Theorems · Theorem · commutative algebra
normalize_apply
∀ {α : Type u_1} [inst : MonoidWithZero α] [inst_1 : NormalizationMonoid α] (x : α), normalize x = x * ↑(normUnit x)- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Units.valstatement · cited by 1,966
- MonoidWithZerostatement and proof · cited by 456
- NormalizationMonoidstatement and proof · cited by 165
- normalizestatement · cited by 137
- NormalizationMonoid.normUnitstatement · cited by 33
Cited by8
Results whose statement or proof uses this declaration.
- Polynomial.map_dvd_map'proof · cited by 14
- Int.normalize_of_nonnegproof · cited by 4
- Ideal.count_span_normalizedFactors_eqproof · cited by 2
- Int.normalize_of_nonposproof · cited by 2
- IsGCDMonoid.isPrincipal_of_exists_mul_ne_zero_isPrincipalproof · cited by 1
- Polynomial.roots_normalizeproof · cited by 0
- Polynomial.normUnit_contentproof · cited by 0
- Polynomial.leadingCoeff_mul_prod_normalizedFactorsproof · cited by 0