R help - Jan 2005 - Cauchy's theorem

In complex analysis, Cauchy's integral theorem states (loosely 
speaking) that the path integral
of any entire differentiable function, around any closed curve, is zero.

I would like to see this numerically, using R (and indeed I would like 
to use the
residue theorem as well).

Has anyone coded up path integration?




--
Robin Hankin
Uncertainty Analyst
Southampton Oceanography Centre
European Way, Southampton SO14 3ZH, UK
  tel  023-8059-7743

I don't know about the 'in R' bit, but ISTR that Monte-Carlo (or
pseudo
Monte-Carlo) Integration is a way of doing this 'numerically'. I know
that
Mathematica implements the (pseudo Monte-Carlo)
Halton-Hammersley-Wozniakowski algorithm as Nintegrate. Perhaps something
equivalent has been coded by someone for WINBUGS (OPENBUGS) (accessible from
R via the BRUGS package).

HTH

Mike

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Robin Hankin
Sent: 20 January 2005 14:14
To: R-help at stat.math.ethz.ch
Subject: [R] Cauchy's theorem

In complex analysis, Cauchy's integral theorem states (loosely
speaking) that the path integral
of any entire differentiable function, around any closed curve, is zero.

I would like to see this numerically, using R (and indeed I would like to
use the residue theorem as well).

Has anyone coded up path integration?




--
Robin Hankin
Uncertainty Analyst
Southampton Oceanography Centre
European Way, Southampton SO14 3ZH, UK
  tel  023-8059-7743

______________________________________________
R-help at stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html