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Given a oneparameter perturbation A(x) of a constant matrix, this package offers functions to recover leading terms and orders (or their bounds) of its eigenvalues from a few low order coefficients of a matrix similar to A(x). For more info, please refer to Chapter 2 of my thesis or to the following articles:
 Jeannerod, CP., and Eckhard Pflügel. "A reduction algorithm for matrices depending on a parameter." Proceedings of the 1999 international symposium on Symbolic and algebraic computation. ACM, 1999.
 Jeannerod, ClaudePierre. "An algorithm for the eigenvalue perturbation problem: reduction of a κmatrix to a Lidskii matrix." Proceedings of the 2000 international symposium on Symbolic and algebraic computation. ACM, 2000.
AlgMoser(A,x,truncation) computes a transformation T(x) such that B = T^{1} A T is in CRV form (has both a maximal valuation v and a minimal number of nonzero volumns of valuation v).
AlgTurnPt1(A,x,truncation) where A(x) is a nonnilpotent matrix, makes use of AlgMoser to compute a transformation T1(x), an integer s (computed using the Newton polygon associated to the characteristic polynomial), and a transformation T2(x), such that applying T1(x), the ramification x =t^s, and T2(x), yields a matrix B(x) whose leading coefficient is not nilpotent (i.e. the coefficient of lowest order).
AlgTurnPt2(A,x,truncation) computes s and a transformation T(x) for the same purpose as above. In other words, it takes T1(x) to be the identity matrix and T2(x) to be T(x).
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