[Maxima-bugs] [ maxima-Bugs-1220227 ] MIN is not correct (problem with "is" function)

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Bugs item #1220227, was opened at 2005-06-14 05:48
Message generated for change (Settings changed) made by dgildea
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Category: Lisp Core
Group: To be reviewed
>Status: Pending
>Resolution: Works For Me
Priority: 5
Private: No
Submitted By: joe532 (joe532)
Assigned to: Nobody/Anonymous (nobody)
Summary: MIN is not correct (problem with "is" function)

Initial Comment:
I have the following problem with MIN : the graph of min 
below does not match the min of the curves on the second 
graph. 
 
session: 
f(h,k,l):=(h^k)*((1/h)*k*(1+l)+(d-k)*2*l); 
g(h,k,l):=2*d*l+(h^k)*((1/h)*k*(1-l)-(d-k)*2*l); d:2; l:0.5; 
plot2d([f((1-v)^(1/2),2,l), f((1-v),1,l), g(v^(1/2),2,l), g(v,1,l)], 
[v,0,1])$  
plot2d(min(f((1-v)^(1/2),2,l), f((1-v),1,l), g(v^(1/2),2,l), g(v,1,l)), 
[v,0,1])$ 
 
on maxima 
Maxima 5.9.1 http://maxima.sourceforge.net 
Using Lisp GNU Common Lisp (GCL) GCL 2.6.6 (aka 
GCL) 
Distributed under the GNU Public License. See the file 
COPYING. 
Dedicated to the memory of William Schelter. 
This is a development version of Maxima. The function 
bug_report() 
provides bug reporting information. 
 

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Comment By: Robert Dodier (robert_dodier)
Date: 2006-08-12 12:34

Message:
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user_id=501686

Not observed in 5.9.3cvs / Clisp 2.38, GCL 2.6.7, SBCL 0.9.9
on Linux. Seems likely that recent modifications to min/max
have fixed this. Marking this report to be retested on
Windows -- if it does not appear there, we can close this
report as fixed.

For the record the following plot2d puts the 3 curves of
interest together with the min of those 3 on one plot.
Should find that the computed min coincides with whichever
curve is lowest.

f(h,k,l):=(h^k)*((1/h)*k*(1+l)+(d-k)*2*l);
g(h,k,l):=2*d*l+(h^k)*((1/h)*k*(1-l)-(d-k)*2*l);
d:2; 
l:0.5; 

plot2d([f((1-v)^(1/2),2,l), f((1-v),1,l), g(v^(1/2),2,l),
g(v,1,l), min(f((1-v)^(1/2),2,l), f((1-v),1,l),
g(v^(1/2),2,l), g(v,1,l))],
[v,0,1])$


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Comment By: Robert Dodier (robert_dodier)
Date: 2005-06-14 10:20

Message:
Logged In: YES 
user_id=501686

OK, I've narrowed the problem. 

  aa: f((1-v)^(1/2),2,l);
  bb: f((1-v),1,l);
  cc: g(v^(1/2),2,l);
  dd: g(v,1,l);

  min (aa, bb, cc, dd)  =>  min((0.5/v-1.0)*v+2.0,
3.0*sqrt(1-v))

OK, that's min (aa, dd). As for bb and dd, bb is equal to dd:

   ratsimp (bb - dd)  =>  0

What about cc ?

  is (cc > aa)  =>  undecided (OK)
  is (cc > bb)  =>  undecided (OK)
  is (cc > dd)  =>  true  (OOPS, should be undecided)
  is (cc > dd)  =>  undecided (OK, but why is it different
from first time?)

trace (ratsimp), then is(cc > aa), is(cc > bb), is(cc > dd),
shows ratsimp is called once by "is". On the second is(cc >
dd), ratsimp is called twice by "is"; seems like the problem
could be in "is".

Given that bb is equal to dd, this is a work around:

  plot2d (min (aa, bb, cc), [v, 0, 1]);


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