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Theorems · Theorem · field theory

Polynomial.derivative_X

∀ {R : Type u} [inst : Semiring R], Polynomial.derivative Polynomial.X = 1
Defined in
Mathlib.Algebra.Polynomial.Derivative
Cited by
34 results in Mathlib
Foundations
Depth 108 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.

Polynomial.Chebyshev.T_derivative_eq_U · cited by 7Chebyshev.T_derivative_eq…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.separable_C_mul_X_pow_add_C_mul_X_add_C · cited by 2Polynomial.separable_C_mu…Polynomial.derivative_X_add_C · cited by 2Polynomial.derivative_X_a…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.derivative_eval₂_C · cited by 1Polynomial.derivative_eva…Polynomial.derivative_expand · cited by 1Polynomial.derivative_exp…galois_poly_separable · cited by 1galois_poly_separableexists_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_selfPolynomial.Bivariate.pderiv_one_equivMvPolynomial · cited by 1Bivariate.pderiv_one_equi…DFunLike.coe · cited by 62936DFunLike.coeRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringLinearMap · cited by 10215LinearMapPolynomial · cited by 5681Polynomialmul_one · cited by 3885mul_oneNat.cast_one · cited by 2501Nat.cast_onePolynomial.X · cited by 1639Polynomial.XPolynomial.C · cited by 1598Polynomial.Cmap_one · cited by 861map_onePolynomial.derivative · cited by 331Polynomial.derivativePolynomial.monomial · cited by 256Polynomial.monomialtsub_self · cited by 154tsub_selfPolynomial.derivative_monomial · cited by 8Polynomial.derivative_mon…Polynomial.derivative_XCITED BYCITES

Cites14

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

Cited by34

Results whose statement or proof uses this declaration.