Re: Bug in Mathematica 6 - Integrate - 54 (Log, regression bug, invalid value)

On 19 , 09:20, Vladimir Bondarenko <v...@xxxxxxxxxxxxxxx> wrote:
On Jul 17, 9:18 am, dimitris <dimmec...@xxxxxxxxx> writes:

DA> I don't consider this integral as something
DA> easy for a CAS.

Hi Syntropho Dimitris,

You have a subtle sense of humor! ;)

Please do not tell us you, given your rare, amazing
transformation skills, could not see the following
solution, - all the same all we will not believe you
if you would say you... :)

simplify(1/(z^4+1)=-1/(z^2+I)/(2*I)+1/(z^2-I)/(2*I));

1/(z^4+1) = -1/(-z^4-1)

int1:=int(-ln(z^2+z+1)/(z^2+I)/(2*I),z = 0 .. infinity):
int2:=int(ln(z^2+z+1)/(z^2-I)/(2*I),z = 0 .. infinity):

# the simplified output is about 4 K,
# so I suppressed it

length(int1+int2);
length(simplify(int1+int2));

5409
4205

evalf(int1+int2);

.8207837857+.45e-9*I

Greetings from Simferopol from your Russian syntrophe Vladimir!

--

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

On Jul 17, 9:18 am, dimitris <dimmec...@xxxxxxxxx> wrote:



On 17 , 09:04, Vladimir Bondarenko <v...@xxxxxxxxxxxxxxx> wrote:

(*************************************************************)

If the same bugs exist through numerous software releases,
I think that is valuable public information.

It just should not happen.

-- Brad Cooper

(*************************************************************)

So our little demo continues... Hello again from the VM machine
which is still ignored by CAS manufacturers.

NIntegrate[Log[z^2 + z + 1]/(z^4 + 1), {z, 0, Infinity}]

0.820784
Okie. Compare:

(* If a single Mathematica version can calculate this? *)

N[Integrate[Log[z^2 + z + 1]/(z^4 + 1), {z, 0, Infinity}]]

(* Mathematica 6 returns this invalid asnwer *)

2.63082 + 6.01376 I

(* Mathematica 5.2 returns this invalid asnwer *)

0.747567 + 4.13051 I

(* Mathematica 4.2 returns this invalid asnwer *)

0.674349

(* Mathematica 3.0 returns the unevaluated integral *)

(*************************************************************)

Let there be a better Computer Algebra,

Vladimir Bondarenko

VM and GEMM architect
Co-founder, CEO, Mathematical Director

http://www.cybertester.com/CyberTester, LLChttp://maple.bug-list.org/Maple Bugs Encyclopaediahttp://www.CAS-testing.org/CASTesting

I don't consider this integral as something easy for a CAS.

In Maple 10

convert("Integrate[Log[z^2 + z + 1]/(z^4 + 1), {z, 0, Infinity}] ",FromMma);

infinity
/ 2
| ln(z + z + 1)
| -------------- dz
| 4
/ z + 1
0

value(%);

Error, (in assuming) when calling 'signum/main'. Received: 'numeric
exception: division by zero'

Dimitris- -

- -

Hello comrade Vladimir!

DA> I don't consider this integral as something
DA> easy for a CAS.

I should have said...

"I don't consider this integral as something easy despite my
(any!) skills in Mathematica...!"

Thank you very much for showing me your solution.

Keep up the good job!

Greetings from (very hot!) Athens

Dimitris





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