Bug in limit or integrate
- Subject: Bug in limit or integrate
- From: Edwin Woollett
- Date: Wed, 4 Jan 2012 14:18:32 -0800
On Jan. 2, 2012, I wrote
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> the definite integral of the real function exp(-x^n) over
> the real interval (0,1) is broken (spurious imaginary parts,
> wrong real parts) for n = 3 through 15, and probably forever.
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A corrected version of defint.lisp has been checked into git
by Dan Gildea in response to my bug report.
The corrected version solves my problem.
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Maxima 5.25.1 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL)
(%i1) load("defint-new.lisp");
(%o1) "c:/work2/defint-new.lisp"
(%i2) exp_test(n) :=
( print (n," qags = ", first( quad_qags (exp(-x^n),x,0,1)),
" integrate = ",
expand(float(rectform(integrate(exp(-x^n),x,0,1))))))$
(%i3) for m thru 15 do exp_test(m)$
1 qags = 0.63212055882856 integrate = 0.63212055882856
2 qags = 0.74682413281243 integrate = 0.74682413281243
3 qags = 0.80751118213967 integrate = 0.80751118213967
4 qags = 0.8448385947571 integrate = 0.8448385947571
5 qags = 0.87007466768589 integrate = 0.87007466768589
6 qags = 0.88826369875194 integrate = 0.88826369875194
7 qags = 0.90199160301324 integrate = 0.90199160301324
8 qags = 0.91271857185875 integrate = 0.91271857185875
9 qags = 0.9213308364909 integrate = 0.9213308364909
10 qags = 0.92839720283799 integrate = 0.92839720283799
11 qags = 0.93429939205577 integrate = 0.93429939205577
12 qags = 0.93930307080183 integrate = 0.93930307080183
13 qags = 0.94359882032526 integrate = 0.94359882032526
14 qags = 0.94732690220079 integrate = 0.94732690220079
15 qags = 0.95059283193 integrate = 0.95059283193
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Ted Woollett