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Statements

Subject Item
dbr:Triangular_decomposition
rdfs:label
Triangular decomposition
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.
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dbc:Computer_algebra_systems dbc:Computer_algebra dbc:Equations dbc:Polynomials dbc:Algebraic_geometry dbc:Algebra
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n10:Triangular_decomposition?oldid=1065437688&ns=0
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1065437688
dbo: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.
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n10:Triangular_decomposition