Theorems · Theorem · field theory
Polynomial.natDegree_C_mul
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R} {a : R} [NoZeroDivisors R],
a ≠ 0 → (Polynomial.C a * p).natDegree = p.natDegree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Lemmas
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNoZeroDivisors
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Cstatement · cited by 1,598
- Polynomial.natDegreestatement · cited by 1,105
- Polynomial.degreeproof · cited by 643
- NoZeroDivisorsstatement and proof · cited by 545
- WithBot.unbotDproof · cited by 49
- Polynomial.degree_C_mulproof · cited by 6
Cited by10
Results whose statement or proof uses this declaration.
- Polynomial.Splits.natDegree_eq_card_rootsproof · cited by 16
- Polynomial.resultant_eq_prod_evalproof · cited by 3
- RatFunc.natDegree_minpolyXproof · cited by 2
- Irreducible.isPrimitiveproof · cited by 2
- Polynomial.splits_iff_comp_splits_of_natDegree_eq_oneproof · cited by 1
- RatFunc.finrank_eq_max_natDegreeproof · cited by 1
- Polynomial.Irreducible.natDegree_dvd_finrankproof · cited by 1
- Polynomial.nextCoeff_C_mulproof · cited by 1
- Polynomial.resultant_eq_prod_roots_subproof · cited by 1
- Polynomial.resultant_eq_zero_iffproof · cited by 0