"integrate((1+erf(sqrt(1/u).(u-1)))/2,u,0,inf);" asks
if FALSE is positive, negative, or zero. That doesn't
seem like a meaningful question.
Since sqrt(1/u).(u-1) increases like sqrt(u), the
integrand approaches a positive constant (namely one)
and so the answer ought to be INF, I think.
I am running Maxima 5.9.0 on RedHat Linux 7.2.
Robert Dodier
2004-11-25
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attempt to fix title: replace ampersand-quot-semicolon w/
quote marks (bug in sourceforge script, apparently)
Robert Dodier
2004-11-25
Robert Dodier
2005-05-16
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Trying this with commutative multiplication instead of
noncommutative (i.e.
integrate((1+erf(sqrt(1/u)*(u-1)))/2,u,0,inf);) yields a
noun form, without asking a question.
Bug is still present in 5.9.1cvs from 3/31/2005 (clisp 2.33,
linux).
Robert Dodier
2006-04-10
Harald Geyer
2007-06-08
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It seem's the original problem has gone quite some time ago. I
couldn't reproduce it under 5.11.0 nor 5.12.0. Now maxima asks
an other (a little bit more meaningful) question:
(%i2) integrate(1+erf(sqrt(u).(u-1)),u,0,inf);
Is 'limit((1/sqrt(u)) . (1/u),u,0,plus) positive, negative, or zero? pos;
(%o2) 'integrate(erf(sqrt(u) . (u-1))+1,u,0,inf)
This seems to be the minimal example, where maxima asks
this kind of question:
(%i9) integrate(1+erf((u .u^2)),u,0,inf);
Is 'limit(u . u^2,u,inf) positive, negative, or zero?pos;
(%o9) 'integrate(erf(u . u^2)+1,u,0,inf)
One might argue, that this question is ok, since it makes sense
if the integral makes any sense at all. OTOH the handling
of "." in integrals seems somewhat strange to me. Not sure
whether this bug should be closed or not.
This are futher cases:
(%i17) integrate(1+erf((u^3 .u^2)),u,0,inf);
Is 'limit(u^3 . u^2,u,inf) positive, negative, or zero?pos;
(%o17) 'integrate(erf(u^3 . u^2)+1,u,0,inf)
(%i18) integrate(1+erf((u^3 .u^n)),u,0,inf);
Is 'limit(u^3 . u^n,u,inf) positive, negative, or zero?pos;
(%o18) 'integrate(erf(u^3 . u^n)+1,u,0,inf)
(%i11) integrate(1+erf((u .a)),u,0,inf);
Is 'limit(u . a,u,inf) positive, negative, or zero?pos;
(%o11) 'integrate(erf(u . a)+1,u,0,inf)
In this cases maxima return a noun form or an actual answer
without asking questions:
(%i16) integrate(1+erf((u^2 .u^2)),u,0,inf);
(%o16) 'integrate(erf((u^2)^^2)+1,u,0,inf)
(%i12) integrate(1+erf((b .a)),u,0,inf);
Integral is divergent -- an error. To debug this try debugmode(true);
... at least this is no worse than with other symbols.
(%i8) integrate(1+erf((u^^2 .u^2)),u,0,inf);
(%o8) 'integrate(erf(u^^2 . u^2)+1,u,0,inf)
Dan Gildea
2007-12-15
Dan Gildea
2007-12-15
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I think the current behavior (described below) is fine.