[Maxima-bugs] [ maxima-Bugs-836780 ] taylor(acosh(x),x,1,1)

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Bugs item #836780, was opened at 2003-11-05 15:55
Message generated for change (Comment added) made by macrakis
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Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Submitted By: Barton Willis (willisbl)
Assigned to: Nobody/Anonymous (nobody)
Summary: taylor(acosh(x),x,1,1)

Initial Comment:
The following is wrong:

(C1) taylor(acosh(x),x,1,1);
(D1) (%PI-2*LOG(SQRT(2)+1))/2-SQRT(2)*(x-1)/2

Converting to log form, we do better -- it's
correct, I believe.  But the result isn't simplified.

(C2) taylor(logarc(acosh(x)),x,1,1);
(D2) +SQRT(2)*SQRT(x-1)
(C3) ?print(%);

((MRAT SIMP
       (((MEXPT RATSIMP) 2 ((RAT) 1 2))
        ((%LOG SIMP)
         ((MPLUS SIMP) |$x|
          ((MEXPT SIMP) ((MPLUS SIMP) -1 ((MEXPT 
SIMP) |$x| 2))
           ((RAT) 1 2))))
        ((MPLUS SIMP) -1 |$x|))
       (#:|2^(1/2)21846| #:|LOG(SQRT(2)+1)21846| 
#:|2^(1/2)21846|
           #:%PI21846 #:|ACOSH(x)21846| #:|x21846|)
       ((|$x| ((1 . 1)) 1 NIL #:|2^(1/2)21846| . 2)) 
TRUNC)
 PS (#:|2^(1/2)21846| . 2) ((1 . 1))
 ((1 . 2) (#:|2^(1/2)21846| 1 1) . 1)) 
(D3) +SQRT(2)*SQRT(x-1)
(C4) 


Barton

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>Comment By: Stavros Macrakis (macrakis)
Date: 2003-11-12 09:49

Message:
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user_id=588346

The leading '+' in Taylor series is a property (bug?) of 1-d 
display.

Compare string(taylor(1,x,0,0)) => +1


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Comment By: Barton Willis (willisbl)
Date: 2003-11-12 09:41

Message:
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No, I wasn't bothered by the unnecessary ratvars; rather,
I was puzzled by the leading '+' in the result:

+SQRT(2)*SQRT(x-1)  <--- why +sqrt(2) ...?

Maybe the leading '+' is harmless; however, it's unusual.

Barton


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Comment By: Stavros Macrakis (macrakis)
Date: 2003-11-10 15:19

Message:
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This was already reported in bug report # 623165.

I am not sure what you mean by "the result isn't simplified".  
Are you thinking that the unnecessary ratvars are a problem?  
That is the usual way that CREs work: in a fresh Maxima, try

(?print(rat(x)), ?print(rat(y)), ?print(rat(x)) )$


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