[Maxima-bugs] [ maxima-Bugs-711885 ] Rootscontract with imaginaries fails

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Bugs item #711885, was opened at 2003-03-29 19:18
Message generated for change (Comment added) made by crategus
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Category: Lisp Core
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Stavros Macrakis (macrakis)
Assigned to: Nobody/Anonymous (nobody)
Summary: Rootscontract with imaginaries fails

Initial Comment:
q: ((SQRT(3)*%I+1)^(3/2)-4*%I)/SQRT(SQRT(3)*%I+1)

rootscontract(q) gives the error "SIGN called on an 
imaginary argument".

The error happens within SIMPEXPT, which is not 
prepared to deal with (1/(SQRT(-3)+1))^(1/2) in the form 
((MEXPT)
 ((MEXPT SIMP)
  ((MPLUS SIMP)
   1
   ((MEXPT SIMP) -3 ((RAT SIMP) 1 2)))
  -1)
 ((RAT) 1 2))

Maxima 5.9.0 GCL 2.5.0 Windows 2000


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>Comment By: Dieter Kaiser (crategus)
Date: 2009-08-30 16:24

Message:
I had a further look at the problem.

First, I think that

((MEXPT SIMP) ((MPLUS SIMP) 1 ((MEXPT SIMP) -3 ((RAT SIMP) 1 2))) -1)

is a valid expression. It is generated by

(%i20) (1/(1+sqrt(-3))),radexpand:false;
(%o20) 1/(sqrt(-3)+1)

The problem is the function sign, which can not handle complex
expressions. This function is called by simpexpt via the routine noneg to
determine the sign of the base, when the power is a even rational number.

I think we have two possibilities:

1. Do a workaround for the function rootscontract.

In the routine rtc-fixitup we set radexpand to true and resimplify the
expression. Expressions like sqrt(-3) will be simplified to sqrt(3)*%i and
the routine sign has no longer a problem.

The routine rootscontract will work correctly.

2. Strengthen the routine noneg in simp.lisp in general.

If we replace the call to sign in noneg with a call to $csign complex
expressions are handled more completely

(defun noneg (p)
  (member ($csign p) '($pos $pz $zero)))

With this change we no longer have a problem and get

(%i23) (1/(1+sqrt(-3))),radexpand:false;
(%o23) 1/(sqrt(-3)+1)
(%i24) sqrt(%);
(%o24) 1/sqrt(sqrt(-3)+1)

I have run the testsuite and the share_testsuite with this change and I
have got no problems. Only seven examples in rtest_integrate.mac have a
different, but equivalent result.

Dieter Kaiser

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Comment By: Dieter Kaiser (crategus)
Date: 2009-08-30 02:30

Message:
I think it is not a problem of rootscontract, but a problem of the
simplifier.

The following user input generates the error:

(%i1) sqrt(1/(sqrt(-3)+1)),radexpand:false;
sign: argument cannot be imaginary; found sqrt(- 3)
 -- an error.  To debug this try debugmode(true);

With radexpand set to false sqrt(-3) does not simplify to sqrt(3)*%i but
both expressions are valid user input. The problem is in simpepxt.

In rootscontract the flag radexpand is set to false too.

Dieter Kaiser

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Comment By: Robert Dodier (robert_dodier)
Date: 2006-07-06 07:47

Message:
Logged In: YES 
user_id=501686

Still present in 5.9.3cvs.

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Comment By: Stavros Macrakis (macrakis)
Date: 2003-08-15 05:59

Message:
Logged In: YES 
user_id=588346

cf bug report 789059

The reason I submitted separate bug reports is that in this 
case, it may be that rootscontract is passing a malformed 
expression to rootscontract, while in 789059, it is clearly a 
general simplifier problem.

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