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Theorems · Theorem · field theory

Polynomial.derivative_sub

∀ {R : Type u} [inst : Ring R] {f g : Polynomial R},
  Polynomial.derivative (f - g) = Polynomial.derivative f - Polynomial.derivative g
Defined in
Mathlib.Algebra.Polynomial.Derivative
Cited by
22 results in Mathlib
Foundations
Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Ring

Around this declaration

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

Polynomial.Chebyshev.T_derivative_eq_U · cited by 7Chebyshev.T_derivative_eq…IsCyclotomicExtension.discr_prime_pow_ne_two · cited by 4IsCyclotomicExtension.dis…Polynomial.iterate_derivative_comp_one_sub_X · cited by 3Polynomial.iterate_deriva…Polynomial.derivative_X_sub_C · cited by 3Polynomial.derivative_X_s…FiniteField.roots_X_pow_card_sub_X · cited by 2FiniteField.roots_X_pow_c…Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_derivative_T_eq_poly_in_T · cited by 1Chebyshev.one_sub_X_sq_mu…Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_derivative_U_eq_poly_in_U · cited by 1Chebyshev.one_sub_X_sq_mu…Polynomial.divByMonic_add_X_sub_C_mul_derivative_divByMonic_eq_derivative · cited by 1Polynomial.divByMonic_add…galois_poly_separable · cited by 1galois_poly_separableLagrange.derivative_nodal · cited by 1Lagrange.derivative_nodalexists_derivative_mul_eq_and_isIntegral_coeff · cited by 1exists_derivative_mul_eq_…WeierstrassCurve.Affine.nonsingular_negAdd_of_eval_derivative_ne_zero · cited by 1Affine.nonsingular_negAdd…eval_minpolyDiv_self · cited by 1eval_minpolyDiv_selfWeierstrassCurve.Affine.derivative_addPolynomial_slope · cited by 1Affine.derivative_addPoly…Polynomial.eval_multiset_prod_X_sub_C_derivative · cited by 1Polynomial.eval_multiset_…DFunLike.coe · cited by 62936DFunLike.coeRingHom.id · cited by 18349RingHom.idLinearMap · cited by 10215LinearMapRing · cited by 7463RingPolynomial · cited by 5681Polynomialmap_sub · cited by 565map_subPolynomial.derivative · cited by 331Polynomial.derivativePolynomial.derivative_subCITED BYCITES

Cites7

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

Cited by22

Results whose statement or proof uses this declaration.