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Re: Advanced symbolic Integration using Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg59743] Re: Advanced symbolic Integration using Mathematica
  • From: "James Gilmore" <james.gilmore at yale.edu>
  • Date: Fri, 19 Aug 2005 04:32:23 -0400 (EDT)
  • Organization: Yale University
  • References: <ddpt6m$orm$1@smc.vnet.net> <dds9ba$912$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

I continued a discussion on this topic offline with a WRI employee. I was 
convinced of the need for Integrate to return conditions on integrals -- a 
safeguard for the user and Mathematica. However, I noted that the
documentation for Integrate and its options, in particular GenerateConditions,
needs to be improved. I suggested the following examples under
"Further Examples" in the "GenerateConditions" section:

Integrate[y*Exp[(-a)*x]*Exp[(-b)*y], {x, 0, Infinity}, {y, 0, Infinity}]
Integrate[y*Exp[(-a)*x]*Exp[(-b)*y], {y, 0, Infinity}, {x, 0, Infinity}]
Integrate[y*Exp[(-a)*x]*Exp[(-b)*y], {x, 0, Infinity}, {y, 0, Infinity}, 
GenerateConditions->False]
Integrate[y*Exp[(-a)*x]*Exp[(-b)*y], {y, 0, Infinity}, {x, 0, Infinity}, 
GenerateConditions->True]

For the beginner, this will clearly demonstrate how Integrate generates 
conditions for multi-dimensional integrals. Given that multi-dimensional 
integrals are extremely common, this inclusion is a must. It may also help 
to reduce the number of bug reports for Integrate with the default setting, 
GenerateConditions->Automatic. Under this setting, only the outer integral 
returns conditions, which can be very hazardous for certain integrals. I 
recall having trouble evaluating Feynman parameter integrals with Mathematica
last semester, especially when working with a 3 loop diagram. This
documentation would have speeded up the solution process.

Any other comments on Integrate Documentation?

-- 
James Gilmore
Graduate Student
Department of Physics
Yale University
New Haven, CT 06520 USA

"James Gilmore" <james.gilmore at yale.edu> wrote in message 
news:dds9ba$912$1 at smc.vnet.net...
>
> On a sidebar, everyone I have talked with dislikes the elaborate 
> conditions
> Integrate generates these days. Warn your group about these to be on the
> safe side. I have thought since 5.0 that Integrate has become too general.
> Perhaps a function, IntegrateNoNosense, which has only the bare essentials
> of Integrate, is required in a future release of Mathematica. Then new and
> experienced users do not have to deal with these annoyances constantly.
> 


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