Welcome into the Maple crisis continuing and extending! A quadrature's ridiculous result
Vladimir Bondarenko
Here is yet another salute to symbolic community and all
honest mathematicians from the VM machine which is still
ignored by CAS manufacturers.
So before you yet another sample of MULTIPLE regression bug
in Maple. Once it worked (1992-1996), then was broken (1997-
1999), then repaired (2000-2006), and now it's broken AGAIN.
...
Maple 11> evalf(Int(1/(z^exp(I)+z^Pi), z= 1..infinity));
-.5000000000 # where on earth is my non-zero imaginary part?!
# for adorers of workarounds
Maple 11> evalf(Int(1/(z^exp(I)+z^Pi), z=1..infinity, _Dexp));
.3384941890-.1978429309e-1*I
All other Maple versions are OK save Maple V 5 of 1997 which
returns
Error, (in evalf/int) unable to handle singularity
.................................................................
Man+Machine Review Of Maple Crisis
The beta 0.1 of the first world's document written by
a human in a close cooperation with a successor of the
GEMM machine, our unique VM automated testing expert
system which is a failure prediction oracle
http://maple.bug-list.org/maple-crisis.php
.................................................................
Best wishes,
Vladimir Bondarenko
VM and GEMM architect
Co-founder, CEO, Mathematical Director
http://www.cybertester.com/ Cyber Tester, LLC
http://maple.bug-list.org/ Maple Bugs Encyclopaedia
http://www.CAS-testing.org/ CAS Testing
Axel Vogt
...
> Maple 11> evalf(Int(1/(z^exp(I)+z^Pi), z= 1..infinity));
>
> -.5000000000 # where on earth is my non-zero imaginary part?!
>
> # for adorers of workarounds
>
> Maple 11> evalf(Int(1/(z^exp(I)+z^Pi), z=1..infinity, _Dexp));
>
> .3384941890-.1978429309e-1*I
Nice :-)
Instead of using a specific integration routine (and I prefer to work with
all the digits for 'hardware float evaluation', i.e. Digits=14 on Windows)
try to decompose the complex integrand:
Int(evalc(1/(z^exp(I)+z^Pi)), z= 1..infinity): evalf(%);
0.33849418897464 - 0.019784293088052 I
which shows the possible source for the behaviour (one of the objectives
of testing ...).
-hypergeom([1,(-1+Pi)/(-exp(I)+Pi)],[(-1+2*Pi-exp(I))/(-exp(I)+Pi)],-1)
/(-1+Pi) is the exact value.
Vladimir Bondarenko
The problem is to comment, what's happened with
Maple 11 and why is this bunk... look here...
Even nicer... (that is worse)
evalf(Int(1/(z^exp(I)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(2*I)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(3*I)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(4*I)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(5*I)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(I/2)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(I/3)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(I/4)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(I/5)+z^Pi), z=1..infinity));
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
Voila!
Best wishes from the VM machine and its architect,
Vladimir Bondarenko
VM and GEMM architect
Co-founder, CEO, Mathematical Director
http://www.cybertester.com/ Cyber Tester, LLC
http://maple.bug-list.org/ Maple Bugs Encyclopaedia
http://www.CAS-testing.org/ CAS Testing
Axel Vogt
and I replied: because of repetitions. This again is such a thing, but
of course feel free to vary it hundred times to find more bugs ...
It obviously has the same source, false decomposition for complex in the
numerical routine.
Say you have all your integrals in one list L (say you want to post some
more ...) use the following code to evaluate the integrands over C:
map( t -> subs(op(1,t)=evalc(op(1,t)),t), L): evalf(%);
So it is not worse, just a mimicry ... that's all ...
Vladimir Bondarenko
why this family produces -1/2, independently of the
parameter value (well, at certain provisos)?
(Yes, it's false but why so nice a value? how come?)
