"What might be so fundamentally wrong at Maplesoft?"

Vladimir Bondarenko

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Aug 1, 2006, 10:00:17 PM8/1/06

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

Peter Luschny writes on Tue, Dec 23 2003 1:39 pm in a message
titled "Re: euler(0,1) shows Maple bugs are really ubiquitous"

http://groups.google.com/group/comp.soft-sys.math.maple/msg/572265481f09ebe5?hl=en&

PL> "What might be so fundamentally wrong at Maplesoft?"

The answer to your question is of extreme importance.

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

DESCRIPTION: None of Maple versions since at least 1994 on
can approximate this trivial integral.

TEST CASE: evalf(Int(1/z^2, z= I..I*infinity));

EXPECTED: -1.*I

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

-1.*I

-------------------- (2005) Maple 10.00 ----------------------
Error, (in evalf/int) non-numeric integration limit encountered
-------------------- (2004) Maple 9.5.1 ----------------------
Error, (in evalf/int) non-numeric integration limit encountered
-------------------- (2004) Maple 9.5 ------------------------
Error, (in evalf/int) non-numeric integration limit encountered
-------------------- (2003) Maple 9 --------------------------
Error, (in evalf/int) non-numeric integration limit encountered
-------------------- (2002) Maple 8 --------------------------
Error, (in evalf/int) non-numeric integration limit encountered
-------------------- (2001) Maple 7 --------------------------
Error, (in evalf/int) non-numeric integration limit encountered
-------------------- (2000) Maple 6 --------------------------
Error, (in evalf/int) non-numeric integration limit encountered
-------------------- (1997) Maple V Rel 5 --------------------
Error, (in evalf/int) non-numeric integration limit encountered
-------------------- (1995) Maple V Rel 4 --------------------
Error, (in evalf/int) non-numeric integration limit encountered
-------------------- (1994) Maple V Rel 3 --------------------
Error, (in evalf/int) non-numeric integration limit encountered
---------------------------------------------------------------

COMPARE: Derive 6 and Mathematica 5.2 yield a correct
result.

APPROX(INT(1/z^2,z,#i,inf))
NIntegrate[1/z^2, {z, I, I Infinity}]

- #i
0. - 1. I

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

Maplesoft: Propagating math crass ignorance worldwide

http://groups.google.com/group/sci.math.symbolic/browse_frm/thread/a21272a3ba5b7f40/7e437e17ffedebda#7e437e17ffedebda

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

Maplesoft is committed to providing the highest level
of blatant lie about support for the products it sells

http://groups.google.com/group/sci.math.symbolic/browse_frm/thread/aa28c5e820f55502/3420cbd5725f952e#3420cbd5725f952e

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

First world's Man+Machine Based Maple Crisis Review (beta 0.1)

http://maple.bug-list.org/maple-crisis.php

(beta 0.2 is already of 450+ pages... selected of the selected)

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

Robert Israel

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Aug 2, 2006, 1:48:57 AM8/2/06

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In article <1154484017....@b28g2000cwb.googlegroups.com>,
Vladimir Bondarenko <v...@cybertester.com> wrote:

|>DESCRIPTION: None of Maple versions since at least 1994 on
|> can approximate this trivial integral.

|>TEST CASE: evalf(Int(1/z^2, z= I..I*infinity));

|>EXPECTED: -1.*I

Not quite trivial! In this case it may be obvious what path you
want to integrate along, but what would you do in general, e.g.
for integrating from 1 to I*infinity? Anyway, the improper numerical
integration routines reject this, because they are only set up
for real intervals. Integrals with complex endpoints are not
mentioned on the ?evalf,Int help page. So you're asking evalf(Int(...))
to do something it was never intended to do. Of course, you can
use a parametrization of the integration path with a real parameter
and get the correct answer:

> Z:= I*t;
evalf(Int(1/Z^2*diff(Z,t), t=1..infinity));

Robert Israel isr...@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

Vladimir Bondarenko

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Aug 2, 2006, 3:12:47 PM8/2/06

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

http://www.maplesoft.com/support/

"Maplesoft is committed to providing the highest level

of support for the products it sells"

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

DESCRIPTION: Yet another regression bug of many 1000s.

TEST CASE: limit(RootOf(I*_Z^2+z), z= 1.);

EXPECTED: .7071067812+.7071067812*I

CHECKUP: evalf(Limit(RootOf(I*_Z^2+z), z= 1));
evalf(limit(RootOf(I*_Z^2+z), z= 1));

.7071067812+.7071067812*I
.7071067812+.7071067812*I

--------------- (2005) Maple 10.00 --------------------------
Error, (in content/polynom) general case of floats not handled
--------------- (2004) Maple 9.5.1 --------------------------
Error, (in content/polynom) general case of floats not handled
--------------- (2004) Maple 9.5 ----------------------------
Error, (in content/polynom) general case of floats not handled
--------------- (2003) Maple 9 ------------------------------
Error, (in content/polynom) general case of floats not handled
--------------- (2002) Maple 8 ------------------------------
.7071067812+.7071067812*I
--------------- (2001) Maple 7 ------------------------------
.7071067812+.7071067812*I
--------------- (2000) Maple 6 ------------------------------
-.7071067812-.7071067812*I
--------------- (1997) Maple V Rel 5 ------------------------
.7071067812+.7071067812*I
--------------- (1995) Maple V Rel 4 ------------------------
-.7071067812-.7071067812*I
--------------- (1994) Maple V Rel 3 ------------------------
-.7071067812-.7071067812*I
--------------------------------------------------------------

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

Peter Luschny writes on Tue, Dec 23 2003 1:39 pm in a message
titled "Re: euler(0,1) shows Maple bugs are really ubiquitous"

http://groups.google.com/group/comp.soft-sys.math.maple/msg/572265481f09ebe5?hl=en&

PL> "What might be so fundamentally wrong at Maplesoft?"

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

Vladimir Bondarenko

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Aug 8, 2006, 11:22:09 PM8/8/06

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

http://www.maplesoft.com/support/

"Maplesoft is committed to providing the highest level
of support for the products it sells"

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

DESCRIPTION: Yet another regression bug of many 1000s.

Only Maple 6 of 2000 can approximate this
trivial integral correctly.

TEST CASE: evalf(Int(1/z, z= 10^16..infinity));

EXPECTED: Float(infinity)

CHECKUP: evalf(int(1/z, z= 10^16..infinity));

Float(infinity)

--------------- (2005) Maple 10.00 ---------------------------
.1396213761e-12
--------------- (2004) Maple 9.5.1 ---------------------------
.1396213761e-12
--------------- (2004) Maple 9.5 -----------------------------
.1396213761e-12
--------------- (2003) Maple 9 -------------------------------
.1396213761e-12
--------------- (2002) Maple 8 -------------------------------
.1396213761e-12
--------------- (2001) Maple 7 -------------------------------
.1396213761e-12
--------------- (2000) Maple 6 -------------------------------
Float(infinity)
--------------- (1997) Maple V Rel 5 -------------------------
Error, (in evalf/int) integrand has a pole in the interval

--------------- (1995) Maple V Rel 4 -------------------------

Error, (in evalf/int) integrand has a pole in the interval

--------------- (1994) Maple V Rel 3 -------------------------

Error, (in evalf/int) integrand has a pole in the interval
---------------------------------------------------------------

Proginoskes

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Aug 9, 2006, 2:57:07 AM8/9/06

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Robert Israel wrote:
> In article <1154484017....@b28g2000cwb.googlegroups.com>,
> Vladimir Bondarenko <v...@cybertester.com> wrote:
>
> |>DESCRIPTION: None of Maple versions since at least 1994 on
> |> can approximate this trivial integral.
>
> |>TEST CASE: evalf(Int(1/z^2, z= I..I*infinity));
>
> |>EXPECTED: -1.*I
>
> Not quite trivial! In this case it may be obvious what path you
> want to integrate along,

It's not obvious to me. Clearly the integral is path-dependent.

> but what would you do in general, e.g.
> for integrating from 1 to I*infinity? Anyway, the improper numerical
> integration routines reject this, because they are only set up
> for real intervals. Integrals with complex endpoints are not
> mentioned on the ?evalf,Int help page. So you're asking evalf(Int(...))
> to do something it was never intended to do. Of course, you can
> use a parametrization of the integration path with a real parameter
> and get the correct answer:
>
> > Z:= I*t;
> evalf(Int(1/Z^2*diff(Z,t), t=1..infinity));

Too bad he didn't reply to this, and just reposted what he had before.
Is "Vladimir Bondarenko" a bot? And if he is so upset about computer
algebra packages, why doesn't he write one that works?

--- Christopher Heckman

isr...@math.ubc.ca

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Aug 9, 2006, 12:04:44 PM8/9/06

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Proginoskes wrote:
> Robert Israel wrote:
> > In article <1154484017....@b28g2000cwb.googlegroups.com>,
> > Vladimir Bondarenko <v...@cybertester.com> wrote:
> >
> > |>DESCRIPTION: None of Maple versions since at least 1994 on
> > |> can approximate this trivial integral.
> >
> > |>TEST CASE: evalf(Int(1/z^2, z= I..I*infinity));
> >
> > |>EXPECTED: -1.*I
> >
> > Not quite trivial! In this case it may be obvious what path you
> > want to integrate along,
>
> It's not obvious to me. Clearly the integral is path-dependent.

