Re: [Maxima-discuss] is(somefunction((a*b)^k=a^k*b^k)) -> true

[Barton W. <wi...@un...>]

If maxima can determine that a & b are positive, expand converts (a*b)^k t0 a^k * b^k.  Alternatively, if
k is a declared integer, expand converts (a*b)^k t0 a^k * b^k. But other than that, I don't know of a function that does this transformation.  You could write a few lines of code that does this.

(%i1) xxx : (a*b)^k$

(%i2) expand(xxx);
(%o2) (a*b)^k

(%i3) assume(a>0,b>0)$

(%i4) expand(xxx);
(%o4) a^k*b^k

And of course (removing all assumptions) we need to be careful

(%i28)      zzz : (a*b)^k / (a^k * b^k);
(%o28)      (a*b)^k/(a^k*b^k)

(%i29)      rectform(subst([a=-1,b=-1, k = 1/2],zzz));
(%o29)      -1

--Barton
________________________________
From: Eduardo Ochs <edu...@gm...>
Sent: Saturday, October 28, 2023 14:33
To: <max...@li...> <max...@li...>
Subject: [Maxima-discuss] is(somefunction((a*b)^k=a^k*b^k)) -> true

Non-NU Email
________________________________
Hi list,

is there a function that simplifies, or expands, (a*b)^k to a^k*b^k?
I've tried this,

  o1 : a^k*b^k = (a*b)^k;
  o2 : a^k*b^k + a^k*c^k = a^k*(b^k+c^k);
  is(o1);             /* false */
  is(o2);             /* false */
  is(ratsimp(o1));    /* false */
  is(ratsimp(o2));    /* true */
  is(ratexpand(o1));  /* false */
  is(ratexpand(o2));  /* true */

I've also tried "is(somefunction(o1))" for all somefunctions in:

(info "(maxima)Functions and Variables for Polynomials")
https://maxima.sourceforge.io/docs/manual/maxima_80.html#Functions-and-Variables-for-Polynomials-1<https://urldefense.com/v3/__https://maxima.sourceforge.io/docs/manual/maxima_80.html*Functions-and-Variables-for-Polynomials-1__;Iw!!PvXuogZ4sRB2p-tU!AEVcDbKf-Ba6aW0lje3nge2ADs5p-9fCnCTVqtJApTcnpy7NNUWwR_WJlLpalxodhvEmClT6VbPFGNXv5mA$>

and I couldn't find anything that makes is(somefunction(o1)) return
true...

  Thanks in advance - and I hope I haven't committed any typos in my
  tests...
    Eduardo Ochs
    http://anggtwu.net/eev-maxima.html<https://urldefense.com/v3/__http://anggtwu.net/eev-maxima.html__;!!PvXuogZ4sRB2p-tU!AEVcDbKf-Ba6aW0lje3nge2ADs5p-9fCnCTVqtJApTcnpy7NNUWwR_WJlLpalxodhvEmClT6VbPFBHg0xdY$>