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.
>