[Maxima-bugs] [ maxima-Bugs-3485031 ] rootscontract anomaly

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Bugs item #3485031, was opened at 2012-02-06 09:28
Message generated for change (Comment added) made by aleksasd
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Category: Lisp Core - Polynomials
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Stavros Macrakis (macrakis)
Assigned to: Nobody/Anonymous (nobody)
Summary: rootscontract anomaly

Initial Comment:
ex: (sqrt(2)+1)^(2/3)$

rootscontract(ex)=> (sqrt(2)+1)^(2/3)    <<< does nothing
rootscontract(2*ex) => 2*(2^(3/2)+3)^(1/3)   <<< squares the inner expression

Though the documentation is not explicit about what it should do in this case (it only talks about products of roots, not about powers of roots), the second behavior is more useful -- if it isn't provided by rootscontract, it should be provided by *some* function.

Practical result of this anomaly:

   rootscontract(    (2^(3/2)+3)^(1/3)-(sqrt(2)+1)^(2/3)   )  => 0  (I don't know any other way to do this simplification in Maxima)
but
   rootscontract( -( (2^(3/2)+3)^(1/3)-(sqrt(2)+1)^(2/3) ))     => remains unsimplified


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Comment By: Aleksas (aleksasd)
Date: 2012-02-06 22:38

Message:
(%i1) r:(sqrt(2)+1)^(2/3)$

(%i2) r=expand(r^3)^(1/3);
(%o2) (sqrt(2)+1)^(2/3)=(2^(3/2)+3)^(1/3)

(%i3) 2*r=expand((2*r)^3)^(1/3);
(%o3) 2*(sqrt(2)+1)^(2/3)=(2^(9/2)+24)^(1/3)

Aleksas

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