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#754 MIN is not correct (problem with "is" function)
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
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Distributed under the GNU Public License. See the file
COPYING.
Dedicated to the memory of William Schelter.
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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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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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This Tracker item was closed automatically by the system. It was
previously set to a Pending status, and the original submitter
did not respond within 14 days (the time period specified by
the administrator of this Tracker).