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Theorems · Theorem · field theory

Polynomial.C_mul

∀ {R : Type u} {a b : R} [inst : Semiring R], Polynomial.C (a * b) = Polynomial.C a * Polynomial.C b
Defined in
Mathlib.Algebra.Polynomial.Basic
Cited by
35 results in Mathlib
Foundations
Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Semiring

Around this declaration

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

minpoly.eq_of_irreducible · cited by 8minpoly.eq_of_irreduciblePolynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_map · cited by 4IsPrimitive.irreducible_i…Polynomial.Splits.of_natDegree_le_one · cited by 4Splits.of_natDegree_le_onePolynomial.Splits.of_natDegree_le_one_of_invertible · cited by 4Splits.of_natDegree_le_on…Polynomial.isUnit_iff_degree_eq_zero · cited by 3Polynomial.isUnit_iff_deg…Polynomial.irreducible_of_monic · cited by 3Polynomial.irreducible_of…WeierstrassCurve.C_Ψ₂Sq · cited by 3WeierstrassCurve.C_Ψ₂SqIsIntegrallyClosed.eq_map_mul_C_of_dvd · cited by 2IsIntegrallyClosed.eq_map…Polynomial.associated_primPart_mul · cited by 2Polynomial.associated_pri…Cubic.C_mul_prod_X_sub_C_eq · cited by 2Cubic.C_mul_prod_X_sub_C_…Polynomial.roots_C_mul_X_sub_C_of_IsUnit · cited by 2Polynomial.roots_C_mul_X_…Polynomial.isCoprime_X_sub_C_of_isUnit_sub · cited by 2Polynomial.isCoprime_X_su…Polynomial.Monic.irreducible_iff_irreducible_map_fraction_map · cited by 2Monic.irreducible_iff_irr…WeierstrassCurve.Affine.CoordinateRing.XYIdeal_add_eq · cited by 1CoordinateRing.XYIdeal_ad…WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eq₁ · cited by 1CoordinateRing.XYIdeal_eq₁DFunLike.coe · cited by 62936DFunLike.coeSemiring · cited by 13802SemiringRingHom · cited by 10189RingHomPolynomial · cited by 5681PolynomialPolynomial.C · cited by 1598Polynomial.CRingHom.map_mul · cited by 45RingHom.map_mulPolynomial.C_mulCITED BYCITES

Cites6

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

Cited by35

Results whose statement or proof uses this declaration.