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About: Pierce–Birkhoff conjecture     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatConjecturesyago:Abstraction100002137yago:Cognition100023271yago:Concept105835747yago:Content105809192yago:Hypothesis105888929yago:Idea105833840yago:PsychologicalFeature100023100yago:Speculation105891783 New Facet based on Instances of this Class

In abstract algebra, the Pierce–Birkhoff conjecture asserts that any piecewise-polynomial function can be expressed as a maximum of finite minima of finite collections of polynomials. It was first stated, albeit in non-rigorous and vague wording, in the 1956 paper of Garrett Birkhoff and in which they first introduced f-rings. The modern, rigorous statement of the conjecture was formulated by and John R. Isbell, who worked on the problem in the early 1960s in connection with their work on f-rings. Their formulation is as follows: The conjecture was proved true for n = 1 and 2 by .