FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2327518860> ?p ?o ?g. }

• W2327518860 abstract "Robbiano classified term orders by using ordered systems of vectors. Unfortunately his classification gives little information as to the intuitive “shape” of these spaces. We seek to understand the structure of the spaces of term orders by introducing a topology on them. We first consider the space of term orders in the bivariate case. We convert weight vectors into slopes and determine that rational slopes require the selection of a “tiebreaking” term order while irrational slopes represent term orders by themselves. By placing an order topology on this space of bivariate term orders, we show that this space has several topological properties. All of these topological properties imply that the space of bivariate term orders is homeomorphic to the Cantor set. We then consider the spaces of term orders in the general case. We set up a description of the space of term orders in n ≥ 2 variables as a subspace of a function space. When we consider the topological properties of this view of the term order space on n ≥ 2 variables, we find that it is homeomorphic to a compact subset of the Cantor set. These topological descriptions yield important facts about the spaces of term orders that are otherwise very difficult to see or prove. In particular the fact that the Grobner fan of an ideal has finitely many cones is implied by the compactness of the space of term orders. This was shown previously, but the proof here is much simpler once the topological description of the spaces of term orders is determined. Finally some facts about the associated geometry are given. The realization of the term order spaces as compact subspaces of Cantor sets leads one to believe certain things about the Grobner fan. We show the relations between the Grobner fan and the Netwon polytopes of elements of the reduced Grobner bases." @default.
• W2327518860 created "2016-06-24" @default.
• W2327518860 creator A5024377310 @default.
• W2327518860 creator A5025625217 @default.
• W2327518860 date "2002-01-01" @default.
• W2327518860 modified "2023-09-23" @default.
• W2327518860 title "Term orders on the polynomial ring and the grobner fan of an ideal" @default.
• W2327518860 cites W1483218536 @default.
• W2327518860 cites W1495410784 @default.
• W2327518860 cites W1524190946 @default.
• W2327518860 cites W1982438618 @default.
• W2327518860 cites W1989763544 @default.
• W2327518860 cites W1996734913 @default.
• W2327518860 cites W2018615018 @default.
• W2327518860 cites W2020759317 @default.
• W2327518860 cites W2056982721 @default.
• W2327518860 cites W2059522106 @default.
• W2327518860 cites W2081659888 @default.
• W2327518860 cites W2099901570 @default.
• W2327518860 cites W2153910269 @default.
• W2327518860 cites W2319466955 @default.
• W2327518860 hasPublicationYear "2002" @default.
• W2327518860 type Work @default.
• W2327518860 sameAs 2327518860 @default.
• W2327518860 citedByCount "1" @default.
• W2327518860 countsByYear W23275188602015 @default.
• W2327518860 crossrefType "dissertation" @default.
• W2327518860 hasAuthorship W2327518860A5024377310 @default.
• W2327518860 hasAuthorship W2327518860A5025625217 @default.
• W2327518860 hasConcept C10138342 @default.
• W2327518860 hasConcept C111472728 @default.
• W2327518860 hasConcept C111919701 @default.
• W2327518860 hasConcept C114614502 @default.
• W2327518860 hasConcept C118615104 @default.
• W2327518860 hasConcept C121332964 @default.
• W2327518860 hasConcept C134306372 @default.
• W2327518860 hasConcept C138885662 @default.
• W2327518860 hasConcept C140936041 @default.
• W2327518860 hasConcept C142730499 @default.
• W2327518860 hasConcept C162324750 @default.
• W2327518860 hasConcept C182306322 @default.
• W2327518860 hasConcept C184720557 @default.
• W2327518860 hasConcept C18648836 @default.
• W2327518860 hasConcept C202444582 @default.
• W2327518860 hasConcept C2776639384 @default.
• W2327518860 hasConcept C2778572836 @default.
• W2327518860 hasConcept C32834561 @default.
• W2327518860 hasConcept C33923547 @default.
• W2327518860 hasConcept C36605576 @default.
• W2327518860 hasConcept C41008148 @default.
• W2327518860 hasConcept C47776270 @default.
• W2327518860 hasConcept C61797465 @default.
• W2327518860 hasConcept C62520636 @default.
• W2327518860 hasConcept C81332173 @default.
• W2327518860 hasConceptScore W2327518860C10138342 @default.
• W2327518860 hasConceptScore W2327518860C111472728 @default.
• W2327518860 hasConceptScore W2327518860C111919701 @default.
• W2327518860 hasConceptScore W2327518860C114614502 @default.
• W2327518860 hasConceptScore W2327518860C118615104 @default.
• W2327518860 hasConceptScore W2327518860C121332964 @default.
• W2327518860 hasConceptScore W2327518860C134306372 @default.
• W2327518860 hasConceptScore W2327518860C138885662 @default.
• W2327518860 hasConceptScore W2327518860C140936041 @default.
• W2327518860 hasConceptScore W2327518860C142730499 @default.
• W2327518860 hasConceptScore W2327518860C162324750 @default.
• W2327518860 hasConceptScore W2327518860C182306322 @default.
• W2327518860 hasConceptScore W2327518860C184720557 @default.
• W2327518860 hasConceptScore W2327518860C18648836 @default.
• W2327518860 hasConceptScore W2327518860C202444582 @default.
• W2327518860 hasConceptScore W2327518860C2776639384 @default.
• W2327518860 hasConceptScore W2327518860C2778572836 @default.
• W2327518860 hasConceptScore W2327518860C32834561 @default.
• W2327518860 hasConceptScore W2327518860C33923547 @default.
• W2327518860 hasConceptScore W2327518860C36605576 @default.
• W2327518860 hasConceptScore W2327518860C41008148 @default.
• W2327518860 hasConceptScore W2327518860C47776270 @default.
• W2327518860 hasConceptScore W2327518860C61797465 @default.
• W2327518860 hasConceptScore W2327518860C62520636 @default.
• W2327518860 hasConceptScore W2327518860C81332173 @default.
• W2327518860 hasLocation W23275188601 @default.
• W2327518860 hasOpenAccess W2327518860 @default.
• W2327518860 hasPrimaryLocation W23275188601 @default.
• W2327518860 hasRelatedWork W103053541 @default.
• W2327518860 hasRelatedWork W1157599850 @default.
• W2327518860 hasRelatedWork W13448296 @default.
• W2327518860 hasRelatedWork W2064504548 @default.
• W2327518860 hasRelatedWork W2090497251 @default.
• W2327518860 hasRelatedWork W2152261259 @default.
• W2327518860 hasRelatedWork W2293517510 @default.
• W2327518860 hasRelatedWork W2493195292 @default.
• W2327518860 hasRelatedWork W2494355497 @default.
• W2327518860 hasRelatedWork W2507334102 @default.
• W2327518860 hasRelatedWork W2763954298 @default.
• W2327518860 hasRelatedWork W2770391733 @default.
• W2327518860 hasRelatedWork W2772457912 @default.
• W2327518860 hasRelatedWork W2783626036 @default.
• W2327518860 hasRelatedWork W2950446711 @default.
• W2327518860 hasRelatedWork W3002826 @default.
• W2327518860 hasRelatedWork W3043360678 @default.
• W2327518860 hasRelatedWork W32971838 @default.

• next