Real tropicalization and negative faces of the Newton polytope

Institut for Matematiske Fag

Real tropicalization and negative faces of the Newton polytope

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Standard

Real tropicalization and negative faces of the Newton polytope. / Telek, Máté L.

I: Journal of Pure and Applied Algebra, Bind 228, Nr. 6, 107564, 2024.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Telek, ML 2024, 'Real tropicalization and negative faces of the Newton polytope', Journal of Pure and Applied Algebra, bind 228, nr. 6, 107564. https://doi.org/10.1016/j.jpaa.2023.107564

APA

Telek, M. L. (2024). Real tropicalization and negative faces of the Newton polytope. Journal of Pure and Applied Algebra, 228(6), [107564]. https://doi.org/10.1016/j.jpaa.2023.107564

Vancouver

Telek ML. Real tropicalization and negative faces of the Newton polytope. Journal of Pure and Applied Algebra. 2024;228(6). 107564. https://doi.org/10.1016/j.jpaa.2023.107564

Author

Telek, Máté L. / Real tropicalization and negative faces of the Newton polytope. I: Journal of Pure and Applied Algebra. 2024 ; Bind 228, Nr. 6.

Bibtex

@article{ee228888771a467daa63f63b2c0f6633,

title = "Real tropicalization and negative faces of the Newton polytope",

abstract = "In this work, we explore the relation between the tropicalization of a real semi-algebraic set S={f1<0,…,fk<0} defined in the positive orthant and the combinatorial properties of the defining polynomials f1,…,fk. We describe a cone that depends only on the face structure of the Newton polytopes of f1,…,fk and the signs attained by these polynomials. This cone provides an inner approximation of the real tropicalization, and it coincides with the real tropicalization if S={f<0} and the polynomial f has generic coefficients. Furthermore, we show that for a maximally sparse polynomial f the real tropicalization of S={f<0} is determined by the outer normal cones of the Newton polytope of f and the signs of its coefficients. Our arguments are valid also for signomials, that is, polynomials with real exponents defined in the positive orthant.",

keywords = "Logarithmic limit set, Semi-algebraic set, Signed support, Signomial",

author = "Telek, {M{\'a}t{\'e} L.}",

note = "Publisher Copyright: {\textcopyright} 2023 The Author(s)",

year = "2024",

doi = "10.1016/j.jpaa.2023.107564",

language = "English",

volume = "228",

journal = "Journal of Pure and Applied Algebra",

issn = "0022-4049",

publisher = "Elsevier BV * North-Holland",

number = "6",

}

RIS

TY - JOUR

T1 - Real tropicalization and negative faces of the Newton polytope

AU - Telek, Máté L.

PY - 2024

Y1 - 2024

N2 - In this work, we explore the relation between the tropicalization of a real semi-algebraic set S={f1<0,…,fk<0} defined in the positive orthant and the combinatorial properties of the defining polynomials f1,…,fk. We describe a cone that depends only on the face structure of the Newton polytopes of f1,…,fk and the signs attained by these polynomials. This cone provides an inner approximation of the real tropicalization, and it coincides with the real tropicalization if S={f<0} and the polynomial f has generic coefficients. Furthermore, we show that for a maximally sparse polynomial f the real tropicalization of S={f<0} is determined by the outer normal cones of the Newton polytope of f and the signs of its coefficients. Our arguments are valid also for signomials, that is, polynomials with real exponents defined in the positive orthant.

AB - In this work, we explore the relation between the tropicalization of a real semi-algebraic set S={f1<0,…,fk<0} defined in the positive orthant and the combinatorial properties of the defining polynomials f1,…,fk. We describe a cone that depends only on the face structure of the Newton polytopes of f1,…,fk and the signs attained by these polynomials. This cone provides an inner approximation of the real tropicalization, and it coincides with the real tropicalization if S={f<0} and the polynomial f has generic coefficients. Furthermore, we show that for a maximally sparse polynomial f the real tropicalization of S={f<0} is determined by the outer normal cones of the Newton polytope of f and the signs of its coefficients. Our arguments are valid also for signomials, that is, polynomials with real exponents defined in the positive orthant.

KW - Logarithmic limit set

KW - Semi-algebraic set

KW - Signed support

KW - Signomial

U2 - 10.1016/j.jpaa.2023.107564

DO - 10.1016/j.jpaa.2023.107564

M3 - Journal article

AN - SCOPUS:85177849957

VL - 228

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 6

M1 - 107564

ER -

ID: 380352938