Rational powers and simplification



Am Sonntag, den 30.08.2009, 14:58 +0200 schrieb Stefano Ferri:
> Is something changes in Maxima handling of powers? In older versions I got 
> this:
> 
> (%i1) 4*sqrt(2);
> (%o1) 4*sqrt(2)
> (%i2) 6*sqrt(2);
> (%o2) 6*sqrt(2)
> 
> 
> while in  Maxima 5.19.1 I get:
> 
> (%i1) 4*sqrt(2);
> (%o1) 2^(5/2)
> (%i2) 6*sqrt(2);
> (%o2) 3*2^(3/2)
> 
> I don't want sqrt(2) to be merged with integer powers of 2. I would like to 
> see 4*sqrt(2) and 6*sqrt(2) instead of 2^(5/2) and 3*2^(3/2). Is there a 
> command to do this?

Yes, the behavior has changed because of revision 1.80 of simp.lisp. We
had a longer discussion on the mailing list about this topic.

The handling of powers of integers has been implemented in a more
consistent way. This solved e.g. the following problems which have been
declared to be a bug:

   BUG ID: 721575 2/sqrt(2) doesn\'t simplify
   BUG ID: 2029041 a*sqrt(2)/2 unsimplified
   BUG ID: 1923119 1/sqrt(8)-sqrt(8)/8
   BUG ID: 1927178 integrate(sin(t),t,%pi/4,3*%pi/4)
   BUG ID: 1480562 2*a*2^k isn't simplified to a*2^(k+1)
   BUG ID: 1853191 rat(2/sqrt(2)),algebraic doesn't cancel
   BUG ID: 1996354 unsimplifed result from expand

Please try the following input with an older version and you will see
the following results:

  sqrt(2)*2  --> 2^(3/2)
  sqrt(2)*4  --> 2^(5/2)
  sqrt(2)*6  --> 3*2^(3/2)

You see that 2*sqrt(2) and sqrt(2)*2 are simplified differently in older
versions. This causes a lot of simplification problems. Both expressions
2*sqrt(2) and sqrt(2)*2 now simplifies to the same expression 2^(3/2).

Dieter Kaiser