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

[Richard F. <fa...@gm...>]

radcan(    a^k*b^k -(a*b)^k)   ;
  radcan( a^k*b^k + a^k*c^k - a^k*(b^k+c^k));

both return 0.

radcan makes certain assumptions about branches.  The assumptions might, as
Barton
points out, be wrong.


On Sat, Oct 28, 2023 at 5:23 PM Barton Willis via Maxima-discuss <
max...@li...> wrote:

>
> 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$>
>
> and I couldn't find anything that makes is(somefunction(o1)) return
> true...
>
>   Thanks in advance - and I hope I haven't committed any typos in my
>   tests...
>     Eduardo Ochs
>     http://anggtwu.net/eev-maxima.html
> <https://urldefense.com/v3/__http://anggtwu.net/eev-maxima.html__;!!PvXuogZ4sRB2p-tU!AEVcDbKf-Ba6aW0lje3nge2ADs5p-9fCnCTVqtJApTcnpy7NNUWwR_WJlLpalxodhvEmClT6VbPFBHg0xdY$>
>
> _______________________________________________
> Maxima-discuss mailing list
> Max...@li...
> https://lists.sourceforge.net/lists/listinfo/maxima-discuss
>