Theorems · Theorem · field theory
Polynomial.leadingCoeff_mul_prod_normalizedFactors
∀ {R : Type u} [inst : Field R] [inst_1 : DecidableEq R] (a : Polynomial R),
Polynomial.C a.leadingCoeff * (UniqueFactorizationMonoid.normalizedFactors a).prod = aThe normalized factors of a polynomial over a field times its leading coefficient give the polynomial.
- Defined in
- Mathlib.Algebra.Polynomial.FieldDivision
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldDecidableEq
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Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Polynomial.Cstatement and proof · cited by 1,598
- map_mulproof · cited by 1,137
- map_oneproof · cited by 861
- Multiset.prodstatement and proof · cited by 528
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