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 stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! R-project.org/posting-guide.html