Theorems · Theorem · field theory
Polynomial.natDegree_monomial
∀ {R : Type u} [inst : Semiring R] [inst_1 : DecidableEq R] (i : ℕ) (r : R),
((Polynomial.monomial i) r).natDegree = if r = 0 then 0 else i- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringDecidableEq
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 and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.monomialstatement and proof · cited by 256
- Polynomial.C_mul_X_pow_eq_monomialproof · cited by 53
- Polynomial.monomial_zero_rightproof · cited by 25
- Polynomial.natDegree_C_mul_X_powproof · cited by 5
Cited by11
Results whose statement or proof uses this declaration.
- Polynomial.leadingCoeff_monomialproof · cited by 6
- Polynomial.eraseLead_monomialproof · cited by 6
- Polynomial.mirror_monomialproof · cited by 2
- Polynomial.natDegree_hasseDeriv_leproof · cited by 1
- Polynomial.coeffList_monomialproof · cited by 1
- Polynomial.natDegree_monomial_eqproof · cited by 1
- Polynomial.monomial_natDegree_leadingCoeff_eq_selfproof · cited by 1
- Polynomial.succ_signVariations_X_sub_C_mul_monomialproof · cited by 0
- Polynomial.signVariations_monomialproof · cited by 0
- Polynomial.natDegree_hasseDerivproof · cited by 0
- Polynomial.natDegree_monomial_leproof · cited by 0