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Symplectic Group Sp(2n), properties and analysis

Jean-Pierre Amiet
Organization: Univ. of Neuchatel, Switzerland
Department: Physics Inst.
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This Mathematica Package is a survey of the symplectic group Sp(2n), with an introduction to its properties, programming of its elements, and analysis of given elements. An abstract of the main properties of the symplectic group, important in Hamilton Mechanics, is given as comments in a first part. Various programming of symplectic matrices and of their Symplectic Jordan Form (a new item I believe) are given in a second part. In a third part, the analysis of a given symplectic matrix is performed, using a "smoothing" of eigenvalues to identify degeneracies that Eigenvalues[] does not reveals by lack of precision when a matrix has less eigenvectors than eigenvalues. Bibliographic references are given in a comment.

*Mathematics > Algebra > Group Theory
*Mathematics > Algebra > Linear Algebra
*Science > Physics > Mechanics

Linear Algebra, Symplectic group, Matrices, Symplectic matrices
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SymplecticGroup.m (46.4 KB) - Package for analyzing symplectic groups