Ummm, in this case the value of the integral is not path-dependent: the

antiderivative is single-valued, and has a limit at complex infinity.
But
of course evalf(Int(...)) should not be expected to know that.

Message has been deleted

Vladimir Bondarenko

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Aug 9, 2006, 9:22:01 PM8/9/06

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Christopher Heckman writes:

CH> Is "Vladimir Bondarenko" a bot?

I claim that I am a human being, but it's up to you to decide.

Give me a call at 380-652-540732 and chat with me on CASs
or any other topic. Then make up you mind on the point.

CH> And if he is so upset about computer algebra packages,
CH> why doesn't he write one that works?

Possibly, one fine day, I should consider doing this...
If I ever do, the key word would be ERGONOMICS.

It means that the customer of such a system should get a
correct answer in the minimal time, and this answer should
be represented in a shape to be most useful for the customer.

Sincerely,

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

Proginoskes

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Aug 10, 2006, 2:37:49 AM8/10/06

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isr...@math.ubc.ca wrote:
> Proginoskes wrote:
> > Robert Israel wrote:
> > > In article <1154484017....@b28g2000cwb.googlegroups.com>,
> > > Vladimir Bondarenko <v...@cybertester.com> wrote:
> > >
> > > |>DESCRIPTION: None of Maple versions since at least 1994 on
> > > |> can approximate this trivial integral.
> > >
> > > |>TEST CASE: evalf(Int(1/z^2, z= I..I*infinity));
> > >
> > > |>EXPECTED: -1.*I
> > >
> > > Not quite trivial! In this case it may be obvious what path you
> > > want to integrate along,
> >
> > It's not obvious to me. Clearly the integral is path-dependent.
>
> Ummm, in this case the value of the integral is not path-dependent: the
> antiderivative is single-valued, and has a limit at complex infinity. But
> of course evalf(Int(...)) should not be expected to know that.

Well, what if you start at i, go around the origin back to i, then go
straight up to i*infinity? Doesn't the fact that 1/z^2 has a nonzero
residue at 0 mean that the integral is path-dependent? (It's been a
while since I've done any complex analysis, so I may be mis-remembering
things here.)

And what if the path goes through the origin?

--- Christopher Heckman

Proginoskes

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Aug 10, 2006, 2:39:56 AM8/10/06

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Vladimir Bondarenko wrote:
> Christopher Heckman writes:
>
> CH> Is "Vladimir Bondarenko" a bot?
>
> I claim that I am a human being, but it's up to you to decide.
>
> Give me a call at 380-652-540732 and chat with me on CASs
> or any other topic. Then make up you mind on the point.

Well, now I know how to get a non-bot reply out of you. 8-) (I asked,
because your answer to a post was to re-post something else.)

> CH> And if he is so upset about computer algebra packages,
> CH> why doesn't he write one that works?
>
> Possibly, one fine day, I should consider doing this...
> If I ever do, the key word would be ERGONOMICS.
>
> It means that the customer of such a system should get a
> correct answer in the minimal time, and this answer should
> be represented in a shape to be most useful for the customer.

Are there any parts of Maple that you have found are guaranteed to give
a correct answer?

--- Christopher Heckman

Robert Israel

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Aug 10, 2006, 11:57:51 AM8/10/06

to

In article <1155191869.2...@h48g2000cwc.googlegroups.com>,
Proginoskes <CCHe...@gmail.com> wrote:

>> Ummm, in this case the value of the integral is not path-dependent: the
>> antiderivative is single-valued, and has a limit at complex
>infinity. But
>> of course evalf(Int(...)) should not be expected to know that.
>
>Well, what if you start at i, go around the origin back to i, then go
>straight up to i*infinity? Doesn't the fact that 1/z^2 has a nonzero
>residue at 0 mean that the integral is path-dependent?

No, 1/z^2 has residue 0 at 0.

>And what if the path goes through the origin?

That's a special case. The integral is undefined then.

Vladimir Bondarenko

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Aug 12, 2006, 3:03:58 PM8/12/06

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Christopher Heckman writes:

CH> Are there any parts of Maple that you have found
CH> are guaranteed to give a correct answer?

A great question, thanks.

I will answer it soon.

Vladimir Bondarenko

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Aug 12, 2006, 3:15:02 PM8/12/06

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

http://www.maplesoft.com/support/

"Maplesoft is committed to providing the highest level

of support for the products it sells"

He-he... Do you still believe this poppycock?

