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.
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.
Source: Wikipedia "Triangular decomposition" · CC BY-SA 4.0
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