sagemath.o...

updated 2013-07-17 12:34:53 +0100

Concerning your first question, you can try this:

sage: x, a = var('x a') 
sage: expr = x^a/x      
sage: expr.full_simplify()
x^(a - 1)

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Thanks! This works. But how Sage or Maxima solve the above equation still troubles me a lot.

Qiang ( 2013-07-18 05:53:12 +0100 )edit

Yes, i agree that sage: sage: x, a = var('x a') sage: solve(x^a == 2*x, x) [x == 1/2*x^a] is not very satisfactory.

tmonteil ( 2013-07-20 19:12:37 +0100 )edit

While full_simplify works on x^a/x, it already fails as soon as x is replaced by something slightly more complicated, like (1-x).

Gustav Delius ( 2013-08-23 09:35:59 +0100 )edit

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Asked: 2013-07-17 11:05:49 +0100

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Last updated: Jul 17 '13

How to simplify x^a/x into x^(a-1) OR how to solve...? edit