Commit 2024-07-24 10:24 60c76bf7

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feat (Algebra/Ring): add isSemireal class for commutative rings (#14941) A semireal ring is a non-trivial commutative ring with unit R in which -1 : R is not a sum of squares. We add this notion to Mathlib and prove that linearly ordered fields are semireal rings. We also introduce the type of sums of squares in a type R endowed with an Add R, Zero R and Mul R instances. This contribution was created as part of the AIM workshop "Formalizing algebraic geometry" in June 2024.

Estimated changes

added theorem SquaresAddClosure
added theorem SquaresInSumSq
added def SumSqIn
added theorem isSumSq.add
added theorem isSumSq.nonneg
added inductive isSumSq