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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.
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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