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Re[2]: [Axiom-developer] [Q] How to classify # integrate(log(%i+z^2), z)
From: |
Vladimir Bondarenko |
Subject: |
Re[2]: [Axiom-developer] [Q] How to classify # integrate(log(%i+z^2), z) -> 2 ? |
Date: |
Mon, 14 Feb 2005 18:15:28 +0200 |
Hi,
Monday, February 14, 2005, 4:16:03 PM, you write:
WS> Axiom may (I am not sure) have interpreted %i as a parameter
WS> with no special property.
If it is the case, this is certainly a bug as %i has a special,
a unique meaning in AXIOM, isn't is so?
-> #integrate(log(%i+z^2), z)
2
mean that in fact the user would have 2 identical answers,
and if we ask AXIOM to calculate
-> 2*3
we sure do not expect to see
[6,6]
but rather
6
?
Even more, if these 2 answers returned by AXIOM for
integrate(log(%i+z^2), z) are NOT identical, it is
obviously a math bug. The must be the same (but maybe
of different form).
Best,
Vladimir
WS> Bill Page wrote:
>>
>> On Friday, February 11, 2005 9:56 AM Vladimir Bondarenko wrote:
>> > ...
>> > ===> Case 2.
>> >
>> > -> integrate(log(%i+z^2), z)
>> >
>> > +-----+ 2
>> > +-----+ z\|- 4%i + z - %i 2
>> > \|- 4%i log(-------------------) + 2z log(z + %i) - 4z
>> > 2
>> > z + %i
>> > [-------------------------------------------------------,
>> > 2
>> > +---+
>> > 2 +---+ \|4%i
>> > z log(z + %i) - \|4%i atan(------) - 2z]
>> > 2z
>> > ...
>> > But why the user really needs 2 forms of the same answer?
>> >
>>
>> I think you should report it as a bug.
>>
WS> I'm not sure, because you can use
(4) ->> complexIntegrate(log(%i+z^2),z)
WS> (4)
WS> +-----+
WS> +-----+ \|- 4%i + 2z 2
WS> \|- 4%i log(-------------) + 2z log(z + %i)
WS> 2
WS> +
WS> +-----+
WS> +-----+ - \|- 4%i + 2z
WS> - \|- 4%i log(---------------) - 4z
WS> 2
WS> /
WS> 2
WS> Type: Expression Complex Integer
WS> to obtain one form. Using integrate when the integrand involves complex
values
WS> and ask for real forms does not sound correct. Axiom may (I am not sure)
have
WS> interpreted %i as a parameter with no special property.
WS> A comparison with a parameter to replace %i shows the form of the answers in
WS> both cases (integrate or complexIntegrate) are the same.
(5) ->> complexIntegrate(log(a+z^2),z)
WS> (5)
WS> +----+ +----+
WS> +----+ \|- 4a + 2z +----+ - \|- 4a + 2z 2
WS> \|- 4a log(------------) - \|- 4a log(--------------) + 2z log(z + a) -
4z
WS> 2 2
WS>
---------------------------------------------------------------------------
WS> 2
WS> Type: Expression
Integer
(6) ->> integrate(log(a+z^2),z)
WS> (6)
WS> +---+ 2
WS> +---+ 2z\|- a + z - a 2
WS> [\|- a log(-----------------) + z log(z + a) - 2z,
WS> 2
WS> z + a
WS> +-+
WS> +-+ \|a 2
WS> - 2\|a atan(----) + z log(z + a) - 2z]
WS> z
WS> Type: Union(List Expression
Integer,...)
Viva la Cyber Tester!
--
Vladimir Bondarenko
GEMM architect
Co-founder, CEO, Mathematical Director
Cyber Tester, LLC
13 Dekabristov Str, Simferopol
Crimea 95000, Ukraine
tel: +38-(0652)-447325
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- [Axiom-developer] [Q] How to classify # integrate(log(%i+z^2), z) -> 2 ?, Vladimir Bondarenko, 2005/02/11
- RE: [Axiom-developer] [Q] How to classify # integrate(log(%i+z^2), z) -> 2 ?, Bill Page, 2005/02/13
- Re: [Axiom-developer] [Q] How to classify # integrate(log(%i+z^2), z) -> 2 ?, William Sit, 2005/02/14
- Re[2]: [Axiom-developer] [Q] How to classify # integrate(log(%i+z^2), z) -> 2 ?,
Vladimir Bondarenko <=
- RE: [Axiom-developer] [Q] How to classify # integrate(log(%i+z^2), z) -> 2 ?, Bill Page, 2005/02/14
- Re: [Axiom-developer] [Q] How to classify # integrate(log(%i+z^2), z) -> 2 ?, William Sit, 2005/02/15
- [Axiom-developer] Archive file naming request, Camm Maguire, 2005/02/15
- RE: [Axiom-developer] Archive file naming request, Bill Page, 2005/02/15