Theorems · Theorem · field theory
LaurentPolynomial.smeval_single
∀ {R : Type u_1} {S : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid S] [inst_2 : SMulWithZero R S]
[inst_3 : Monoid S] (x : Sˣ) (n : ℤ) (r : R), LaurentPolynomial.smeval (AddMonoidAlgebra.single n r) x = r • ↑(x ^ n)- Defined in
- Mathlib.Algebra.Polynomial.Laurent
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Monoidstatement and proof · cited by 3,887
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- zero_smulproof · cited by 716
- AddMonoidAlgebra.singlestatement · cited by 250
- Finsupp.sum_single_indexproof · cited by 130
- SMulWithZerostatement and proof · cited by 113
- LaurentPolynomial.smevalstatement · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- LaurentPolynomial.smeval_C_mul_T_nproof · cited by 1
- LaurentPolynomial.smeval_T_powproof · cited by 1
- LaurentPolynomial.smeval_Cproof · cited by 0