About: Triangular decomposition

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In computer algebra, a triangular decomposition of a polynomial system S is a set of simpler polynomial systems S1, ..., Se such that a point is a solution of S if and only if it is a solution of one of the systems S1, ..., Se.

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rdfs:label	Triangular decomposition (en)
rdfs:comment	In computer algebra, a triangular decomposition of a polynomial system S is a set of simpler polynomial systems S1, ..., Se such that a point is a solution of S if and only if it is a solution of one of the systems S1, ..., Se. (en)
sameAs	Triangular decomposition Triangular decomposition
dbp:wikiPageUsesTemplate	dbt:= dbt:Math dbt:Mvar dbt:Reflist dbt:Short_description
Subject	Algebra Algebraic geometry Computer algebra Computer algebra systems Equations Polynomials
gold:hypernym	Set
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Triangular_decomposition?oldid=1065437688&ns=0
Wikipage page ID	29321051 (xsd:integer)
page length (characters) of wiki page	12130 (xsd:nonNegativeInteger)
Wikipage revision ID	1065437688 (xsd:integer)
has abstract	In computer algebra, a triangular decomposition of a polynomial system S is a set of simpler polynomial systems S1, ..., Se such that a point is a solution of S if and only if it is a solution of one of the systems S1, ..., Se. When the purpose is to describe the solution set of S in the algebraic closure of its coefficient field, those simpler systems are regular chains. If the coefficients of the polynomial systems S1, ..., Se are real numbers, then the real solutions of S can be obtained by a triangular decomposition into regular semi-algebraic systems. In both cases, each of these simpler systems has a triangular shape and remarkable properties, which justifies the terminology. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Triangular_decomposition
is Link from a Wikipage to another Wikipage of	Daniel Lazard List of polynomial topics Elimination theory

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