The Fedosov ∗-product in Mathematica

The computer program ‘Fecom.nb’ implementing the Fedosov ∗-product in Darboux coordinates is presented. It has been written in Mathematica 6.0 but it can be easily modified to be run in some earlier version of Mathematica. To optimize computations elements of the Weyl algebra are treated as polynomials. Several procedures which order the terms are included.Program summaryProgram title: Fecom.nbCatalogue identifier: AEBU_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBU_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 4758No. of bytes in distributed program, including test data, etc.: 40 585Distribution format: tar.gzProgramming language: Mathematica v.6.0Computer: Any computer able to run MathematicaOperating system: Any operating system capable of running MathematicaRAM: Sufficient for the installation of MathematicaClassification: 17.16Nature of problem: Computing the ∗-product of the Weyl type in the Fedosov formalism in a Darboux chart.Solution method: Inputting the dimension of the phase space, coefficients of the symplectic connection, the range of approximation and the functions to be multiplied; computing the Abelian connection and the flat sections of the Weyl bundle representing the multiplied functions; calculating the projection of the o- product of these flat sections on the phase space.Running time: Details of the time taken for various example runs are given in Section 4 of the manuscript. The test run provided with the distribution took approximately 2 minutes using Mathematica 5.1 on a Windows XP machine.