# Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5

Serdica Mathematical Journal (2002)

- Volume: 28, Issue: 2, page 117-152
- ISSN: 1310-6600

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topKostov, Vladimir. "Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5." Serdica Mathematical Journal 28.2 (2002): 117-152. <http://eudml.org/doc/11551>.

@article{Kostov2002,

abstract = {∗ Research partially supported by INTAS grant 97-1644A real polynomial of one real variable is hyperbolic (resp.
strictly hyperbolic) if it has only real roots (resp. if its roots are real and
distinct). We prove that there are 116 possible non-degenerate configurations
between the roots of a degree 5 strictly hyperbolic polynomial and
of its derivatives (i.e. configurations without equalities between roots).
The standard Rolle theorem allows 286 such configurations. To obtain
the result we study the hyperbolicity domain of the family P (x; a, b, c) =
x^5 − x^3 + ax^2 + bx + c (i.e. the set of values of a, b, c ∈ R for which the
polynomial is hyperbolic) and its stratification defined by the discriminant
sets Res(P^(i) , P^(j) ) = 0, 0 ≤ i < j ≤ 4.},

author = {Kostov, Vladimir},

journal = {Serdica Mathematical Journal},

keywords = {Hyperbolic Polynomial; Hyperbolicity Domain; Overdetermined Stratum; hyperbolic polynomial; hyperbolicity domain; overdetermined stratum},

language = {eng},

number = {2},

pages = {117-152},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5},

url = {http://eudml.org/doc/11551},

volume = {28},

year = {2002},

}

TY - JOUR

AU - Kostov, Vladimir

TI - Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5

JO - Serdica Mathematical Journal

PY - 2002

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 28

IS - 2

SP - 117

EP - 152

AB - ∗ Research partially supported by INTAS grant 97-1644A real polynomial of one real variable is hyperbolic (resp.
strictly hyperbolic) if it has only real roots (resp. if its roots are real and
distinct). We prove that there are 116 possible non-degenerate configurations
between the roots of a degree 5 strictly hyperbolic polynomial and
of its derivatives (i.e. configurations without equalities between roots).
The standard Rolle theorem allows 286 such configurations. To obtain
the result we study the hyperbolicity domain of the family P (x; a, b, c) =
x^5 − x^3 + ax^2 + bx + c (i.e. the set of values of a, b, c ∈ R for which the
polynomial is hyperbolic) and its stratification defined by the discriminant
sets Res(P^(i) , P^(j) ) = 0, 0 ≤ i < j ≤ 4.

LA - eng

KW - Hyperbolic Polynomial; Hyperbolicity Domain; Overdetermined Stratum; hyperbolic polynomial; hyperbolicity domain; overdetermined stratum

UR - http://eudml.org/doc/11551

ER -

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