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

DESCRIPTION: Yet another regression bug of many 1000s.

Only Maple V Rel 4 of 1995 and Maple V Rel 5 of
1997 can calculate this integral correctly.

TEST CASE: int(int(abs(y^2-x), x= -1..1), y= 0..1);

EXPECTED: 6/5

1.200000000

CHECKUP: evalf(Int(Int(abs(y^2-x), x= -1..1), y= 0..1));

1.199999956

--------------- (2005) Maple 10.00 -----------------------------
Maple keeps running after 10000 seconds + SEVERE SWAPPING
--------------- (2004) Maple 9.5.1 -----------------------------
int(2*y^2+2*y^2*PIECEWISE([0, y-I < 0],[1, otherwise])-PIECEWISE(
[0, y+I < 0],[1, otherwise])-y^4*PIECEWISE([0, y+I < 0],[1, other
wise])+P,................ Blah-blah-blah Maplesoft is the best!
--------------- (2004) Maple 9.5 -------------------------------
int(2*y^2-y^4*PIECEWISE([0, y+I < 0],[1, otherwise])+PIECEWISE([0
, y-I < 0],[1,otherwise])-PIECEWISE([0, y+I < 0],[1, otherwise])+
y^4*PIECE................ Go and buy Maple 11 coming soon!
--------------- (2003) Maple 9 ---------------------------------
int(2*y^2+PIECEWISE([0, y-I < 0],[1, otherwise])+2*y^2*PIECEWISE(
[0, y-I < 0],[1, otherwise])-PIECEWISE([0, y+I < 0],[1, otherwise
])+y^4*PI................ Off with Vladimir Bondarenko!
--------------- (2002) Maple 8 ---------------------------------
int(2*y^2+2*y^2*Heaviside(y-1)+Heaviside(y+1)+y^4*Heaviside(y+1)-
Heaviside(y-1)-y^4*Heaviside(-y+1)-2*y^2*Heaviside(y+1)-2*y^4*Hea
viside(y-................ VB is a villain! He is a commie.
--------------- (2001) Maple 7 ---------------------------------
int(2*y^2+y^4*Heaviside(y+1)+2*y^2*Heaviside(y-1)-2*y^2*Heaviside
(y+1)+Heaviside(y+1)-y^4*Heaviside(-y+1)-Heaviside(y-1)-2*y^4*Hea
viside(y-................ Long live Maplesoft! Hurrah! Hurrah!
--------------- (2000) Maple 6 ---------------------------------
int(2*y^2-Heaviside(y-1)+2*y^2*Heaviside(y-1)+y^4*Heaviside(y+1)-
2*y^2*Heaviside(y+1)-y^4*Heaviside(-y+1)+Heaviside(y+1)-2*y^4*Hea
viside(y-................ We the Maplesoft are zero cool!
--------------- (1997) Maple V Rel 5 ---------------------------
6/5
--------------- (1995) Maple V Rel 4 ---------------------------
6/5
--------------- (1994) Maple V Rel 3 ---------------------------
int(-(y^2-1)^2*signum(y^2-1)/2+(y^2+1)^2*signum(y^2+1)/2,y=0..1)
-----------------------------------------------------------------

COMMENT: Mathematica 5.2 and Derive 6 calculate this
integral correctly.

int(int(abs(y-x),x,-1,1),y,0,1)
Integrate[Abs[y^2-x], {y,0,1}, {x,-1,1}]

6/5
6/5

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

First world's Man+Machine Based Maple Crisis Review (beta 0.1)

http://maple.bug-list.org/maple-crisis.php

(beta 0.2 is already of 500+ pages... selected of the selected)

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

Axel Vogt

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Aug 12, 2006, 4:05:52 PM8/12/06

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It seems that Maple does not take into account the restrictions given
by the integration bounds, since assuming them works.

Vladimir Bondarenko

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Aug 16, 2006, 7:10:40 PM8/16/06

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

http://www.maplesoft.com/support/

"Maplesoft is committed to providing the highest level
of support for the products it sells"

Don't give me any of that bull.

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

DESCRIPTION: None of Maple versions since at least 1994 on

can calculate this TRIVIAL limit corectly.

TEST CASE: limit((z^I-(2*z)^I)/z^I, z= 0);

EXPECTED: 1 - 2^I

.2307610986-.6389612763*I

CHECKUP: limit((z^I-(2*z)^I)/z^I, z= -0.001);
limit((z^I-(2*z)^I)/z^I, z= 0.001);

.2307610986-.6389612764*I
.2307610986-.6389612763*I

--------------- (2005) Maple 10.00 ---------------------------