Abstract
One of the classical problems of mathematics is to solve a polynomial equation. One approach to this is to take account of the fact that polynomials have symmetries that can be realized in geometric spaces. The idea is to solve an equation in an elegant way. During the past eight years I have pursued this goal by developing solutions based on iteration. This involves the repeated application of a process that possesses the very symmetries of the polynomial to be solved. An iterative procedure for solving an equation has two aspects:
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Geometric: a space where the polynomial’s symmetry can be realized
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Dynamical: an iterated transformation that respects the symmetry of the equation
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References
S. Crass. Solving the sextic by iteration: A study in complex geometry and dynamics. Experiment. Math. 8 (1999) No. 3, 209–240.
S. Crass, 2001. Solving the quintic by iteration in three dimensions. Experiment. Math. 10 (2001) No. 1, 1–24.
H. Nusse and J. Yorke. Dynamics: Numerical Explorations Springer-Verlag, 1994. UNIX implementation by E. Kostelich.
H. Nusse and J. Yorke. Dynamics: Numerical Explorations, 2e Springer-Verlag, 1998. Computer program Dynamics 2 by B. Hunt and E. Kostelich.
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© 2002 Springer-Verlag Berlin Heidelberg
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Crass, S. (2002). Solving Polynomials by Iteration. In: Bruter, C.P. (eds) Mathematics and Art. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04909-9_9
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DOI: https://doi.org/10.1007/978-3-662-04909-9_9
Publisher Name: Springer, Berlin, Heidelberg
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