Theorems · Definition · field theory
LaurentPolynomial
(R : Type u_3) → [Semiring R] → Type (max u_3 0)
The semiring of Laurent polynomials with coefficients in the semiring R.
We denote it by R[T;T⁻¹].
The ring homomorphism C : R →+* R[T;T⁻¹] includes R as the constant polynomials.
- Defined in
- Mathlib.Algebra.Polynomial.Laurent
- Cited by
- 98 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 4 definitions · uses no axioms
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- AddMonoidAlgebraproof · cited by 649
Cited by109
Results whose statement or proof uses this declaration.
- LaurentPolynomial.Tstatement · cited by 55
- LaurentPolynomial.Cstatement · cited by 47
- Polynomial.toLaurentstatement · cited by 29
- LaurentPolynomial.smevalstatement and proof · cited by 11
- LaurentPolynomial.degreestatement and proof · cited by 10
- LaurentPolynomial.eval₂statement · cited by 8
- LaurentPolynomial.invertstatement · cited by 8
- LaurentPolynomial.single_eq_C_mul_Tstatement · cited by 8
- LaurentPolynomial.T_zerostatement · cited by 6
- LaurentPolynomial.extstatement and proof · cited by 6
- Polynomial.toLaurent_Cstatement and proof · cited by 6
- Polynomial.toLaurent_X_powstatement · cited by 6