[Maxima-bugs] [maxima:bugs] Re: #3317 How does solve treat (-1)^(1/3)?

[Barton W. <wil...@us...>]

Using the negative real as the branch cut of the cube root function, we have (-1)^(1/3) = exp(%i * %pi / 3) =/= -1.  So -1 isn't in the solution set of x^(1/3) = -1. For -1 to be in the solution set, we need to use ph(-1) = 3 %pi. Then (-1)^(1/3) = exp(3 * %pi  * %i / 3)   = exp(%pi * %i) = -1.


The to poly solver could be greatly simplified by gutting the logic that imposes a branch for for the non-integer powers along the negative real axis. As I see it, that would make, for example,  %i/2 (and -%i/2) both solutions to


     sqrt(x) + sqrt(-x) = %i.


That is arguably true, but it requires that the two square roots be defined using different branches. That is, I think, problematic.


--Barton
________________________________
From: Robert Dodier <rob...@us...>
Sent: Saturday, July 8, 2017 5:40:53 PM
To: [maxima:bugs]
Subject: [maxima:bugs] #3317 How does solve treat (-1)^(1/3)?


Hmm, I see that to_poly (x^(1/3) = -1, [x]) yields [[%g7+1, x = %g7^3], [-%pi/3 < parg(%g7), parg(%g7) <= %pi/3], []]. Does that seem right?

solve([%g7+1, x = %g7^3], [x, %g7]) yields [[x = - 1, %g7 = - 1]]. I wonder why to_poly_solve doesn't return x = -1.

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[bugs:#3317]<https://urldefense.proofpoint.com/v2/url?u=https-3A__sourceforge.net_p_maxima_bugs_3317_&d=DwMCAg&c=9ZQuuHhOefNvAzlN-3viIA&r=Y-7rxY5GkJ0PrHulpV2qSA&m=2fnU5_5JMMoV90p1xZilYqcpUTnsEGsliUWoqWEvHGo&s=LIGB0HoJtBMT-c5KHOQRJlZWqnkYnulQ_DlncLQzX_I&e=> How does solve treat (-1)^(1/3)?

Status: open
Group: None
Created: Thu Jul 06, 2017 08:53 PM UTC by Stavros Macrakis
Last Updated: Thu Jul 06, 2017 08:53 PM UTC
Owner: Barton Willis

%solve(x^(1/3) = -1) => %union(), regardless of the setting of domain.

Not -1? Is this working as intended?

Maxima version: "5.38.0"
Maxima build date: "2016-04-03 08:56:53"
Host type: "x86_64-apple-darwin15.4.0"
Lisp implementation type: "SBCL"
Lisp implementation version: "1.2.10"

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** [bugs:#3317] How does solve treat (-1)^(1/3)?**

**Status:** open
**Group:** None
**Created:** Thu Jul 06, 2017 08:53 PM UTC by Stavros Macrakis
**Last Updated:** Sat Jul 08, 2017 10:40 PM UTC
**Owner:** Barton Willis


%solve(x^(1/3) = -1) => %union(), regardless of the setting of domain.

Not -1? Is this working as intended?

Maxima version: "5.38.0"
Maxima build date: "2016-04-03 08:56:53"
Host type: "x86_64-apple-darwin15.4.0"
Lisp implementation type: "SBCL"
Lisp implementation version: "1.2.10"



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