Polynomial

📁 Source: MathlibTest/Polynomial.lean

Statistics

Metric	Count
Definitions Polynomial	1
Theorems	0
Total	1

(root)

Definitions

Name	Category	Theorems
Polynomial 📖	CompData	3278 math math: Polynomial.fderiv, Polynomial.mul_div_eq_iff_isRoot, PowerSeries.coeff_mul_eq_coeff_trunc_mul_trunc₂, MvPolynomial.pUnitAlgEquiv_symm_monomial, RatFunc.instFaithfulSMulPolynomialLaurentSeries, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_apply, Polynomial.IsMonicOfDegree.add_left, Polynomial.rightInverse_ofMultiset_roots, Polynomial.support_monomial, Polynomial.logMahlerMeasure_one, Polynomial.units_coeff_zero_smul, Polynomial.coeff_prod_mem_ideal_pow_tsub, Polynomial.isUnit_C_add_X_mul_iff, WeierstrassCurve.map_ψ₂, Polynomial.natDegree_mul_X_pow, Polynomial.degree_normalize, Polynomial.isMonicOfDegree_X_add_one, Polynomial.natDegree_mul_leadingCoeff_inv, Polynomial.degreeLT.addLinearEquiv_symm_apply_inr, Lagrange.interpolate_one, Polynomial.taylor_eval, IsAdjoinRoot.repr_add_sub_repr_add_repr_mem_span, minpoly.prime_of_isIntegrallyClosed, Polynomial.ker_mapRingHom, Polynomial.isLeftCancelMulZero_iff, Polynomial.MonicDegreeEq.monic, Polynomial.degree_pow_le_of_le, RatFunc.mk_def_of_ne, Polynomial.X_pow_mul_assoc_C, Polynomial.mem_aroots', Polynomial.separable_X_add_C, Lagrange.eval_iterate_derivative_eq_sum, Polynomial.mahlerMeasure_const, Ideal.Filtration.submodule_closure_single, Polynomial.eraseLead_monomial, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, RatFunc.ofFractionRing_mk', Derivation.apply_eval_eq, Polynomial.monic_X_pow, Polynomial.leadingCoeff_mul_X_pow, Polynomial.degree_mul_le, Polynomial.coe_eq_one_iff, Polynomial.mul_divByMonic_cancel_left, Polynomial.eq_X_sub_C_of_separable_of_root_eq, Lagrange.interpolate_eq_of_values_eq_on, Polynomial.primPart_zero, Polynomial.derivative_X_sq, Polynomial.coe_normUnit_of_ne_zero, Ideal.Filtration.submodule_eq_span_le_iff_stable_ge, Polynomial.separable_X_pow_sub_C_unit, Polynomial.IsWeaklyEisensteinAt.mul, Polynomial.smeval_monomial_mul, IntermediateField.aeval_gen_minpoly, Polynomial.coeff_add_eq_left_of_lt, RatFunc.mk_coe_def, Polynomial.degree_add_div, Polynomial.splits_iff_exists_multiset, Polynomial.Chebyshev.T_eq_X_mul_U_sub_U, Polynomial.IsDistinguishedAt.mul, Polynomial.reflect_sub, polynomialFunctions.eq_adjoin_X, Polynomial.IsSplittingField.mul, Polynomial.ofFn_zero, Polynomial.toLaurent_eq_zero, Polynomial.roots_normalize, Polynomial.mem_lifts_iff_mem_alg, Polynomial.splits_of_splits_gcd_right, Polynomial.roots_expand, taylorWithin_succ, MvPolynomial.pUnitAlgEquiv_apply, PolyEquivTensor.toFunBilinear_apply_eq_sum, Polynomial.algEquivCMulXAddC_apply, Polynomial.lcoeff_comp_mapAlgHom_eq, Polynomial.mul_divByMonic_eq_iff_isRoot, Polynomial.coe_taylorAlgHom, Polynomial.eval_multiset_prod, Polynomial.transcendental, LaurentPolynomial.mk'_one_X_pow, Polynomial.cardPowDegree_zero, LinearMap.exists_monic_and_aeval_eq_zero, Polynomial.monic_X_sub_C, Polynomial.monomial_eq_monomial_iff, Polynomial.ofFinsupp_zero, RatFunc.toFractionRing_injective, RatFunc.num_div, PolynomialModule.comp_single, Polynomial.mem_image_comap_C_basicOpen, Polynomial.coeff_X_pow_mul', Polynomial.coeff_derivative, Polynomial.map_one, Polynomial.coeff_natTrailingDegree_eq_zero, Polynomial.degreeLT.instFreeSubtypeMemSubmodule, Polynomial.one_add_X_pow_sub_X_pow, Polynomial.eval₂_finset_prod, AnalyticOn.aeval_polynomial, ringKrullDim_succ_le_ringKrullDim_polynomial, PowerBasis.exists_eq_aeval, FixedPoints.minpoly.irreducible, Polynomial.eq_cyclotomic_iff, Polynomial.eval₂_multiset_prod, MvPolynomial.support_finSuccEquiv, Polynomial.algebraMap_pi_eq_aeval, Polynomial.Sequence.basis_natDegree_strictMono, Polynomial.ker_evalRingHom, Polynomial.Monic.free_quotient, StandardEtalePair.inv_aeval_X_g, Polynomial.eval₂_intCastRingHom_X, IsPurelyInseparable.minpoly_eq', LaurentPolynomial.mk'_mul_T, Polynomial.expand_eq_sum, Polynomial.root_X_sub_C, Algebra.Norm.Transitivity.polyToMatrix_cornerAddX, polynomial_smul_apply', AlgebraicGeometry.Polynomial.isOpenMap_comap_C, Polynomial.hasseDeriv_zero', Polynomial.continuous_aeval, X_pow_sub_C_splits_of_isPrimitiveRoot, Lagrange.eval_interpolate_not_at_node', Differential.implicitDeriv_C, Matrix.pow_eq_aeval_mod_charpoly, MvPolynomial.mem_image_support_coeff_finSuccEquiv, WeierstrassCurve.Affine.CoordinateRing.smul, Polynomial.resultant_X_add_C_right, Polynomial.pow_rootMultiplicity_dvd, Polynomial.derivWithin_aeval, AdjoinRoot.minpoly_root, X_pow_sub_C_eq_prod, Algebraic.cardinalMk_lift_le_mul, Polynomial.derivative_intCast_mul, Polynomial.toMatrix_sylvesterMap', Polynomial.rootMultiplicity_eq_rootMultiplicity, eval_minpolyDiv_self, Polynomial.leadingCoeff_multiset_prod', Ideal.mem_ofPolynomial, Polynomial.toAlgHom_taylorEquiv, Polynomial.resultant_one_right, PolynomialModule.smul_def, IsAdjoinRoot.mem_ker_map, Polynomial.aroots_smul_nonzero, Polynomial.isJacobsonRing_polynomial_iff_isJacobsonRing, Polynomial.isIntegral_coeff_prod, Polynomial.coeff_one, Polynomial.mapAlgEquiv_id, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, mem_reesAlgebra_iff_support, Polynomial.derivative_C_mul, Polynomial.aeval_algebraMap_apply_eq_algebraMap_eval, eval₂_minpolyDiv_self, Polynomial.support_trinomial, Polynomial.divX_X_pow, AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_symm_mk, RatFunc.num_div_dvd, KaehlerDifferential.polynomialEquiv_symm, Polynomial.degree_smul_of_smul_regular, Ideal.exists_mem_span_singleton_map_residueField_eq, Polynomial.iterate_derivative_zero, Polynomial.cyclotomic_six, Mathlib.Tactic.ComputeDegree.degree_smul_le_of_le, Polynomial.rootMultiplicity_eq_natTrailingDegree, Polynomial.aeval_algebraMap_eq_zero_iff, Mathlib.Tactic.ComputeDegree.coeff_intCast_ite, Polynomial.card_rootSet_le_derivative, PowerSeries.weierstrassDistinguished_mul, ConjRootClass.aeval_minpoly_iff, Ideal.exists_nonzero_mem_of_ne_bot, PowerSeries.coeff_trunc, WeierstrassCurve.map_φ, Polynomial.contract_expand, Polynomial.wronskian_self_eq_zero, Polynomial.derivative_mul, Polynomial.toFinsupp_zsmul, PowerSeries.trunc_mul_trunc, Polynomial.eval_prod, Polynomial.div_def, Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_derivative_U_eq_poly_in_U, Polynomial.cyclotomic.irreducible, Cubic.of_a_eq_zero', Polynomial.Monic.add_of_left, finrank_quotient_span_eq_natDegree_norm, WeierstrassCurve.ΨSq_even, Polynomial.C_inj, Polynomial.MonicDegreeEq.degree, Polynomial.coeff_mul_natTrailingDegree_add_natTrailingDegree, Polynomial.opRingEquiv_op_monomial, Polynomial.natDegree_monomial_le, Polynomial.eraseLead_natDegree_lt_or_eraseLead_eq_zero, Polynomial.Sequence.span, Polynomial.prod_X_sub_C_nextCoeff, Polynomial.mem_roots_sub_C', Polynomial.natDegree_add_le_iff_right, Polynomial.Monic.leadingCoeff_C_mul, Ideal.mem_leadingCoeffNth_zero, Polynomial.leadingCoeff_quadratic, Polynomial.idealX_span, Multiset.prod_X_sub_X_eq_sum_esymm, PowerSeries.trunc_X_pow_self_mul, Polynomial.eraseLead_X_pow, Polynomial.coeffList_C_mul, Polynomial.support_C_mul_X, Polynomial.exists_partition_polynomial, Polynomial.divByMonic_eq_of_not_monic, Lagrange.derivative_nodal, Polynomial.nnqsmul_eq_C_mul, IsPrimitiveRoot.minpoly_dvd_pow_mod, PolynomialModule.map_smul, Polynomial.leadingCoeff_C_mul_of_isUnit, WeierstrassCurve.Affine.monic_polynomial, Polynomial.monomial_mem_lifts, Polynomial.aroots_X_sub_C, PowerSeries.zero_weierstrassMod, MvPolynomial.optionEquivLeft_C, Polynomial.taylor_mul, Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity_of_ne_zero, Polynomial.degree_quadratic_lt, Polynomial.natDegree_sub_le_iff_right, WeierstrassCurve.Affine.CoordinateRing.basis_one, Polynomial.sum_bernoulli, Polynomial.cyclotomic_dvd_geom_sum_of_dvd, Polynomial.C_mul_X_eq_monomial, RatFunc.num_one, Polynomial.natSepDegree_pow, eval_det_add_X_smul, RatFunc.smul_def, Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq, Polynomial.leadingCoeff_one, Polynomial.mem_rootSet_of_injective, Polynomial.dvd_iff_content_dvd_content_and_primPart_dvd_primPart, Polynomial.X_mem_lifts, Polynomial.not_isUnit_of_natDegree_pos, LaurentSeries.LaurentSeriesRingEquiv_def, Polynomial.logMahlerMeasure_C_mul, FirstOrder.Field.realize_genericMonicPolyHasRoot, Polynomial.C_1, Polynomial.aeval_map_algebraMap, Polynomial.degree_pow_le, Polynomial.homogenize_smul, eval₂_minpolyDiv_of_eval₂_eq_zero, Polynomial.map_mul, Polynomial.sum_smul_index', Polynomial.charZero, Polynomial.IsMonicOfDegree.natDegree_sub_X_pow, WeierstrassCurve.