Finding All Solutions to a System of Polynomial Equations
- 1 January 1985
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 44 (169) , 125-133
- https://doi.org/10.2307/2007797
Abstract
Given a polynomial equation of degree d over the complex domain, the Fundamental Theorem of Algebra tells us that there are d solutions, assuming that the solutions are counted by multiplicity. These solutions can be approximated by deforming a standard nth degree equation into the given equation, and following the solutions through the deformation. This is called the homotopy method. The Fundamental Theorem of Algebra can be proved by the same technique.Keywords
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