Lesson plan
Triangular decomposition
In computer algebra, a triangular decomposition of a polynomial system is a set of simpler polynomial systems such that a point is a solution of if and only if it is a solution of one of the systems . When the purpose is to describe the solution set of in the algebraic closure of its coefficient field, those simpler systems are regular chains. If the coefficients of the polynomial systems are real numbers, then the real solutions of 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.
Article summary
In computer algebra, a triangular decomposition of a polynomial system is a set of simpler polynomial systems such that a point is a solution of if and only if it is a solution of one of the systems . When the purpose is to describe the solution set of in the algebraic closure of its coefficient field, those simpler systems are regular chains. If the coefficients of the polynomial systems are real numbers, then the real solutions of 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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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
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- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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