ψ₂_sq, instIsScalarTowerPolynomial_1, Polynomial.hasseDeriv_one', Polynomial.derivative_comp_one_sub_X, MvPolynomial.optionEquivLeft_X_some, PolynomialModule.comp_smul, Polynomial.monic_X_pow_add_C, Polynomial.monic_multisetProd_X_sub_C, Polynomial.smeval_mul_X, Polynomial.contentIdeal_one, Polynomial.derivative_pow_eq_zero, Polynomial.toFinsupp_pow, Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero, descPochhammer_succ_comp_X_sub_one, PolyEquivTensor.right_inv, Polynomial.toPowerSeries_toMvPowerSeries, PolynomialModule.aeval_equivPolynomial, Polynomial.algEquivOfCompEqX_symm, Polynomial.leadingCoeff_det_X_one_add_C, MvPolynomial.pUnitAlgEquiv_symm_apply, Polynomial.quotientSpanXSubCAlgEquiv_symm_apply, Polynomial.degreeLT_mono, RatFunc.denom_one, Polynomial.map_div, Polynomial.roots_monomial, Polynomial.coeff_zero_of_isScalarTower, X_pow_sub_C_irreducible_iff_of_odd, Polynomial.coeff_one_add_X_pow, Polynomial.zero_notMem_multiset_map_X_sub_C, Polynomial.card_roots_sub_C', Polynomial.rootMultiplicity_expand_pow, Polynomial.irreducible_of_monic, Polynomial.aeval_iterate_derivative_of_ge, Polynomial.eq_C_of_degree_eq_zero, Polynomial.derivative_expand, Polynomial.degree_pow, Polynomial.derivative_sum, Polynomial.isCoveringMapOn_eval, Polynomial.nextCoeffUp_C_eq_zero, X_pow_sub_C_irreducible_of_odd, Polynomial.aeval_fn_apply, Polynomial.derivative_pow_succ, Polynomial.Sequence.basis_eq_self, Polynomial.coeff_pow_eq_ite_of_natDegree_le_of_le, MvPolynomial.natDegree_finSuccEquiv, Polynomial.mod_eq_self_iff, WeierstrassCurve.map_Ψ, StandardEtalePresentation.toPresentation_algebra_smul, sum_smul_minpolyDiv_eq_X_pow, Polynomial.derivative_ofNat, RatFunc.denom_mul_dvd, Polynomial.coeff_sub_eq_left_of_lt, Matrix.charmatrix_reindex, Polynomial.monomial_one_one_eq_X, Polynomial.natDegree_mul_X, Ideal.quotient_map_C_eq_zero, Polynomial.natDegree_X_pow_sub_C, Polynomial.Splits.eval_derivative, Polynomial.irreducible_iff_roots_eq_zero_of_degree_le_three, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C, Polynomial.derivative_smul, Polynomial.nextCoeffUp_zero, Polynomial.isNilpotent_X_mul_iff, Polynomial.splits_neg_iff, Polynomial.Splits.monomial, Polynomial.roots_C_mul_X_pow, IsAdjoinRoot.adjoinRootAlgEquiv_symm_apply_eq_mk, Polynomial.IsDistinguishedAt.map_eq_X_pow, Polynomial.subalgebraNontrivial, Polynomial.dickson_two_zero, LaurentPolynomial.mk'_one_X, Polynomial.natDegree_smul, Polynomial.eval₂_mul_X, RatFunc.laurent_algebraMap, Polynomial.iterate_derivative_eq_factorial_smul_sum, Polynomial.iterate_derivative_X_add_pow, Polynomial.mirror_neg, PowerBasis.quotientEquivQuotientMinpolyMap_apply, Polynomial.eq_one_of_roots_le, WeierstrassCurve.ΨSq_odd, Polynomial.Chebyshev.S_eq_U_comp_half_mul_X, Polynomial.degree_gcd_le_left, Polynomial.pUnitAlgEquiv_symm_toPowerSeries, Polynomial.eval₂_X_pow, Polynomial.degree_C_mul_of_isUnit, RatFunc.mk_smul, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero', Polynomial.derivative_X, Polynomial.sumIDeriv_map, Polynomial.comp_neg_X_eq_zero_iff, Polynomial.degree_mul_leadingCoeff_inv, Polynomial.eval₂_one, Lagrange.eval_interpolate_not_at_node, AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin, Polynomial.eq_prod_roots_of_splits, Polynomial.map_injective_iff, Polynomial.eq_prod_roots_of_monic_of_splits_id, WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_C, Polynomial.mirror_monomial, WeierstrassCurve.Affine.Y_sub_negPolynomial, Module.AEval.of_symm_smul, Polynomial.dvd_iterate_derivative_pow, Polynomial.coeffs_monomial, KaehlerDifferential.polynomialEquiv_D, MvPolynomial.optionEquivLeft_apply, minpoly_algHom_toLinearMap, Polynomial.ofFn_eq_sum_monomial, Polynomial.hilbertPoly_smul, MvPolynomial.totalDegree_coeff_finSuccEquiv_add_le, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eq₂, Polynomial.chebyshev_U_eq_dickson_two_one, Polynomial.prime_C_iff, Mathlib.Tactic.ComputeDegree.natDegree_zero_le, AdjoinRoot.mk_surjective, Derivation.mapCoeffs_X, Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C, Polynomial.pow_comp, finrank_quotient_span_eq_natDegree', Polynomial.splits_of_splits_gcd_left, Polynomial.cyclotomic_expand_eq_cyclotomic_mul, LinearMap.charpoly_nilpotent_tfae, WeierstrassCurve.Affine.CoordinateRing.coe_basis, Lagrange.interpolate_eq_sum_interpolate_insert_sdiff, Polynomial.natSepDegree_X_sub_C_pow, Polynomial.resultant_zero_right, Polynomial.isMonicOfDegree_two_iff', Polynomial.leadingCoeff_opRingEquiv, Polynomial.not_isRoot_C, Polynomial.content_eq_zero_iff, Multiset.prod_X_add_C_coeff, Polynomial.exists_partition_polynomial_aux, Polynomial.natDegree_C_add, Polynomial.Splits.eval_root_derivative, Polynomial.IsMonicOfDegree.natDegree_sub_lt, Polynomial.Monic.eq_X_pow_char_pow_sub_C_pow_of_natSepDegree_eq_one, Polynomial.C_mul', Polynomial.eraseLead_add_C_mul_X_pow, matPolyEquiv_map_smul, RatFunc.laurent_div, minpoly.natSepDegree_eq_one_iff_eq_X_pow_sub_C, Polynomial.natDegree_sub_eq_right_of_natDegree_lt, Polynomial.isMonicOfDegree_X_sub_one, Polynomial.degreeLT.basis_val, Polynomial.natDegree_mul_mirror, WeierstrassCurve.Affine.Point.toClass_zero, Polynomial.Chebyshev.S_neg_sub_two, Polynomial.reverse_mul_X_pow, Polynomial.derivative_monomial, ConjRootClass.minpoly.map_eq_prod, Polynomial.not_dvd_of_degree_lt, Polynomial.content_zero, Polynomial.aeval_sumIDeriv, Polynomial.hilbertPoly_eq_zero_of_le_rootMultiplicity_one, WeierstrassCurve.Affine.map_polynomialY, Polynomial.Chebyshev.S_add_one, Polynomial.Monic.natDegree_pow, Polynomial.coe_one, Polynomial.sumIDeriv_C, Polynomial.Chebyshev.T_derivative_eq_U, Subalgebra.aeval_coe, matPolyEquiv_diagonal_X, Polynomial.coeff_taylor_natDegree, Polynomial.length_coeffList_eq_ite, Polynomial.eval₂_zero, Matrix.charmatrix_toSquareBlock, Polynomial.supNorm_zero, Polynomial.roots_C_mul, Ideal.Filtration.mem_submodule, Polynomial.coeff_divByMonic_X_sub_C_rec, Polynomial.zero_comp, Polynomial.leadingCoeff_mul, gal_X_pow_isSolvable, Subfield.splits_bot, Polynomial.restriction_one, Polynomial.degree_list_prod, Polynomial.monic_X_pow_add, Polynomial.degree_lt_degree_mul_X, RatFunc.liftOn_ofFractionRing_mk, Polynomial.leadingCoeff_X_pow_add_C, Polynomial.eval_C, Polynomial.Chebyshev.iterate_derivative_T_eval_one_recurrence, Polynomial.smeval_X_pow, Matrix.charmatrix_apply_eq, Polynomial.toFinsupp_monomial, Polynomial.modByMonic_one, Lagrange.nodal_insert_eq_nodal, Polynomial.mapAlgHom_eq_eval₂AlgHom'_CAlgHom, Polynomial.coe_monomial, Polynomial.root_mul_right_of_isRoot, Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity, Polynomial.instIsRightCancelMulZeroOfIsCancelAdd, PolyEquivTensor.toFunAlgHom_apply_tmul, Polynomial.map_list_prod, Polynomial.divByMonic_eq_zero_iff, Matrix.charpoly_natCast, Polynomial.degree_add_eq_right_of_degree_lt, Polynomial.coeff_mul_X_zero, Polynomial.reverse_eq_zero, Polynomial.eval_divByMonic_eq_trailingCoeff_comp, Polynomial.algebraMap_apply, ConjRootClass.minpoly_injective, Polynomial.add_mod, Polynomial.evalEval_finset_sum, PowerBasis.equivAdjoinSimple_symm_aeval, adjoin_monomial_eq_reesAlgebra, MvPolynomial.optionEquivRight_C, Lagrange.basis_singleton, Polynomial.natDegree_mul, Polynomial.monomial_mul_C, Polynomial.Monic.geom_sum', WeierstrassCurve.preΨ'_zero, Polynomial.IsPrimitive.isUnit_iff_isUnit_map_of_injective, Polynomial.X_pow_eq_monomial, Polynomial.coe_eq_zero_iff, FunctionField.ringOfIntegers.instIsIntegralClosureSubtypeMemSubalgebraPolynomial, Polynomial.Bivariate.Polynomial.Bivariate.pderiv_one_equivMvPolynomial, X_pow_sub_C_irreducible_iff_forall_prime_of_odd, Polynomial.not_isUnit_of_degree_pos_of_isReduced, Polynomial.trunc_toLaurent, Polynomial.toAddCircle_X_pow_eq_fourier, Polynomial.map_surjective, Polynomial.UniversalCoprimeFactorizationRing.homEquiv_comp_snd, Polynomial.as_sum_range_C_mul_X_pow', Matrix.derivative_det_one_add_X_smul, Polynomial.integralNormalization_C, Polynomial.Splits.mem_lift_of_roots_mem_range, Polynomial.roots_zero, Polynomial.rootMultiplicity_eq_zero_iff, Polynomial.rootMultiplicity_X_sub_C_pow, Polynomial.Monic.prime_of_degree_eq_one, Polynomial.resultant_X_sub_C_right, Polynomial.differentiableOn_aeval, Polynomial.mem_iff_eq_smul_annIdealGenerator, MvPolynomial.degreeOf_coeff_finSuccEquiv, Polynomial.derivative_rootMultiplicity_of_root, transcendental_iff_injective, Polynomial.taylor_injective, Polynomial.iterate_derivative_mul_X, Polynomial.eval₂RingHom_eval₂RingHom, Polynomial.isUnit_map, Polynomial.Chebyshev.S_eq_X_mul_S_add_C, Polynomial.update_eq_add_sub_coeff, Polynomial.monic_finprod_X_sub_C, Polynomial.degree_C_mul_of_mul_ne_zero, Ideal.jacobson_bot_polynomial_le_sInf_map_maximal, IsCyclotomicExtension.aeval_zeta, Real.Polynomial.isRoot_cos_pi_div_five, Polynomial.coe_C, Polynomial.Chebyshev.S_comp_two_mul_X, Polynomial.instIsDomainOfIsCancelAdd, WeierstrassCurve.Affine.C_addPolynomial, Polynomial.sumIDeriv_eq_self_add, Polynomial.self_sub_monomial_natDegree_leadingCoeff, Polynomial.bernoulli_generating_function, Polynomial.natDegree_finset_prod_X_sub_C_eq_card, Polynomial.support_C_mul_X', Polynomial.monic_of_isUnit_leadingCoeff_inv_smul, Polynomial.prod_cyclotomic_eq_X_pow_sub_one, Mathlib.Tactic.ComputeDegree.coeff_mul_add_of_le_natDegree_of_eq_ite, Polynomial.iterate_derivative_X, MvPolynomial.nonempty_support_finSuccEquiv, Polynomial.degree_list_prod_le, RatFunc.coe_X, Polynomial.natDegree_sum_le, Polynomial.eval₂_monomial, Matrix.charpoly_mul_comm_of_le, Module.AEval'.X_smul_of, AdjoinRoot.smul_mk, instIsAlgebraicPolynomialOfNoZeroDivisors_1, Polynomial.Splits.eval_derivative_eq_eval_mul_sum, AdjoinRoot.quotEquivQuotMap_symm_apply_mk, RatFunc.isCoprime_num_denom, Polynomial.coe_compRingHom_apply, WeierstrassCurve.Affine.irreducible_polynomial, FunctionField.inftyValuation.polynomial, Polynomial.pow_rootMultiplicity_not_dvd, Polynomial.divByMonic_add_X_sub_C_mul_derivative_divByMonic_eq_derivative, AdjoinRoot.evalEval_apply, Lagrange.basisDivisor_self, Polynomial.derivative'_apply, Polynomial.eval_surjective, Polynomial.constantCoeff_apply, Polynomial.mem_support_derivative, Polynomial.aeval_X_pow, instIsIntegralPolynomial, PowerSeries.eq_shift_mul_X_pow_add_trunc, Polynomial.Chebyshev.S_eq, Polynomial.monomial_pow, Polynomial.coeff_mul_X_pow, Polynomial.evalEval_intCast, Polynomial.Monic.natDegree_eq_zero, Polynomial.Bivariate.aveal_eq_map_swap, Polynomial.le_trailingDegree_C, WeierstrassCurve.Affine.polynomial_eq, WeierstrassCurve.preΨ'_one, Polynomial.eval₂_finset_sum, Polynomial.ofFinsupp_natCast, Polynomial.coeff_mul_ofNat, WeierstrassCurve.preΨ_odd, Polynomial.toLaurent_C_mul_T, Polynomial.resultant_X_pow_right, Polynomial.one_scaleRoots, Polynomial.card_roots_le_derivative, Polynomial.aevalTower_algebraMap, Polynomial.rootsExpandPowEquivRoots_apply, Polynomial.height_eq_height_add_one, Polynomial.Bivariate.swap_apply, Matrix.minpoly_dvd_charpoly, Lagrange.eq_interpolate_iff, RatFunc.coe_coe, Polynomial.derivative_eval, WeierstrassCurve.Ψ_one, Polynomial.natDegree_smul_of_smul_regular, Polynomial.leadingCoeff_zero, Polynomial.logMahlerMeasure_mul_eq_add_logMahelerMeasure, LindemannWeierstrass.exp_polynomial_approx, Lagrange.nodal_empty, Polynomial.map_expand, PolynomialModule.monomial_smul_single, Ideal.injective_quotient_le_comap_map, Polynomial.C_eq_zero, Polynomial.dvd_comp_X_add_C_iff, Polynomial.separable_X_pow_sub_C, Polynomial.span_singleton_annIdealGenerator, Polynomial.Monic.eq_X_pow_iff_natDegree_le_natTrailingDegree, Polynomial.dvd_comp_C_mul_X_add_C_iff, Polynomial.algEquivCMulXAddC_symm_eq, Polynomial.mapEquiv_symm_apply, Polynomial.valuation_of_mk, Polynomial.isRightCancelMulZero_iff, Polynomial.natDegree_prod', Polynomial.X_pow_smul_rTensor_monomial, Polynomial.unique_int_coeff_of_cycl, Polynomial.eval₂_list_sum, Polynomial.X_pow_sub_one_splits, WeierstrassCurve.Affine.natDegree_polynomial, Polynomial.natDegree_prod, Polynomial.coeff_C_ne_zero, Polynomial.isMonicOfDegree_add_add_two, instIsPushoutFractionRingPolynomial_1, Polynomial.degree_X_pow_add_C, Matrix.det_one_add_smul, Polynomial.coeff_list_sum_map, Polynomial.smul_monomial, Polynomial.Monic.comp_X_sub_C, WeierstrassCurve.Affine.CoordinateRing.instIsScalarTowerPolynomial, Polynomial.leadingCoeff_smul_integralNormalization, Polynomial.eval_pow, Lagrange.basisDivisor_add_symm, Polynomial.gaussNorm_eq_zero_iff, MvPolynomial.eval₂_const_pUnitAlgEquiv_symm, MvPolynomial.eval_comp_toMvPolynomial, Polynomial.degree_X_sub_C, Polynomial.iterate_derivative_X_sub_pow, MvPolynomial.support_finSuccEquiv_nonempty, Polynomial.eval₂_mul', Polynomial.support_trinomial', Polynomial.map_mod, Polynomial.cardPowDegree_isEuclidean, Polynomial.splits_zero, Polynomial.C_0, LaurentSeries.inducing_coe, isSplittingField_X_pow_sub_C_of_root_adjoin_eq_top, PowerSeries.degree_trunc_lt, Polynomial.irreducible_of_eisenstein_criterion, IsAdjoinRootMonic.basis_repr, PowerSeries.IsWeierstrassFactorization.isWeierstrassDivision, Polynomial.expand_eq_comp_X_pow, FirstOrder.Field.lift_genericMonicPoly, Polynomial.exists_finset_of_splits, Polynomial.Chebyshev.T_two, Submodule.IsPrincipal.contentIdeal_le_span_iff_dvd, IntermediateField.aeval_coe, ascPochhammer_succ_comp_X_add_one, WeierstrassCurve.ΨSq_ofNat, Polynomial.Splits.multisetProd, Polynomial.ofFinsupp_sub, LaurentSeries.continuous_coe, Matrix.charpoly_of_upperTriangular, Polynomial.Monic.not_dvd_of_natDegree_lt, Polynomial.Chebyshev.T_add_one, LaurentSeries.algebraMap_C_mem_adicCompletionIntegers, Polynomial.Monic.normalize_eq_self, Polynomial.irreducible_mul_leadingCoeff_inv, IsSepClosed.roots_eq_zero_iff, Polynomial.eval₂_list_prod, Polynomial.natCast_mul, MvPolynomial.degree_optionEquivLeft, Polynomial.wronskian_add_right, Polynomial.aeval_one, Module.AEval.instIsScalarTowerOrigPolynomial, gal_X_pow_sub_C_isSolvable, Lagrange.interpolate_eq_sum, Module.AEval.C_smul, Polynomial.sum_C_index, Matrix.charmatrix_apply_ne, Polynomial.aeval_eq_zero_of_mem_rootSet, Polynomial.degreeLT.addLinearEquiv_castAdd, KaehlerDifferential.polynomialEquiv_comp_D, Polynomial.logMahlerMeasure_mul_eq_add_logMahlerMeasure, Polynomial.coeff_X_pow_mul, IsLocalization.integerNormalization_map_to_map, FiniteField.roots_X_pow_card_sub_X, Algebra.discr_powerBasis_eq_norm, Polynomial.natTrailingDegree_C, PowerBasis.quotientEquivQuotientMinpolyMap_apply_mk, Polynomial.X_mul_C, Polynomial.algebraMap_def, RatFunc.mk_eq_localization_mk, Derivation.mapCoeffs_C, Polynomial.coeff_C_mul_X, Polynomial.leadingCoeff_cubic, Polynomial.eval_X_pow, Polynomial.map_monomial, Polynomial.expand_one, Polynomial.resultant_C_zero_right, Polynomial.sum_smul_index, Polynomial.natDegree_eq_one, Polynomial.isCancelMulZero_iff, Polynomial.factor_dvd_of_natDegree_ne_zero, Polynomial.Chebyshev.C_eq_S_sub_X_mul_S, Polynomial.aeval_subalgebra_coe, minpoly.sub_algebraMap, WeierstrassCurve.