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How to find all roots of complex polynomials by Newton’s method
complex polynomials Newton’s method
2015/8/26
We investigate Newton’s method to find roots of polynomials of fixed degree d, appropriately normalized: we construct a finite set of points such that, for every root of every such polynomial, at leas...
A generalized Steinberg section and branching rules for quantum groups at roots of 1
generalized Steinberg section branching rules quantum groups
2011/8/23
Abstract: In this paper we construct a generalization of the classical Steinberg section for the quotient map of a semisimple group with respect to the conjugation action. We then give various applica...
On Square Roots of the Haar State on Compact Quantum Groups
Compact quantum group Haar state normal subgroup
2011/1/20
The paper is concerned with the extension of the classical study of probability measures on a compact group which are square roots of the Haar measure, due to Diaconis and Shahshahani, to the context ...
Geometry of the locus of polynomials of degree 4 with iterative roots
Geometry polynomials iterative roots
2010/11/23
We study polynomial iterative roots of polynomials and describe the locus of complex polynomials of degree 4 admitting a polynomial iterative square root.
Complete Numerical Isolation of Real Roots in Zero-dimensional Triangular Systems
Triangular system real zero isolation sleeve bound evaluation bound
2013/9/9
We present a complete numerical algorithm of isolating all the real zeros of a zero-dimensional triangular polynomial system Fn μ Z. Our system Fn is general, with no further assumptions. In particula...
Roots of any Polynomial with Complex Integer Coefficients using Replacement Sequences, Ruler and Compass
Roots Polynomial Complex Integer Coefficients Replacement Sequences
2010/11/1
The roots of any polynomial of degree m with complex integer coefficients can be computed by manipulation of sequences made from distinct symbols and counting the different symbols in the sequences. T...
Finding roots of unity among quotients of the roots of an integral polynomial
Finding roots unity among quotients the roots integral polynomial
2013/9/3
We present an efficient algorithm for testing whether a given integral polynomial has two distinct roots a, B such that fflp is a root of unity. The test is based on results obtained by investigation ...