Matches in SemOpenAlex for { <https://semopenalex.org/work/W2963163057> ?p ?o ?g. }
Showing items 1 to 81 of
81
with 100 items per page.
- W2963163057 abstract "Tropical algebra emerges in many fields of mathematics such as algebraic geometry, mathematical physics and combinatorial optimization. In part, its importance is related to the fact that it makes various parameters of mathematical objects computationally accessible. Tropical polynomials play a fundamental role in this, especially for the case of algebraic geometry. On the other hand, many algebraic questions behind tropical polynomials remain open. In this paper we address four basic questions on tropical polynomials closely related to their computational properties: 1. Given a polynomial with a certain support (set of monomials) and a (finite) set of inputs, when is it possible for the polynomial to vanish on all these inputs? 2. A more precise question, given a polynomial with a certain support and a (finite) set of inputs, how many roots can this polynomial have on this set of inputs? 3. Given an integer $k$, for which $s$ there is a set of $s$ inputs such that any non-zero polynomial with at most $k$ monomials has a non-root among these inputs? 4. How many integer roots can have a one variable polynomial given by a tropical algebraic circuit? In the classical algebra well-known results in the direction of these questions are Combinatorial Nullstellensatz due to N. Alon, J. Schwartz - R. Zippel Lemma and Universal Testing Set for sparse polynomials respectively. The classical analog of the last question is known as $tau$-conjecture due to M. Shub - S. Smale. In this paper we provide results on these four questions for tropical polynomials." @default.
- W2963163057 created "2019-07-30" @default.
- W2963163057 creator A5038669776 @default.
- W2963163057 creator A5058530409 @default.
- W2963163057 date "2017-05-31" @default.
- W2963163057 modified "2023-09-27" @default.
- W2963163057 title "Tropical Combinatorial Nullstellensatz and Fewnomials Testing" @default.
- W2963163057 hasPublicationYear "2017" @default.
- W2963163057 type Work @default.
- W2963163057 sameAs 2963163057 @default.
- W2963163057 citedByCount "0" @default.
- W2963163057 crossrefType "posted-content" @default.
- W2963163057 hasAuthorship W2963163057A5038669776 @default.
- W2963163057 hasAuthorship W2963163057A5058530409 @default.
- W2963163057 hasConcept C11252640 @default.
- W2963163057 hasConcept C114614502 @default.
- W2963163057 hasConcept C118615104 @default.
- W2963163057 hasConcept C134306372 @default.
- W2963163057 hasConcept C136119220 @default.
- W2963163057 hasConcept C177264268 @default.
- W2963163057 hasConcept C18903297 @default.
- W2963163057 hasConcept C199360897 @default.
- W2963163057 hasConcept C202444582 @default.
- W2963163057 hasConcept C202652594 @default.
- W2963163057 hasConcept C2777759810 @default.
- W2963163057 hasConcept C2780990831 @default.
- W2963163057 hasConcept C33923547 @default.
- W2963163057 hasConcept C41008148 @default.
- W2963163057 hasConcept C46757340 @default.
- W2963163057 hasConcept C68363185 @default.
- W2963163057 hasConcept C86803240 @default.
- W2963163057 hasConcept C90119067 @default.
- W2963163057 hasConcept C9376300 @default.
- W2963163057 hasConcept C97137487 @default.
- W2963163057 hasConceptScore W2963163057C11252640 @default.
- W2963163057 hasConceptScore W2963163057C114614502 @default.
- W2963163057 hasConceptScore W2963163057C118615104 @default.
- W2963163057 hasConceptScore W2963163057C134306372 @default.
- W2963163057 hasConceptScore W2963163057C136119220 @default.
- W2963163057 hasConceptScore W2963163057C177264268 @default.
- W2963163057 hasConceptScore W2963163057C18903297 @default.
- W2963163057 hasConceptScore W2963163057C199360897 @default.
- W2963163057 hasConceptScore W2963163057C202444582 @default.
- W2963163057 hasConceptScore W2963163057C202652594 @default.
- W2963163057 hasConceptScore W2963163057C2777759810 @default.
- W2963163057 hasConceptScore W2963163057C2780990831 @default.
- W2963163057 hasConceptScore W2963163057C33923547 @default.
- W2963163057 hasConceptScore W2963163057C41008148 @default.
- W2963163057 hasConceptScore W2963163057C46757340 @default.
- W2963163057 hasConceptScore W2963163057C68363185 @default.
- W2963163057 hasConceptScore W2963163057C86803240 @default.
- W2963163057 hasConceptScore W2963163057C90119067 @default.
- W2963163057 hasConceptScore W2963163057C9376300 @default.
- W2963163057 hasConceptScore W2963163057C97137487 @default.
- W2963163057 hasLocation W29631630571 @default.
- W2963163057 hasOpenAccess W2963163057 @default.
- W2963163057 hasPrimaryLocation W29631630571 @default.
- W2963163057 hasRelatedWork W12341063 @default.
- W2963163057 hasRelatedWork W1519898734 @default.
- W2963163057 hasRelatedWork W156656824 @default.
- W2963163057 hasRelatedWork W164167060 @default.
- W2963163057 hasRelatedWork W1676075617 @default.
- W2963163057 hasRelatedWork W2130918732 @default.
- W2963163057 hasRelatedWork W2269650202 @default.
- W2963163057 hasRelatedWork W2399652977 @default.
- W2963163057 hasRelatedWork W2403492326 @default.
- W2963163057 hasRelatedWork W2565421891 @default.
- W2963163057 hasRelatedWork W2620849562 @default.
- W2963163057 hasRelatedWork W2734482326 @default.
- W2963163057 hasRelatedWork W2785277260 @default.
- W2963163057 hasRelatedWork W2888169115 @default.
- W2963163057 hasRelatedWork W293719221 @default.
- W2963163057 hasRelatedWork W2952034740 @default.
- W2963163057 hasRelatedWork W2964244809 @default.
- W2963163057 hasRelatedWork W2965416181 @default.
- W2963163057 hasRelatedWork W2973199724 @default.
- W2963163057 hasRelatedWork W3104134886 @default.
- W2963163057 isParatext "false" @default.
- W2963163057 isRetracted "false" @default.
- W2963163057 magId "2963163057" @default.
- W2963163057 workType "article" @default.