φ_three, AdjoinRoot.mk_eq_mk, Polynomial.X_pow_mul_assoc, Polynomial.natDegree_neg_le_of_le, matPolyEquiv_coeff_apply_aux_1, Polynomial.leadingCoeffHom_apply, fermatLastTheoremWith'_polynomial, Polynomial.degreeLT.addLinearEquiv_apply_fst, PowerSeries.intValuation_eq_of_coe, Polynomial.C_eq_natCast, isConjRoot_iff_aeval_eq_zero, Polynomial.rootMultiplicity_mul, Polynomial.coeff_X_pow, RatFunc.mk_eq_mk', Polynomial.derivative_X_sub_C_sq, Matrix.charpoly_sub_scalar, MvPolynomial.optionEquivRight_X_none, Polynomial.aeval_X_left_apply, Polynomial.smul_eq_C_mul, FiniteField.instIsSplittingFieldExtensionHSubPolynomialHPowNatXCard, Polynomial.card_eq_of_natDegree_le_of_coeff_le, Polynomial.opRingEquiv_op_C, WeierstrassCurve.baseChange_ψ₂, RatFunc.mk_def, Polynomial.cyclotomic_two, Polynomial.Chebyshev.U_two, Polynomial.monic_multiset_prod_of_monic, Polynomial.C_eq_intCast, Polynomial.smeval.linearMap_apply, Polynomial.degree_C_lt_degree_C_mul_X, Polynomial.aroots_C_mul, Polynomial.isScalarTower, Polynomial.eval_derivative_of_splits, Polynomial.isUnit_iff, Polynomial.Splits.X_pow, Polynomial.isAlt_wronskianBilin, Polynomial.support_neg, Polynomial.roots_X_pow_char_pow_sub_C_pow, Polynomial.isRegular_X, Polynomial.coeff_mapAlgHom_apply, Multiset.prod_X_sub_C_dvd_iff_le_roots, divRadical_dvd_derivative, Polynomial.aeval_prod_apply, Polynomial.leadingCoeff_mul_prod_normalizedFactors, RatFunc.mk_eq_div', RatFunc.ofFractionRing_div, Module.AEval'.of_symm_X_smul, Polynomial.squarefree_cyclotomic, Polynomial.aeval_add_of_sq_eq_zero, monomial_mem_adjoin_monomial, Matrix.IsHermitian.charpoly_cfc_eq, Polynomial.mem_span_C_X_sub_C_X_sub_C_iff_eval_eval_eq_zero, Polynomial.derivativeFinsupp_apply_toFun, Polynomial.Chebyshev.aeval_T, Polynomial.aeval_comp, Polynomial.deriv_aeval, Polynomial.Chebyshev.U_eq, Polynomial.zero_divByMonic, Polynomial.Chebyshev.S_sq_add_S_sq, Polynomial.nextCoeff_C_mul_X_add_C, Polynomial.monic_mapAlg_iff, matPolyEquiv_symm_apply_coeff, Polynomial.ofFinsupp_single, Polynomial.splits_pow, Polynomial.toLaurent_injective, Polynomial.eval₂_natCast, Polynomial.le_trailingDegree_monomial, Polynomial.X_pow_sub_one_dvd_prod_cyclotomic, Polynomial.prod_multiset_root_eq_finset_root, Polynomial.dvd_C_mul, RatFunc.toFractionRing_smul, Polynomial.iterate_derivative_derivative_mul_X_sq, Polynomial.Monic.irreducible_iff_lt_natDegree_lt, Polynomial.toMvPolynomial_eq_rename_comp, WeierstrassCurve.Affine.baseChange_negPolynomial, Polynomial.ofFinsupp_pow, Derivation.comp_aeval_eq, Polynomial.toFinsupp_injective, Polynomial.X_pow_sub_C_separable_iff, Polynomial.wronskian_neg_right, Polynomial.aeval_homogenize_X_one, instIsPushoutPolynomial_1, Polynomial.eval_natCast, Polynomial.reverse_mul_of_domain, IsPurelyInseparable.minpoly_eq, Polynomial.cauchyBound_smul, Ideal.polynomial_not_isField, Polynomial.nextCoeff_mul_C, Polynomial.coeff_X_sub_C_mul, WeierstrassCurve.Affine.CoordinateRing.mk_ψ, Cubic.of_a_eq_zero, Polynomial.comp_C_mul_X_eq_zero_iff, Polynomial.modByMonic_eq_zero_iff_quotient_eq_zero, Polynomial.evalEval_sum, Polynomial.comap_taylorEquiv_degreeLT, Polynomial.natSepDegree_zero, Polynomial.UniversalFactorizationRing.jacobian_resentation, Polynomial.ofReal_eval, Polynomial.degree_quadratic, Polynomial.evalEval_X, Polynomial.coeffs_empty_iff, PowerSeries.trunc_trunc_mul_trunc, MvPolynomial.transcendental_polynomial_aeval_X_iff, FunctionField.classNumber_eq_one_iff, Polynomial.monic_X_pow_sub_C, IsFractionRing.integerNormalization_eq_zero_iff, Polynomial.rootsExpandEquivRoots_apply, Polynomial.gaussNorm_zero, Polynomial.leadingCoeff_linear, Polynomial.aeval_prod, Polynomial.rootMultiplicity_eq_natFind_of_ne_zero, Polynomial.isMonicOfDegree_two_iff, ascPochhammer_mul, Polynomial.C_mul_X_pow_eq_monomial, Polynomial.signVariations_zero, Polynomial.nextCoeff_X_add_C, StandardEtalePair.equivMvPolynomialQuotient_symm_apply, Polynomial.not_monic_zero, denomsClearable_zero, PowerSeries.trunc_mul_C, Polynomial.nontrivial_iff, Polynomial.eq_X_add_C_of_degree_le_one, Polynomial.taylor_zero', Polynomial.cyclotomic'_one, MvPolynomial.eval_eq_eval_mv_eval', Polynomial.isUnit_iff', WeierstrassCurve.preΨ'_even, Polynomial.evalEvalRingHom_eq, Polynomial.degree_lt_wf, Polynomial.expand_C, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply_mk, Polynomial.logMahlerMeasure_X_sub_C, Matrix.charmatrix_blockTriangular_iff, Polynomial.C_mem_lifts, Polynomial.aevalTower_toAlgHom, Polynomial.monomial_eq_zero_iff, Polynomial.homogenize_add, Polynomial.card_roots_toFinset_le_card_roots_derivative_diff_roots_succ, RatFunc.num_denom_add, MvPolynomial.optionEquivLeft_X_none, IsAdjoinRootMonic.map_modByMonic, Polynomial.coeff_injective, Polynomial.IsPrimitive.mul, Polynomial.mahlerMeasure_eq_zero_iff, Polynomial.natDegree_mul_leadingCoeff_self_inv, Polynomial.CAlgHom_apply, Polynomial.trailingDegree_C_mul_X_pow, RatFunc.instIsFractionRingPolynomial, Polynomial.X_pow_sub_one_eq_prod, Polynomial.toAddCircle.integrable, Polynomial.prod_multiset_X_sub_C_dvd, MvPolynomial.optionEquivRight_symm_apply, Polynomial.degree_cubic_lt, AdjoinRoot.mul_div_root_cancel, Polynomial.eq_X_add_C_of_natDegree_le_one, minpoly.natSepDegree_eq_one_iff_eq_X_sub_C_pow, Polynomial.leadingCoeff_normalize, FunctionField.algebraMap_injective, Polynomial.degree_C, Cubic.of_b_eq_zero, Polynomial.mkDerivation_one_eq_derivative', Polynomial.natTrailingDegree_mul_X_pow, Polynomial.derivative_X_add_C, Polynomial.smeval_smul, Polynomial.hermite_succ, descPochhammer_succ_right, Polynomial.Chebyshev.U_sub_one, Polynomial.mul_scaleRoots_of_noZeroDivisors, Polynomial.natDegree_prod_le, Polynomial.Sequence.natDegree_strictMono, Real.fibRec_charPoly_eq, Polynomial.instCharP, Matrix.charpoly_zero, PolyEquivTensor.toFunLinear_mul_tmul_mul, RatFunc.ofFractionRing_one, Polynomial.MonicDegreeEq.freeMonic_coe, Polynomial.hermite_eq_iterate, Polynomial.ofFinsupp_algebraMap, Polynomial.aeval_pi_apply, Polynomial.hasseDeriv_comp, IsAdjoinRoot.map_repr, Polynomial.aevalTower_comp_algebraMap, WeierstrassCurve.Affine.CoordinateRing.C_addPolynomial, AdjoinRoot.aeval_eq_of_algebra, Polynomial.trailingDegree_zero, WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_neg_mul, Polynomial.support_binomial', prodXSubSMul.smul, Polynomial.exists_image_comap_of_monic, Polynomial.cyclotomic_eq_prod_X_sub_primitiveRoots, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_add_eq, Polynomial.roots_pow, Polynomial.X_add_C_scaleRoots, Polynomial.resultant_C_right, Polynomial.splits_C, Polynomial.Splits.comp_X_sub_C, Polynomial.iterate_derivative_natCast_mul, WeierstrassCurve.