Structures · Algebra
IsRealClosed
A field R is real closed if all of the following hold:
1. R is real (that is, -1 is not a sum of squares in R).
2. for every x in R, one of x or -x is a square.
3. every odd-degree polynomial over R has a root in R.
- Defined in
- Mathlib.FieldTheory.IsRealClosed.Basic
- Shape
- One type argument · adds isSquare_or_isSquare_neg, exists_isRoot_of_odd_natDegree
Extends1
Extended by0
Nothing extends this class yet.
Concrete types that are instances0
No instance on a concrete type; it is reached through other classes.
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Assumed by13
- IsRealClosed.isSquare_or_isSquare_neg
- IsRealClosed.exists_eq_pow_of_isSquare
- IsRealClosed.exists_eq_pow_of_odd
- IsSquare.of_nonneg
- IsRealClosed.exists_eq_zpow_of_isSquare
- IsRealClosed.nonneg_iff_isSquare
- IsRealClosed.exists_isRoot_of_odd_natDegree
- IsRealClosed.isSquare_neg_of_not_isSquare
- IsRealClosed.toIsSemireal
- IsRealClosed.exists_eq_zpow_of_odd
- IsSquare.of_not_isSquare_neg
- IsRealClosed.exists_eq_pow_of_nonneg
- IsRealClosed.exists_eq_zpow_of_nonneg