Theorems · Definition · field theory
LaurentPolynomial.degree
{R : Type u_1} → [inst : Semiring R] → LaurentPolynomial R → WithBot ℤThe degree of a Laurent polynomial takes values in WithBot ℤ.
If f : R[T;T⁻¹] is a Laurent polynomial, then f.degree is the maximum of its support of f,
or ⊥, if f = 0.
- Defined in
- Mathlib.Algebra.Polynomial.Laurent
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- WithBotstatement · cited by 1,498
- Finsupp.supportproof · cited by 828
- AddMonoidAlgebra.coeffproof · cited by 365
- LaurentPolynomialstatement and proof · cited by 98
- Finset.maxproof · cited by 50
Cited by10
Results whose statement or proof uses this declaration.
- LaurentPolynomial.degree_C_mul_Tstatement · cited by 4
- LaurentPolynomial.degree_C_mul_T_lestatement and proof · cited by 2
- LaurentPolynomial.degree_Cstatement and proof · cited by 1
- LaurentPolynomial.degree_zerostatement · cited by 1
- LaurentPolynomial.degree_C_itestatement and proof · cited by 0
- LaurentPolynomial.degree_C_lestatement and proof · cited by 0
- LaurentPolynomial.degree_C_mul_T_itestatement and proof · cited by 0
- LaurentPolynomial.degree_Tstatement and proof · cited by 0
- LaurentPolynomial.degree_T_lestatement and proof · cited by 0
- LaurentPolynomial.degree_eq_bot_iffstatement and proof · cited by 0