Ψ_ofNat, Polynomial.splits_one, Polynomial.eq_zero_of_natDegree_lt_card_of_eval_eq_zero', Polynomial.eval₂_sum, Cubic.of_d_eq_zero, Polynomial.aevalTower_X, AdjoinRoot.mk_leftInverse, Polynomial.transcendental_X, Polynomial.natDegree_C_mul_X, Polynomial.degree_mul_le_of_le, Polynomial.differentiable_aeval, Polynomial.natTrailingDegree_monomial, Polynomial.comp_C, Polynomial.coeff_mul_X_sub_C, bernsteinPolynomial.iterate_derivative_at_1_eq_zero_of_lt, finrank_quotient_span_eq_natDegree, Polynomial.eval_monomial_one_add_sub, RatFunc.numDenom_div, Polynomial.smeval_sub, Polynomial.roots_expand_map_frobenius, IsUnit.scaleRoots_dvd_iff, Polynomial.map_pow, gal_X_pow_sub_one_isSolvable, Polynomial.natDegree_X_add_C, Polynomial.int_cyclotomic_rw, Polynomial.existsUnique_hilbertPoly, Polynomial.map_taylor, LieAlgebra.engel_isBot_of_isMin.lieCharpoly_map_eval, Polynomial.aeval_X_left, Polynomial.map_under_lt_comap_of_weaklyQuasiFiniteAt, MvPolynomial.finSuccEquiv_coeff_coeff, Polynomial.restriction_zero, Polynomial.UniversalCoprimeFactorizationRing.homEquiv_comp_fst, Polynomial.support_C, Derivation.mapCoeffs_monomial, Polynomial.Chebyshev.U_one, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C', Polynomial.roots_expand_image_frobenius, Polynomial.smeval_natCast, Polynomial.degreeLT.addLinearEquiv_apply_snd, Polynomial.natSepDegree_C_mul_X_sub_C_pow, Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_map, Polynomial.height_map_C, RatFunc.num_C, WeierstrassCurve.Ψ_neg, Polynomial.modByMonicHom_apply, minpoly.dvd_iff, Polynomial.X_sub_C_mul_divByMonic_eq_sub_modByMonic, IsNilpotent.charpoly_eq_X_pow_finrank, Polynomial.addHom_ext'_iff, RatFunc.smul_eq_C_mul, Polynomial.roots_C_mul_X_sub_C_of_IsUnit, PowerSeries.trunc_X_of, Polynomial.bUnion_roots_finite, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_symm_quotQuotMk, Polynomial.evalEval_multiset_prod, Polynomial.toFinsupp_eq_zero, Polynomial.derivative_X_pow_succ, Polynomial.degree_X_pow_le, bernsteinPolynomial.flip', Polynomial.ofFinsupp_add, Polynomial.eq_C_of_natDegree_le_zero, Polynomial.monic_X_add_C, Differential.coeff_mapCoeffs, Mathlib.Tactic.ComputeDegree.natDegree_natCast_le, Polynomial.not_separable_zero, Polynomial.logMahlerMeasure_X_add_C, Polynomial.aevalTower_C, LaurentSeries.exists_ratFunc_val_lt, Polynomial.modByMonic_eq_zero_iff_dvd, WeierstrassCurve.Affine.addPolynomial_slope, Polynomial.reflect_add, cfc_map_polynomial, Polynomial.coeff_C_mul, RatFunc.num_algebraMap, Polynomial.idealSpan_range_update_divByMonic, Polynomial.degree_monomial_le, Polynomial.rootMultiplicity_eq_nat_find_of_nonzero, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero, Polynomial.coeff_monomial_of_ne, Polynomial.derivative_X_sub_C_pow, Polynomial.cyclotomic_mul_prime_dvd_eq_pow, Lagrange.degree_interpolate_erase_lt, Polynomial.ofFinsupp_eq_one, Polynomial.natTrailingDegree_natCast, MvPolynomial.optionEquivRight_X_some, RatFunc.ofFractionRing_zero, Polynomial.toFinsupp_nsmul, Polynomial.natDegree_C_mul_eq_of_mul_eq_one, Polynomial.IsMonicOfDegree.exists_natDegree_lt, Polynomial.list_prod_comp, Polynomial.eraseLead_C_mul_X, Polynomial.natDegree_C, Matrix.charpoly_fromBlocks_zero₂₁, Polynomial.hilbertPoly_succ, Polynomial.ker_constantCoeff, X_pow_sub_C_irreducible_iff_of_prime_pow, Lagrange.basis_eq_prod_sub_inv_mul_nodal_div, RatFunc.ofFractionRing_add, WeierstrassCurve.Affine.map_negPolynomial, Polynomial.natDegree_sub_le_of_le, IsAdjoinRoot.map_X, Polynomial.Monic.eq_X_pow_iff_natTrailingDegree_eq_natDegree, Polynomial.toLaurent_comp_C, polynomialFunctions.starClosure_eq_adjoin_X, Polynomial.factor_dvd_of_degree_ne_zero, Polynomial.IsRoot.mul_div_eq, Polynomial.sum_C_mul_X_pow_eq, LinearMap.pow_eq_aeval_mod_charpoly, IsSMulRegular.polynomial, PowerSeries.normalized_count_X_eq_of_coe, Polynomial.not_isUnit_of_degree_pos, PowerBasis.liftEquiv_symm_apply, Polynomial.natTrailingDegree_mul_mirror, Module.AEval'.X_pow_smul_of, Polynomial.splits_prod, Polynomial.isOpen_image_comap_of_monic, Polynomial.as_sum_support_C_mul_X_pow, Polynomial.toFinsupp_X_pow, Polynomial.derivWithin, Polynomial.natTrailingDegree_eq_zero, Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T, Polynomial.degree_quadratic_le, Polynomial.eq_quadratic_of_degree_le_two, Polynomial.natDegree_add_eq_left_of_degree_lt, WeierstrassCurve.φ_one, Polynomial.adjSylvester_comp_sylveserMap, Polynomial.exists_iterate_derivative_eq_factorial_smul, RatFunc.num_dvd, Polynomial.divX_eq_zero_iff, Polynomial.rootsExpandPowToRoots_apply, Polynomial.reflect_one, Polynomial.content_X_mul, MulSemiringAction.charpoly_eq_prod_smul, Polynomial.monomial_injective, Polynomial.taylor_eq_zero, AdjoinRoot.mk_eq_zero, Polynomial.natDegree_list_sum_le, Polynomial.card_support_eq, Polynomial.reflect_monomial, Lagrange.degree_interpolate_lt, Polynomial.leadingCoeff_pow_X_add_C, Polynomial.exists_dvd_map_of_isAlgebraic, PowerBasis.equivAdjoinSimple_aeval, AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_C_compl_zeroLocus, rank_polynomial_polynomial, Polynomial.cauchyBound_C, Polynomial.mem_lifts, Polynomial.multiset_prod_comp, Polynomial.bernoulli_zero, Polynomial.contract_add, RatFunc.laurentAux_div, traceForm_dualSubmodule_adjoin, Polynomial.coeff_mul_X, Polynomial.coeff_zero_prod, Polynomial.X_pow_sub_X_sub_one_irreducible, Polynomial.coeff_mul, polyEquivTensor_symm_apply_tmul, Polynomial.roots_C_mul_X_add_C, Polynomial.natDegree_C_mul_le, Polynomial.divX_hom_toFun, Polynomial.eq_zero_of_eq_zero, LinearMap.charpoly_eq_X_pow_iff, Polynomial.natDegree_eq_support_max', Polynomial.sum_comp, Polynomial.leadingCoeff_X_pow_sub_C, LaurentPolynomial.mk'_eq, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some, AdjoinRoot.span_maximal_of_irreducible, WeierstrassCurve.baseChange_φ, Polynomial.coeff_sub_eq_neg_right_of_lt, AdjoinRoot.quotEquivQuotMap_apply, Polynomial.degreeLT.instFiniteSubtypeMemSubmodule, IsAdjoinRootMonic.modByMonicHom_map, Polynomial.derivativeFinsupp_apply_apply, Polynomial.noZeroDivisors_iff, RatFunc.mk_eq_div, Polynomial.Bivariate.equivMvPolynomial_symm_X_0, minpoly.eq_X_sub_C_of_algebraMap_inj, Polynomial.taylor_apply, Polynomial.map_add, Polynomial.charP, Polynomial.natDegree_C_mul_of_mul_ne_zero, Polynomial.eval_derivative_eq_eval_mul_sum_of_splits, WeierstrassCurve.Affine.C_addPolynomial_slope, Polynomial.natDegree_mul', Polynomial.iterate_derivative_comp_one_sub_X, Polynomial.Splits.eq_prod_roots, Polynomial.evalEvalRingHom_apply, spectralNorm.spectralNorm_pow_natDegree_eq_prod_roots, instIsScalarTowerPolynomial, Polynomial.rootMultiplicity_add, LinearMap.minpoly_dvd_charpoly, Polynomial.Monic.not_dvd_of_degree_lt, PowerSeries.IsWeierstrassDivisorAt.mod'_mk_eq_mod, Polynomial.notMem_nonZeroDivisors_iff, FunctionField.ringOfIntegers.instIsDomainSubtypeMemSubalgebraPolynomial, Polynomial.wronskian_neg_eq, Polynomial.degree_derivative_lt, Polynomial.div_wf_lemma, Matrix.charmatrix_fromBlocks, Polynomial.exists_approx_polynomial_aux, Polynomial.derivative_natCast_mul, Polynomial.mapAlgEquiv_comp, Polynomial.eq_X_add_C_of_degree_eq_one, Polynomial.Splits.zero, Polynomial.degree_neg_le_of_le, Polynomial.prod_cyclotomic'_eq_X_pow_sub_one, Polynomial.fderiv_aeval, Polynomial.Splits.eval_derivative_div_eval_of_ne_zero, Polynomial.natCast_coeff_zero, Polynomial.mahlerMeasure_C_mul_X_add_C, Polynomial.not_quasiFiniteAt, IsAlgebraic.exists_nonzero_coeff_and_aeval_eq_zero, Module.End.aeval_apply_of_hasEigenvector, PowerBasis.mem_span_pow', KummerDedekind.emultiplicity_factors_map_eq_emultiplicity, Polynomial.eq_C_of_natDegree_eq_zero, Polynomial.eval₂_C_X, MulSemiringAction.smul_charpoly, Polynomial.sum_monomial_index, Polynomial.derivativeFinsupp_derivative, Polynomial.lifts_iff_ringHom_rangeS, RatFunc.num_zero, Polynomial.smeval_C, Algebra.adjoin_singleton_eq_range_aeval, Polynomial.smeval_mul, mem_span_C_coeff, WeierstrassCurve.Affine.CoordinateRing.norm_smul_basis, Polynomial.hilbertPoly_zero_left, Polynomial.natDegree_add_eq_left_of_natDegree_lt, Polynomial.isCoprime_expand, IsCyclotomicExtension.isSplittingField_X_pow_sub_one, Polynomial.X_mul_divX_add, Matrix.GeneralLinearGroup.fixpointPolynomial_eq_zero_iff, Polynomial.card_support_binomial, Polynomial.Chebyshev.U_eq_zero_iff, Polynomial.sum_monomial_eq, Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_C', Lagrange.basis_empty, Polynomial.eval₂_sub, PowerSeries.trunc_trunc_mul, Polynomial.MonicDegreeEq.coeff_of_ge, gal_prod_isSolvable, PowerSeries.IsWeierstrassDivision.eq_zero, WeierstrassCurve.Affine.CoordinateRing.degree_norm_smul_basis, Polynomial.Splits.comp_X_add_C, Polynomial.Monic.isUnit_iff, Polynomial.degree_derivative_eq, Polynomial.C_mul_monomial, Polynomial.natDegree_sub_le_iff_left, Polynomial.ofFinsupp_one, Polynomial.natDegree_hasseDeriv_le, Polynomial.evalEval_prod, MvPolynomial.optionEquivLeft_coeff_coeff, Polynomial.natDegree_add_le_of_degree_le, Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_one, Polynomial.separable_X_pow_sub_C', Matrix.charpoly.optionEquivLeft_symm_univ_isHomogeneous, Polynomial.Monic.natDegree_eq_zero_iff_eq_one, Mathlib.Tactic.ComputeDegree.natDegree_intCast_le, Polynomial.fact_irreducible_factor, IsCyclotomicExtension.splits_X_pow_sub_one, transcendental_aeval_iff, Polynomial.coeff_pow_mul_natDegree, Polynomial.Splits.aeval_eq_prod_aroots, Polynomial.iterate_comp_eval, Polynomial.as_sum_range, Polynomial.toLaurent_apply, Polynomial.coeff_natCast_ite, Mathlib.Tactic.ComputeDegree.natDegree_smul_le_of_le, Polynomial.isOpenMap_comap_C, Polynomial.not_isField, Polynomial.expand_inj, Polynomial.zero_of_eval_zero, PolynomialModule.isScalarTower', Polynomial.opRingEquiv_op_X, RatFunc.num_inv_dvd, Polynomial.natDegree_mul_C_eq_of_mul_eq_one, Polynomial.Chebyshev.U_zero, Polynomial.Chebyshev.S_sub_one, Polynomial.content_C_mul, Polynomial.natTrailingDegree_one, Polynomial.Splits.eq_X_sub_C_of_single_root, Polynomial.coeff_det_X_add_C_card, bernsteinPolynomial.flip, Polynomial.isUnit_of_coeff_isUnit_isNilpotent, Polynomial.eq_zero_of_forall_eval_zero_of_natDegree_lt_card, Polynomial.not_isUnit_of_natDegree_pos_of_isReduced, Polynomial.modByMonic_eq_sub_mul_div, Polynomial.Monic.nextCoeff_mul, Polynomial.rootSet_zero, Polynomial.quotientSpanXSubCAlgEquiv_mk, Cubic.of_c_eq_zero', Polynomial.cyclotomic_prime_pow_eq_geom_sum, Polynomial.smeval_X_pow_mul, evalRingHom_mapMatrix_comp_polyToMatrix, Polynomial.natDegree_add_eq_right_of_natDegree_lt, Polynomial.divX_add, Polynomial.aeval_X_left_eq_map, Lagrange.X_sub_C_dvd_nodal, Polynomial.eval_mul, Polynomial.Monic.isRegular, Polynomial.det_taylorLinearEquiv_toLinearMap, Polynomial.roots_X_sub_C, Polynomial.mkDerivationEquiv_symm_apply, Polynomial.IsMonicOfDegree.mul, Polynomial.isUnit_C, Polynomial.eval_list_prod, Polynomial.intCast_comp, PowerSeries.smul_weierstrassMod, Polynomial.Chebyshev.U_neg_sub_one, Polynomial.Splits.def, Polynomial.map_injective, Polynomial.expand_expand, WeierstrassCurve.C_Ψ₂Sq, Polynomial.natDegree_quadratic_le, Polynomial.Bivariate.swap_Y, Polynomial.rootSet_C_mul_X_pow, Polynomial.natDegree_sum_le_of_forall_le, Polynomial.monomial_mul_X, Polynomial.rootSet_derivative_subset_convexHull_rootSet, Polynomial.mapAlgHom_monomial, Polynomial.Chebyshev.iterate_derivative_T_eval_zero_recurrence, Polynomial.iterate_derivative_X_pow_eq_natCast_mul, AnalyticWithinAt.aeval_polynomial, PowerSeries.WithPiTopology.denseRange_toPowerSeries, Polynomial.le_rootMultiplicity_iff, Polynomial.natDegree_taylor, Polynomial.degree_taylor, Polynomial.smul_X, Polynomial.isUnit_resultant_iff_isCoprime, Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative_of_mem_nonZeroDivisors, Polynomial.natDegree_add_le_iff_left, Polynomial.annIdealGenerator_mem, Polynomial.coe_smul, Polynomial.support_C_subset, Polynomial.hasFDerivAt, Polynomial.splits_iff, Cubic.of_b_eq_zero', WeierstrassCurve.Affine.derivative_addPolynomial_slope, Polynomial.support_C_mul_X_pow', RatFunc.ofFractionRing_comp_algebraMap, Polynomial.aeval_apply_smul_mem_of_le_comap, Polynomial.eq_C_content_mul_primPart, Polynomial.degree_sum_le, Polynomial.C'_mem_lifts, Polynomial.rootMultiplicity_mul_X_sub_C_pow, RatFunc.algebraMap_X, Module.AEval.isTorsion_of_finiteDimensional, Ideal.mem_leadingCoeff, Lagrange.basisDivisor_eq_zero_iff, Polynomial.map_intCast, Polynomial.degreeLT.addLinearEquiv_apply, FunctionField.ringOfIntegers.instIsIntegrallyClosedSubtypeMemSubalgebraPolynomial, Polynomial.smul_eq_map, minpoly.ker_aeval_eq_span_minpoly, Polynomial.coe_add, Polynomial.Chebyshev.aeval_S, Polynomial.reflect_one_X, Polynomial.algebraMap_pi_self_eq_eval, Lagrange.eq_interpolate, Polynomial.mem_annIdeal_iff_aeval_eq_zero, Polynomial.card_support_eq', Polynomial.valuation_aeval_eq_valuation_X_pow_natDegree_of_one_lt_valuation_X, instIsNoetherianRingSubtypePolynomialMemSubalgebraReesAlgebra, Polynomial.C_eq_algebraMap, Polynomial.coeff_natCast_mul, Polynomial.mapAlg_eq_map, Polynomial.separable_def', IsPrimitiveRoot.minpoly_dvd_expand, Polynomial.eval_unique, Polynomial.derivative_of_natDegree_zero, Finset.prod_X_add_C_coeff, Polynomial.Bivariate.equivMvPolynomial_symm_C, Matrix.charpoly_one, Polynomial.divX_mul_X_add, Subfield.roots_X_pow_char_sub_X_bot, Polynomial.aeval_eq_smeval, Polynomial.toFinsuppIsoLinear_symm_apply_toFinsupp, Polynomial.cyclotomic.isCoprime_rat, Polynomial.natSepDegree_X_pow_char_pow_sub_C, Polynomial.card_support_mul_le, LaurentPolynomial.algebraMap_X_pow, Polynomial.homogenize_X_pow, Polynomial.evalEval_sub, minpoly.isRadical, Polynomial.le_trailingDegree_mul, Polynomial.prime_of_degree_eq_one, Polynomial.IsPrimitive.Int.irreducible_iff_irreducible_map_cast, Polynomial.coeffList_C, Polynomial.Splits.taylor, Polynomial.coeff_add_eq_right_of_lt, RatFunc.num_denom_mul, Matrix.det_one_add_X_smul, Algebra.adjoin_mem_exists_aeval, coe_polyEquivTensor'_symm, Polynomial.degree_multiset_prod_of_monic, Polynomial.hilbertPoly_add_left, FiniteField.isSplittingField_of_nat_card_eq, reesAlgebra.monomial_mem, Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative, minpoly.prime, Ideal.Filtration.inf_submodule, Polynomial.roots_expand_image_frobenius_subset, IsPrimitiveRoot.minpoly_dvd_mod_p, PowerSeries.derivativeFun_coe, Polynomial.smul_eval_smul, Polynomial.comp_eq_zero_iff, Polynomial.isNilpotent_aeval_sub_of_isNilpotent_sub, Module.End.IsSemisimple.aeval, Polynomial.coeff_monomial, RatFunc.smul_eq_C_smul, Polynomial.UniversalFactorizationRing.monicDegreeEq_coe, WeierstrassCurve.Affine.addPolynomial_eq, Polynomial.resultant_mul_left, RatFunc.valuation_eq_LaurentSeries_valuation, Differential.mapCoeffs_monomial, MvPolynomial.support_coeff_finSuccEquiv, Module.AEval.X_pow_smul_of, minpoly.aeval, Polynomial.degree_X_pow_sub_C, Polynomial.taylor_coeff_zero, Polynomial.degree_add_eq_left_of_degree_lt, Polynomial.Chebyshev.T_eq, Polynomial.leadingCoeff_add_of_degree_eq, descPochhammer_eq_ascPochhammer, Polynomial.content_mul_aux, Polynomial.mul_eq_sum_sum, Polynomial.mkDerivationEquiv_apply, Polynomial.eraseLead_add_of_degree_lt_right, Polynomial.support_add, coe_polyEquivTensor', Polynomial.toFinsupp_one, Polynomial.natDegree_X_pow_add_C, Polynomial.instExpChar, Polynomial.isUnit_iff_coeff_isUnit_isNilpotent, Polynomial.divX_C_mul, PowerSeries.eq_X_pow_mul_shift_add_trunc, Polynomial.Chebyshev.C_eq, Polynomial.iterate_derivative_C, Polynomial.degree_mul_leadingCoeff_self_inv, PowerSeries.trunc_trunc_of_le, Polynomial.isRoot_gcd_iff_isRoot_left_right, Polynomial.mahlerMeasure_X_add_C, PolynomialModule.comp_apply, WeierstrassCurve.