Theorems · Theorem · field theory
Polynomial.map_expand
∀ {R : Type u} [inst : CommSemiring R] {S : Type v} [inst_1 : CommSemiring S] {p : ℕ} {f : R →+* S} {q : Polynomial R},
Polynomial.map f ((Polynomial.expand R p) q) = (Polynomial.expand S p) (Polynomial.map f q)- Defined in
- Mathlib.Algebra.Polynomial.Expand
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- map_zeroproof · cited by 1,614
- Polynomial.Cproof · cited by 1,598
- Polynomial.coeffproof · cited by 1,045
- Polynomial.mapstatement and proof · cited by 806
- Polynomial.evalproof · cited by 796
- Polynomial.extproof · cited by 118
- Polynomial.coeff_mapproof · cited by 114
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.natSepDegree_expandproof · cited by 4
- Polynomial.cyclotomic_expand_eq_cyclotomicproof · cited by 2
- Polynomial.cyclotomic_expand_eq_cyclotomic_mulproof · cited by 2
- polynomial_expand_eqproof · cited by 1
- IsPrimitiveRoot.minpoly_dvd_pow_modproof · cited by 1
- Polynomial.cyclotomic_mul_prime_dvd_eq_powproof · cited by 1
- Polynomial.cyclotomic_mul_prime_eq_pow_of_not_dvdproof · cited by 0