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Theorems · Inductive type · field theory

Polynomial.IsMonicOfDegree

{R : Type u_1} → [inst : Semiring R] → Polynomial R → ℕ → Prop

This says that p has natDegree n and is monic.

Defined in
Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree
Cited by
39 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
Semiring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Polynomial.IsMonicOfDegree.natDegree_eq · cited by 6IsMonicOfDegree.natDegree…Polynomial.IsMonicOfDegree.add_right · cited by 6IsMonicOfDegree.add_rightPolynomial.IsMonicOfDegree.leadingCoeff_eq · cited by 5IsMonicOfDegree.leadingCo…Polynomial.IsMonicOfDegree.monic · cited by 5IsMonicOfDegree.monicPolynomial.isMonicOfDegree_iff · cited by 5Polynomial.isMonicOfDegre…Polynomial.isMonicOfDegree_X_pow · cited by 3Polynomial.isMonicOfDegre…Polynomial.IsMonicOfDegree.mul · cited by 2IsMonicOfDegree.mulPolynomial.IsMonicOfDegree.of_mul_left · cited by 2IsMonicOfDegree.of_mul_le…Polynomial.IsMonicOfDegree.coeff_eq · cited by 2IsMonicOfDegree.coeff_eqPolynomial.isMonicOfDegree_X · cited by 2Polynomial.isMonicOfDegre…Polynomial.isMonicOfDegree_X_add_one · cited by 2Polynomial.isMonicOfDegre…Polynomial.isMonicOfDegree_sub_add_two · cited by 2Polynomial.isMonicOfDegre…Polynomial.isMonicOfDegree_zero_iff · cited by 1Polynomial.isMonicOfDegre…Polynomial.IsMonicOfDegree.of_mul_right · cited by 1IsMonicOfDegree.of_mul_ri…Polynomial.IsMonicOfDegree.sub · cited by 1IsMonicOfDegree.subSemiring · cited by 13802SemiringPolynomial · cited by 5681PolynomialPolynomial.IsMonicOfDegreeCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by41

Results whose statement or proof uses this declaration.