[Maxima-bugs] [ maxima-Bugs-626760 ] zeroequiv extremely slow (minor)

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Bugs item #626760, was opened at 2002-10-22 04:19
Message generated for change (Comment added) made by macrakis
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Category: Lisp Core
Group: None
>Status: Closed
>Resolution: Fixed
Priority: 5
Private: No
Submitted By: Stavros Macrakis (macrakis)
Assigned to: Nobody/Anonymous (nobody)
Summary: zeroequiv extremely slow (minor)

Initial Comment:
expr:
 LOG(x^2+SQRT(2)*x+1)
-LOG(x^2-SQRT(2)*x+1)
+2*ATAN((2*x+SQRT(2))/SQRT(2))
+2*ATAN((2*x-SQRT(2))/SQRT(2))
+SQRT(2)*LOG(x+1)
-SQRT(2)*LOG(x-1)
-2*SQRT(2)*ATAN(1/x)$

zeroequiv(expr,x) takes over a minute, though it is not at 
all subtle how non-zero it is:

rectform(expr),numer,
..., x=0.1 => -3.31-4.44i
..., x=0.9 => 6.39-4.44i
..., x=1.1 => 7.38
..., x=1.5 => 6.38
..., x=20 =>  6.28

Zeroequiv is really supposed to be quick and dirty....


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>Comment By: Stavros Macrakis (macrakis)
Date: 2009-01-17 16:49

Message:
In Maxima 5.15, the original expression (but in lower case) takes 0.02 sec
and correctly gives false.

zeroequiv(LOG(1),x) correctly gives dontknow and returns instantaneously
since Maxima function names are now lower-case (unlike in 2002 when the bug
report was submitted).

Closing as fixed.

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Comment By: Dieter Kaiser (crategus)
Date: 2009-01-17 16:35

Message:
This bug report is related to SF[593530] "Zeroequiv issues". zeroequiv is
not used for in core functions. Problems are known and documented. This is
the result for the example:

(%i9)
expr:LOG(x^2+SQRT(2)*x+1)-LOG(x^2-SQRT(2)*x+1)+2*ATAN((2*x+SQRT(2))/SQRT(2))
                          +2*ATAN((2*x-SQRT(2))/SQRT(2))+SQRT(2)*LOG(x+1)
                          -SQRT(2)*LOG(x-1)-2*SQRT(2)*ATAN(1/x)
(%i10) zeroequiv(expr,x);
(%o10) dontknow

On a Windows system with GCL 2.6.8 and a CPU with 1.8 GHZ we get

(%i11) for i:1 thru 100000 do zeroequiv(expr,x);
Evaluation took 15.8900 seconds (15.8900 elapsed)
(%o11) done

One call to zeroequiv needs about 16/100,000 seconds. Setting resolution
to "wont fix" and status to pending.

Dieter Kaiser

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