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Mar 30, 2008, 8:05:06 AM3/30/08

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Can Maple 11 calculate the TABLE integrals?

Enjoy yet another VM machine discovery.

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Mathematica 6.0.2

Integrate[1/z^2,{z,1,I Infinity}]

1

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Derive 6.1

INT(1/z^2,z,1,#i*inf)

1

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MuPAD 4.0.2

int(1/z^2, z = 1..I*infinity);

1

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Now, what about Maplesoft, after 25+ years of Maple development?

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Maple 11.02> int(1/z^2, z = 1..I*infinity);

int(1/z^2,z = 1 .. infinity*I)

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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

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"We must understand that technologies

like these are the way of the future."

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Mar 30, 2008, 8:27:15 AM3/30/08

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Maple 11.02> int(1/(1+z)^2, z = 0..I*infinity);

Maple 11.02> int(1/(1+z)^2, z = 1..I*infinity);

Maple 11.02> int(1/(1+z)^2, z = 1..I*infinity);

1

int(1/(1+z)^2,z = 1 .. infinity*I)

Enjoy!

> http://www.cybertester.com/ Cyber Tester, LLChttp://maple.bug-list.org/ Maple Bugs Encyclopaediahttp://www.CAS-testing.org/ CAS Testing

Mar 30, 2008, 9:59:00 AM3/30/08

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On Mar 30, 3:27 pm, Vladimir Bondarenko <v...@cybertester.com> wrote:

> Maple 11.02> int(1/(1+z)^2, z = 0..I*infinity);

> Maple 11.02> int(1/(1+z)^2, z = 1..I*infinity);

>

> 1

> int(1/(1+z)^2,z = 1 .. infinity*I)

>

> Enjoy!

>

> Maple 11.02> int(1/(1+z)^2, z = 0..I*infinity);

> Maple 11.02> int(1/(1+z)^2, z = 1..I*infinity);

>

> 1

> int(1/(1+z)^2,z = 1 .. infinity*I)

>

> Enjoy!

>

One must be very careful when using such "complex infinities".

It is much better to transform first the integral e.g. over

[0,infinity)

DERIVE simply computes INT(f,a,b) = F(b) - F(a) where F is an

antiderivative,

even if a,b are "infinities". Do you think that this is a so smart

approach?

Mar 30, 2008, 10:25:51 AM3/30/08

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I did expect a comment like yours (about the complex plane).

I agree. In this respect, Derive's approach is (too) simplistic.

But what you'd say about Mathematica 6 and MuPAD 4?

Mar 30, 2008, 8:19:52 PM3/30/08

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...................................................

Just a remark on the ubiqiutous Maple bugs...

# Jacques Carette, Mar 24, 2008

Maple 11.02> assume(z>0);

Maple 11.02> is(sin(z)^2+cos(z)^2*z^2 > 0);

false (!) # Maple bugs strike again!

...................................................

So, what you'd say about Mathematica 6 and MuPAD 4?

...................................................

> On Mar 30, 6:59 am, Mate <mmat...@personal.ro> wrote:

> > approach?- Hide quoted text -

>

> - Show quoted text -

Mar 30, 2008, 8:29:57 PM3/30/08

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...........................................

Just yet another ubiqiutous Maple 11 bug...

# Axel Vogt, Mar 28, 2008

Maple 11.02> Ei(1,1):

Maple 11.02> evalf(%=convert(%,Sum));

.2193839344 = 1.

Mar 31, 2008, 5:18:49 AM3/31/08

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honestly you should give reference to http://www.mapleprimes.com/tracker

Mar 31, 2008, 6:33:29 AM3/31/08

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Agree! The reader would feel the problem better if given

the context and accompanying instructive discussion.

the context and accompanying instructive discussion.

So here is the link to a hot Axel Vogt's Ei-related bug

description a simplified form of which I presented:

http://www.mapleprimes.com/blog/axelvogt/errrexponentialintegralsum

Savour! ;)

I can only sing in sync with Herr Vogt, Arghrrrr! ;-)

Mar 31, 2008, 4:10:56 PM3/31/08

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How does Maplesoft fix the bugs in Maple?

A live discussion in Russian at http://forum.ru-board.com

http://forum.ru-board.com/topic.cgi?forum=5&topic=9935&start=180

http://forum.ru-board.com/topic.cgi?forum=5&topic=9935&start=200

Apr 2, 2008, 8:36:34 PM4/2/08

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Vladimir Bondarenko <v...@cybertester.com> wrote:

> I did expect a comment like yours (about the complex plane).

>

> I agree. In this respect, Derive's approach is (too) simplistic.

> I did expect a comment like yours (about the complex plane).

>

> I agree. In this respect, Derive's approach is (too) simplistic.

I must say that I don't agree. It seems to me that Derive's approach here

is theoretically correct and as simple as possible.

> But what you'd say about Mathematica 6 and MuPAD 4?

>

> On Mar 30, 6:59=A0am, Mate <mmat...@personal.ro> wrote:

> > On Mar 30, 3:27 pm, Vladimir Bondarenko <v...@cybertester.com> wrote:

> >

> > > Maple 11.02> =A0int(1/(1+z)^2, z =3D 0..I*infinity);

> > > Maple 11.02> =A0int(1/(1+z)^2, z =3D 1..I*infinity);

> >

> > > 1

> > > int(1/(1+z)^2,z =3D 1 .. infinity*I)

> >

> > > Enjoy!

> >

> > One must be very careful when using such "complex infinities".

I'd be interested in seeing some examples showing why one must be very

careful when using such infinities.

> > It is much better to transform first the integral e.g. over

> > [0,infinity)

> > DERIVE simply computes INT(f,a,b) = F(b) - F(a) where F is an

> > antiderivative,

> > even if a,b are "infinities". Do you think that this is a so smart

> > approach?

The manual for Derive states that it computes definite integrals in

essentially that way. As a warning example, it mentions that

int(1/x^2, x, -1, 1)

yields -2, a result "which even Cauchy would call wrong." It then advises

"As is the case when using integral tables, it is your responsibility to

find singularities..." IMO, since the manual is adequately explicit about

this matter, I do not consider giving -2 for int(1/x^2, x, -1, 1) to be a

bug in the program.

David

Apr 4, 2008, 3:48:08 PM4/4/08

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This was just one of my (thought-?)provocative comments :)

The other day Mate said

M> One must be very careful when using such "complex infinities".

And I challenged him to show that both Wolfram Research and SciFace

GmbH engineers are wrong when they return 1 for this integral. But

he did not reply...

As as matter of fact I do not feel much that Albert Rich was wrong

returning 1 for this integral...

After all, we see that Maple returns a reasonable stuff for the

upper limit like I or 2*I... so why we cannot direct the upper

limit to I*infinity infinity and get this 1?

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