"Sometime ago, I wrote a bit of code that attempts to determine when an
expression is continuous."
I came up with this bit of code. It works pretty well.
continuousp(__e, __x, __p):=block
(
[inflag : true, ratprint:false, _p, _l],
_p : errcatch
(
if is(equal(_l : limit(__e, __x, __p, 'plus), limit(__e, __x, __p,
'minus))) then
if is(equal(_l, at(__e, [__x=__p]))) = true then
true
else
false
else
false
),
if emptyp(_p) then
if is(equal(error, ["expt: undefined: 0 to a negative
exponent."]))=true then
false
else
[]
else
first(_p)
);
-----Original Message-----
From: Barton Willis
Sent: Saturday, December 31, 2011 8:57 AM
To: rich.hennessy at verizon.net
Cc: maxima at math.utexas.edu
Subject: Re: [Maxima] Bug in limit or integrate
The function x |-> -gamma_incomplete(1/4,x^4)*x/(4*abs(x)) is not
continuous at zero. To do
the calculation correctly, you need to consider the intervals (-inf,0) and
(0, inf) separately.
Doing that, the definite integral is correct, I think.
Sometime ago, I wrote a bit of code that attempts to determine when an
expression is continuous. I know
that in general this is algorithmically impossible--I was aiming for a
satisficing (good enough) method.
--Barton
-----maxima-bounces at math.utexas.edu wrote: -----
I get this incorrect result for the following calculations:
(%i4) kill(all);
(%o0) done
(%i1) exp(-x^4);
(%o1) %e^-x^4
(%i2) integrate(%o1,x,minf,inf);
(%o2) gamma(1/4)/2
(%i3) integrate(%o1,x);
(%o3) -gamma_incomplete(1/4,x^4)*x/(4*abs(x))
(%i4) limit(%o3,x,inf)-limit(%o3,x,minf);
(%o4) 0
The limit should give the same answer as the more direct definite integral.
I can’t take the analysis much further because I know very little
about the gamma_incomplete function. It looks like a bug.
Rich
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