Displaying similar documents to “Geometry of the locus of polynomials of degree 4 with iterative roots”

Algebraic condition for decomposition of large-scale linear dynamic systems

Henryk Górecki (2009)

International Journal of Applied Mathematics and Computer Science

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The paper concerns the problem of decomposition of a large-scale linear dynamic system into two subsystems. An equivalent problem is to split the characteristic polynomial of the original system into two polynomials of lower degrees. Conditions are found concerning the coefficients of the original polynomial which must be fulfilled for its factorization. It is proved that knowledge of only one of the symmetric functions of those polynomials of lower degrees is sufficient for factorization...

On Roots of Polynomials and Algebraically Closed Fields

Christoph Schwarzweller (2017)

Formalized Mathematics

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In this article we further extend the algebraic theory of polynomial rings in Mizar [1, 2, 3]. We deal with roots and multiple roots of polynomials and show that both the real numbers and finite domains are not algebraically closed [5, 7]. We also prove the identity theorem for polynomials and that the number of multiple roots is bounded by the polynomial’s degree [4, 6].