Best wishes,
Vladimir Bondarenko
VM and GEMM architect
Co-founder, CEO, Mathematical Director
http://www.cybertester.com/ Cyber Tester, LLC
http://maple.bug-list.org/ Maple Bugs Encyclopaedia
http://www.CAS-testing.org/ CAS Testing
Vladimir Bondarenko
evalf(Int(1/(z^exp(2*I)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(3*I)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(4*I)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(5*I)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(I/2)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(I/3)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(I/4)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(I/5)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(sqrt(3)*I)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(sqrt(Pi)*I)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(sqrt(15)*I)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(3^(1/3)*I)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(7^(1/5)*I)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(7^(1/5)*I)+z^Pi), z=1..infinity));
evalf(Int(1/(z^exp(7^(1/5)*I)+z^sqrt(Pi)), z=1..infinity));
evalf(Int(1/(z^exp(7^(1/5)*I)+z^sqrt(3)), z=1..infinity));
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
-.5000000000
Why this?
On Jul 13, 2:43 pm, Vladimir Bondarenko <v...@cybertester.com> wrote:
> 'Fraid you don't see my point...
>
> why this family produces -1/2, independently of the
> parameter value (well, at certain provisos)?
>
> (Yes, it's false but why so nice a value? how come?)
>
> Best wishes,
>
> Vladimir Bondarenko
>
> VM and GEMM architect
> Co-founder, CEO, Mathematical Director
>
> http://www.cybertester.com/ Cyber Tester, LLChttp://maple.bug-list.org/ Maple Bugs Encyclopaediahttp://www.CAS-testing.org/ CAS Testing
Vladimir Bondarenko
In the past, our automated machinery already discovered some
Maple defects with an especially funny behaviour. For example,
http://groups.google.com/group/sci.math.symbolic/msg/dd5e6a02c428dad9?hl=en&
Maple 9.5.1> int(z-z+z^2+z^3, z= 0..1);
int(z-z+z^2+z^3, z= 0..1);
int(z-z+z^2+z^3, z= 0..1);
int(z-z+z^2+z^3, z= 0..1);
int(z-z+z^2+z^3, z= 0..1);
int(z-z+z^2+z^3, z= 0..1);
int(z-z+z^2+z^3, z= 0..1);
int(z-z+z^2+z^3, z= 0..1);
7/12
7/6
7/12
7/6
7/12
7/6
7/12
7/6
http://groups.google.com/group/comp.soft-sys.math.maple/msg/aebf455797427824
Bernhard Roider writes
> z-z+a+b;
> z-z+a+b;
a + b
2 a + 2 b
Paul DeMarco, Manager of Kernel Development, Maplesoft writes
http://groups.google.com/group/comp.soft-sys.math.maple/msg/5a7f09a0e965f819
"It appears that this bug was introduced in Maple 9.5 as
part of the automatic-simplification project (see
?updates,Maple9_5,compatibility). Expressions of the form
x-x are no longer automatically reduced to 0 since x-x is
not always 0; as is the case when x is a matrix.
The handling of SUMs containing common sub-expressions
(including the constant multiplier) are being corrupted
after the first-pass of simplification before evaluation
occurs. The first usage of said expression works perfectly.
When the second instance the same expression occurs, the
partial result is used, leading to surprising results."
Is there a Maple Expert or a Maplesoft representative
competent enough to shed some light on why all these
quadratures manifest such a funny defect showing for
a wide range of parameters the same invalid result,
-1/2 ?
Best wishes,
Vladimir Bondarenko
VM and GEMM architect
Co-founder, CEO, Mathematical Director
http://www.cybertester.com/ Cyber Tester, LLC
http://maple.bug-list.org/ Maple Bugs Encyclopaedia
http://www.CAS-testing.org/ CAS Testing
> >http://www.cybertester.com/Cyber Tester, LLChttp://maple.bug-list.org/ Maple Bugs Encyclopaediahttp://www.CAS-testing.org/CAS Testing