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Theorems · Theorem · field theory

Polynomial.map_mul

∀ {R : Type u} {S : Type v} [inst : Semiring R] {p q : Polynomial R} [inst_1 : Semiring S] (f : R →+* S),
  Polynomial.map f (p * q) = Polynomial.map f p * Polynomial.map f q
Defined in
Mathlib.Algebra.Polynomial.Eval.Defs
Cited by
90 results in Mathlib
Foundations
Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringSemiring

Around this declaration

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

Polynomial.mapRingHom · cited by 98Polynomial.mapRingHomPolynomial.Splits.map · cited by 19Splits.mapPolynomial.derivative_map · cited by 17Polynomial.derivative_mapdescPochhammer_succ_right · cited by 14descPochhammer_succ_rightPolynomial.map_comp · cited by 14Polynomial.map_compPolynomial.map_dvd_map' · cited by 14Polynomial.map_dvd_map'Polynomial.Separable.map · cited by 14Separable.mapascPochhammer_succ_right · cited by 11ascPochhammer_succ_righthasDerivAt_bernoulliFun · cited by 5hasDerivAt_bernoulliFunWeierstrassCurve.map_Ψ₂Sq · cited by 5WeierstrassCurve.map_Ψ₂SqascPochhammer_map · cited by 5ascPochhammer_mapPolynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_map · cited by 4IsPrimitive.irreducible_i…WeierstrassCurve.map_preΨ₄ · cited by 4WeierstrassCurve.map_preΨ₄WeierstrassCurve.map_Ψ₃ · cited by 4WeierstrassCurve.map_Ψ₃WeierstrassCurve.Affine.map_polynomial · cited by 4Affine.map_polynomialDFunLike.coe · cited by 62936DFunLike.coeSemiring · cited by 13802SemiringRingHom · cited by 10189RingHomPolynomial · cited by 5681PolynomialPolynomial.X · cited by 1639Polynomial.XPolynomial.C · cited by 1598Polynomial.CPolynomial.coeff · cited by 1045Polynomial.coeffRingHom.comp · cited by 899RingHom.compPolynomial.map · cited by 806Polynomial.mapPolynomial.eval₂ · cited by 267Polynomial.eval₂Commute.symm · cited by 79Commute.symmPolynomial.commute_X · cited by 13Polynomial.commute_XPolynomial.eval₂_mul_noncomm · cited by 7Polynomial.eval₂_mul_nonc…Polynomial.map_mulCITED BYCITES

Cites13

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

Cited by91

Results whose statement or proof uses this declaration.