ψ_even, Polynomial.coeff_pow_of_natDegree_le, Polynomial.taylor_X_pow, Mathlib.Tactic.ComputeDegree.coeff_add_of_eq, Polynomial.leadingCoeff_prod, Polynomial.reverse_X_pow_mul, Polynomial.degree_le_mul_left, Matrix.GeneralLinearGroup.fixpointPolynomial_aeval_eq_zero_iff, LaurentPolynomial.algebraMap_eq_toLaurent, Polynomial.eq_C_coeff_zero_iff_natDegree_eq_zero, Differential.mapCoeffs_C, Polynomial.mahlerMeasure_mul, Polynomial.IsUnitTrinomial.not_isUnit, Polynomial.comp_C_mul_X_coeff, Ideal.mem_leadingCoeffNth, Polynomial.cyclotomic_prime_pow_mul_X_pow_sub_one, Polynomial.natDegree_add_coeff_mul, Polynomial.int_eval₂_eq, gal_C_isSolvable, evalRingHom_mapMatrix_comp_compRingEquiv, Polynomial.coeff_add, Polynomial.resultant_X_sub_C_pow_left, Polynomial.mirror_involutive, Polynomial.separable_one, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none, Polynomial.nontrivial, bernsteinPolynomial.variance, Polynomial.toFn_zero, Polynomial.toLaurent_X_pow, Polynomial.ofFn_zero', RatFunc.instIsScalarTowerOfIsDomainOfPolynomial, Polynomial.derivative_C_mul_X, Polynomial.Bivariate.swap_X, AdjoinRoot.lift_mk, Polynomial.eval_iterate_derivative_rootMultiplicity, Polynomial.lcoeff_apply, Polynomial.iterate_derivative_derivative_mul_X, Polynomial.cauchyBound_one, Polynomial.Chebyshev.add_one_mul_self_mul_T_eq_poly_in_T, Polynomial.sub_mod, WeierstrassCurve.Affine.CoordinateRing.map_mk, bernsteinPolynomial.sum_smul, Polynomial.Splits.X_add_C, Polynomial.bernoulli_eq_sub_sum, descPochhammer_succ_left, Polynomial.natDegree_zero, Polynomial.degree_C_lt, Polynomial.neg_modByMonic, Polynomial.leadingCoeff_pow', padic_polynomial_dist, Polynomial.comp_neg_X_leadingCoeff_eq, Polynomial.aeval_conj, Polynomial.nextCoeff_C_eq_zero, Polynomial.iterate_derivative_eq_zero, Polynomial.hasseDeriv_coeff, Polynomial.prod_mahlerMeasure_eq_mahlerMeasure_prod, Polynomial.degree_C_mul_X_pow_le, Polynomial.separable_prod_X_sub_C_iff', Polynomial.le_trailingDegree_C_mul_X_pow, Polynomial.map_mapRingHom_evalEval, Polynomial.algEquivAevalNegX_symm_apply, Polynomial.Monic.mul_right_eq_zero_iff, Polynomial.derivative_rootMultiplicity_of_root_of_mem_nonZeroDivisors, descPochhammer_mul, AdjoinRoot.root_isInv, Polynomial.monomial_zero_one, FiniteField.splits_X_pow_nat_card_sub_X, Polynomial.hasseDeriv_mul, Polynomial.isCentralScalar, PowerSeries.trunc_one_left, LaurentSeries.coe_X_compare, WeierstrassCurve.preΨ_zero, IsAdjoinRoot.adjoinRootAlgEquiv_apply_eq_map, Polynomial.self_mul_modByMonic, Polynomial.coeff_mul_C, PowerSeries.IsWeierstrassDivisorAt.mod_add, Polynomial.hermite_eq_deriv_gaussian', Polynomial.eraseLead_add_of_degree_lt_left, Polynomial.aeval_smul, Polynomial.rootMultiplicity_C, Polynomial.eq_prod_roots_of_splits_id, Polynomial.eraseLead_add_monomial_natDegree_leadingCoeff, RatFunc.laurentAux_algebraMap, IsAdjoinRoot.repr_zero_mem_span, Polynomial.coeff_C, AdjoinRoot.modByMonicHom_mk, Polynomial.degree_zero, Polynomial.eval_zero, Ideal.Filtration.submodule_span_single, Polynomial.wronskian_zero_left, RatFunc.one_def, Polynomial.degree_intCast_le, Polynomial.natDegree_X_sub_C, Polynomial.degree_list_sum_le_of_forall_degree_le, WeierstrassCurve.Affine.CoordinateRing.mk_φ, Polynomial.div_eq_zero_iff, Polynomial.toFinsupp_natCast, Polynomial.Bivariate.equivMvPolynomial_symm_X_1, Polynomial.iterate_derivative_X_pow_eq_smul, WeierstrassCurve.ψ_zero, Matrix.matPolyEquiv_charmatrix, Polynomial.natDegree_C_mul, PowerBasis.mem_span_pow, Polynomial.card_support_eq_three, Polynomial.linearIndependent_powers_iff_aeval, Polynomial.aeval_def, RatFunc.algebraMap_apply_div, Polynomial.Chebyshev.derivative_U_eval_one, Polynomial.Chebyshev.U_eq_X_mul_U_add_T, RatFunc.div_smul, Polynomial.aeval_mul, Polynomial.modByMonic_zero, Polynomial.monomial_one_eq_iff, Polynomial.resultant_X_sub_C_pow_right, StandardEtalePresentation.toSubmersivePresentation_jacobian, Polynomial.smeval_C_mul, IsAlgClosed.exists_aeval_eq_zero_of_injective, Polynomial.X_sub_C_dvd_sub_C_eval, Polynomial.expand_eq_zero, Polynomial.degreeLT.addLinearEquiv_apply', WeierstrassCurve.Ψ_three, Polynomial.differentiableAt_aeval, WeierstrassCurve.Affine.Y_sub_polynomialY, Polynomial.hasseDeriv_zero, Polynomial.prime_X_sub_C, Polynomial.mul_comp_neg_X, Matrix.charmatrix_natCast, Polynomial.eraseLead_zero, Polynomial.coeff_monomial_zero_mul, Polynomial.hilbertPoly_X_pow_succ, Polynomial.Monic.mem_nonZeroDivisors, Lagrange.iterate_derivative_interpolate, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, Polynomial.taylorAlgHom_apply, Polynomial.splits_mul_iff, Polynomial.pow_sub_dvd_iterate_derivative_pow, AlgebraicClosure.Monics.splits_finsetProd, RatFunc.inv_def, Polynomial.hasFDerivAt_aeval, IsAdjoinRoot.lift_map, Polynomial.C_sub, Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero, Polynomial.algEquivOfCompEqX_symm_apply, Polynomial.roots_X_pow_char_sub_C_pow, Polynomial.finset_sum_coeff, Polynomial.mem_nonZeroDivisors_iff, Polynomial.mem_nonZeroDivisors_of_trailingCoeff, Polynomial.aeval_eq_prod_aroots_sub_of_monic_of_splits, MvPolynomial.mem_support_coeff_optionEquivLeft, Polynomial.intCast_inj, Polynomial.coeff_sum, Polynomial.Bivariate.swap_C_C, Algebra.IsAlgebraic.lift_cardinalMk_le_sigma_polynomial, AdjoinRoot.liftAlgHom_mk, Polynomial.natDegree_derivative_le, Polynomial.isMonicOfDegree_zero_iff, Polynomial.cyclotomic_zero, Polynomial.isCompact_image_comap_of_monic, RatFunc.faithfulSMul, instIsIntegrallyClosedPolynomialOfIsDomain, LinearMap.aeval_eq_aeval_mod_charpoly, Polynomial.reflect_zero, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, Polynomial.leadingCoeff_mul_X, Matrix.BlockTriangular.charmatrix, LinearMap.hasEigenvalue_zero_tfae, Polynomial.iterate_derivative_eq_sum, PolynomialModule.smul_apply, Polynomial.algEquivAevalXAddC_symm_apply, MvPolynomial.aeval_toMvPolynomial, Polynomial.Chebyshev.iterate_derivative_U_eval_zero_recurrence, Polynomial.resultant_pow_right, Polynomial.isMaximal_comap_C_of_isJacobsonRing, Polynomial.nextCoeff_X_sub_C, Polynomial.natDegree_C_mul_X_pow, Polynomial.wronskianBilin_apply, AdjoinRoot.coe_mkₐ, Polynomial.evalEval_pow, PolyEquivTensor.invFun_add, Polynomial.dvd_mul_leadingCoeff_inv, RatFunc.algebraMap_C, Polynomial.C_mul_X_pow_eq_self, Polynomial.leadingCoeff_X_pow, AnalyticAt.aeval_polynomial, WeierstrassCurve.Affine.CoordinateRing.instIsDomain, Polynomial.degree_X_sub_C_le, PowerSeries.trunc_C, Polynomial.instIsCancelMulZeroOfIsCancelAdd, Polynomial.Monic.mem_rootSet, Polynomial.smeval_X_mul, Polynomial.cardPowDegree_apply, spectrum.map_polynomial_aeval_of_nonempty, AdjoinRoot.Minpoly.coe_toAdjoin_mk_X, Polynomial.sumIDeriv_apply, Polynomial.mirror_mul_of_domain, Polynomial.sylvesterDeriv_updateRow, RatFunc.instIsScalarTowerPolynomial, Polynomial.degree_C_mul_X_le, Polynomial.mul_X_pow_comp, Polynomial.dvd_derivative_iff, Polynomial.coeff_mul_monomial_zero, Polynomial.roots_ofMultiset, PowerSeries.weierstrassMod_zero_left, Polynomial.reverse_mul_X, Polynomial.expand_zero, Polynomial.cyclotomic.dvd_X_pow_sub_one, Polynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRing, Polynomial.mul_self_modByMonic, Polynomial.eraseLead_C_mul_X_pow, Polynomial.roots_expand_pow_map_iterateFrobenius_le, Polynomial.Monic.natSepDegree_eq_one_iff, Polynomial.resultant_taylor, Polynomial.trailingDegree_C, Polynomial.leadingCoeff_sum_of_degree_eq, Polynomial.coeff_mul_add_eq_of_natDegree_le, Ideal.is_fg_degreeLE, Polynomial.primPart_dvd, X_pow_sub_C_irreducible_of_prime, Polynomial.roots_multiset_prod_X_sub_C, Polynomial.homogenize_finsetSum, PowerBasis.equivOfMinpoly_aeval, Polynomial.degreeLT.addLinearEquiv_symm_apply_inl, MvPolynomial.aeval_toPolynomialAdjoinImageCompl_eq_zero, Polynomial.degreeLT.addLinearEquiv_symm_apply_inr_basis, Polynomial.ofFinsupp_smul, Polynomial.mirror_zero, Polynomial.neg_cancelLeads, Polynomial.natDegree_hasseDeriv, Polynomial.Chebyshev.S_neg_two, Polynomial.homogenize_C_mul, Polynomial.Chebyshev.S_zero, AdjoinRoot.powerBasisAux'_repr_symm_apply, Polynomial.Bivariate.swap_monomial_monomial, instIsAlgebraicPolynomialOfNoZeroDivisors, RatFunc.num_eq_zero_iff, Polynomial.leadingCoeff_smul_of_smul_regular, Polynomial.rootMultiplicity_expand, Polynomial.cyclotomic_injective, Polynomial.bernoulli_comp_one_add_X, Polynomial.X_pow_dvd_iff, Polynomial.contract_C, Matrix.charpoly_fin_two, RatFunc.ofFractionRing_smul, Polynomial.eval₂_mul_C', Polynomial.eval_derivative_div_eval_of_ne_zero_of_splits, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_eval, Polynomial.separable_prod_X_sub_C_iff, MvPolynomial.totalDegree_coeff_optionEquivLeft_add_le, Polynomial.resultant_C_left, LinearMap.charpoly_constantCoeff_eq_zero_iff, PolynomialModule.equivPolynomial_single, Polynomial.resultant_add_mul_right, Polynomial.natDegree_mul_C_of_isUnit, Polynomial.dickson_add_two, Polynomial.toFn_comp_ofFn_eq_id, AdjoinRoot.quotEquivQuotMap_apply_mk, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply, Polynomial.irreducible_of_degree_eq_one_of_isRelPrime_coeff, Polynomial.exists_eq_pow_rootMultiplicity_mul_and_not_dvd, Polynomial.supNorm_monomial, Polynomial.Bivariate.swap_map_C, Polynomial.derivative_comp, Polynomial.Monic.eq_X_add_C, transcendental_iff_ker_eq_bot, WeierstrassCurve.Affine.CoordinateRing.mk_Ψ_sq, Polynomial.mapRingHom_comp_C, Polynomial.IsMonicOfDegree.eq_isMonicOfDegree_one_or_two_mul, Polynomial.eq_C_of_degree_le_zero, Polynomial.mem_nonZeroDivisors_of_leadingCoeff, minpoly.dvd_map_of_isScalarTower, Polynomial.leadingCoeff_sub_of_degree_lt, Polynomial.gaussNorm_monomial, Polynomial.expand_X, Polynomial.eq_zero_of_natDegree_lt_card_of_eval_eq_zero, Polynomial.contentIdeal_C, Polynomial.Splits.dvd_iff_roots_le_roots, Polynomial.resultant_zero_left, Polynomial.taylor_taylor, WeierstrassCurve.Φ_ofNat, Polynomial.exists_approx_polynomial, Polynomial.eval_C_X_eval₂_map_C_X, Polynomial.map_prod, Polynomial.eraseLead_X, Polynomial.toFinsupp_mul, minpoly.isIntegrallyClosed_dvd_iff, Polynomial.degree_mul', Polynomial.expand_monomial, natDegree_radical_le, PolynomialModule.smul_single_apply, Polynomial.supNorm_C, Polynomial.Monic.irreducible_iff_natDegree, Polynomial.eval_finset_sum, Polynomial.Chebyshev.C_sub_one, Polynomial.eval₂_mul, Polynomial.degree_add_le_of_le, Polynomial.trailingCoeff_zero, Polynomial.degree_one_le, minpoly.subsingleton, RatFunc.intDegree_add, matPolyEquiv_map_C, Polynomial.aroots_zero, Polynomial.card_roots_X_pow_sub_C, WeierstrassCurve.baseChange_Ψ, Polynomial.monic_prod_of_monic, Algebra.Norm.Transitivity.eval_zero_comp_det, Polynomial.reverse_X_mul, Polynomial.instIsTorsionFree, Polynomial.pow_scaleRoots_of_isReduced, Polynomial.add_comp, Polynomial.mul_scaleRoots, Polynomial.X_pow_sub_one_separable_iff, WeierstrassCurve.Affine.map_polynomial, Polynomial.derivative_sq, Polynomial.leadingCoeff_C_mul_X_pow, Polynomial.mem_roots_sub_C, Polynomial.hermite_eq_deriv_gaussian, Differential.mapCoeffs_X, Polynomial.Monic.finite_quotient, WeierstrassCurve.Φ_three, MvPolynomial.optionEquivLeft_coeff_some_coeff_none, Polynomial.isMaximal_comap_C_of_isMaximal, Polynomial.not_isUnit_X_add_C, Polynomial.roots_smul_nonzero, Polynomial.natDegree_iterate_comp, Polynomial.eval_intCast, Polynomial.Chebyshev.U_add_two, Polynomial.degree_cubic, LinearMap.isNilpotent_iff_charpoly, Polynomial.natSepDegree_C_mul, Algebra.adjoin_eq_exists_aeval, WeierstrassCurve.ψ_one, Polynomial.hasseDeriv_monomial, PowerSeries.trunc_trunc_pow, RatFunc.zero_def, RatFunc.denom_X, Polynomial.degree_smul_of_isRightRegular_leadingCoeff, isPurelyInseparable_iff_minpoly_eq_X_sub_C_pow, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_neg_mul, Polynomial.Bivariate.pderiv_zero_equivMvPolynomial, Algebra.IsAlgebraic.cardinalMk_le_sigma_polynomial, Polynomial.cyclotomic_mul_prime_pow_eq, Polynomial.derivativeFinsupp_map, Polynomial.Splits.pow, Polynomial.gcd_map, Polynomial.mem_roots_iff_aeval_eq_zero, Polynomial.dickson_one_one_charP, RatFunc.ofFractionRing_injective, Polynomial.degree_X_pow, IsLocalization.scaleRoots_commonDenom_mem_lifts, Polynomial.cardinalMk_eq_max, WeierstrassCurve.Affine.baseChange_polynomialX, Polynomial.monomial_add, minpoly.eq_zero, Polynomial.one_lt_rootMultiplicity_iff_isRoot_gcd, Polynomial.natCast_inj, Polynomial.content_one, WeierstrassCurve.preΨ'_odd, Polynomial.resultant_X_add_C_left, gal_X_sub_C_isSolvable, Polynomial.hilbertPoly_mul_one_sub_succ, Polynomial.Bivariate.equivMvPolynomial_X, Polynomial.hasDerivWithinAt_aeval, Polynomial.homogenize_finsetProd, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eq₁, Polynomial.Gal.mul_splits_in_splittingField_of_mul, Cubic.equiv_symm_apply_b, Polynomial.coeff_monomial_same, reesAlgebra.fg, Polynomial.eval₂_evalRingHom, Module.AEval.of_symm_X_smul, Polynomial.aeval_coe_eq_smeval, Polynomial.natDegree_pow_le_of_le, FiniteField.isSplittingField_of_card_eq, Polynomial.natSepDegree_mul_eq_iff, Polynomial.IsMonicOfDegree.aeval_add, cyclotomic_prime_pow_comp_X_add_one_isEisensteinAt, Polynomial.natDegree_multiset_prod_X_sub_C_eq_card, Polynomial.smeval_one, AlgebraicClosure.toSplittingField_coeff, Polynomial.C_dvd_iff_dvd_coeff, Polynomial.hasStrictDerivAt_aeval, Polynomial.dickson_one_one_zmod_p, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, MvPolynomial.natDegree_optionEquivLeft, Polynomial.span_of_finite_le_degreeLT, Polynomial.aeval_algebraMap_eq_zero_iff_of_injective, StandardEtalePresentation.exists_mul_aeval_x_g_pow_eq_aeval_x, Polynomial.Splits.C_mul_X_pow, bernsteinPolynomial.iterate_derivative_succ_at_0_eq_zero, Polynomial.iterate_derivative_eq_zero_of_degree_lt, Polynomial.toFinsuppIsoLinear_apply, Polynomial.natDegree_one, Polynomial.exists_eq_X_add_C_of_natDegree_le_one, Polynomial.natSepDegree_smul_nonzero, Matrix.charpoly_coeff_eq_prod_coeff_of_le, PowerSeries.subst_coe, AdjoinRoot.Polynomial.quotQuotEquivComm_mk, RatFunc.denom_div, Polynomial.opRingEquiv_symm_C_mul_X_pow, WeierstrassCurve.Affine.CoordinateRing.exists_smul_basis_eq, bernsteinPolynomial.linearIndependent_aux, MvPolynomial.mem_support_finSuccEquiv, Polynomial.isRoot_iterate_derivative_of_lt_rootMultiplicity, minpoly.aeval_algHom, Polynomial.coeff_smul, Polynomial.mapAlgEquiv_toAlgHom, Polynomial.monic_expand_iff, Polynomial.iterate_derivative_prod_X_sub_C, Polynomial.commute_X, Polynomial.monic_geom_sum_X, Polynomial.signVariations_eraseLead_mul_X_sub_C, Polynomial.support_smul, eval_det, Polynomial.dvd_content_iff_C_dvd, Polynomial.natSepDegree_expand, Polynomial.degree_one, Polynomial.coeff_C_succ, IsArtinianRing.instDecompositionMonoidPolynomial, Polynomial.opRingEquiv_symm_monomial, ascPochhammer_zero, Polynomial.toAddCircle_monomial_eq_smul_fourier, instIsPushoutPolynomial, Polynomial.separable_C, Polynomial.Splits.splits, Polynomial.Chebyshev.U_neg, Polynomial.instIsLocalHomRingHomC, Polynomial.aeval_apply_smul_mem_of_le_comap', RatFunc.ofFractionRing_sub, Polynomial.X_pow_sub_one_mul_prod_cyclotomic_eq_X_pow_sub_one_of_dvd, Polynomial.natDegree_sub_eq_left_of_natDegree_lt, Polynomial.MonicDegreeEq.map_coe, RatFunc.intDegree_polynomial, Polynomial.degree_prod_le, cfc_eval_C, Polynomial.reflect_mul, Polynomial.mahlerMeasure_X_sub_C, RatFunc.v_def, minpoly.add_algebraMap, MvPolynomial.rename_comp_toMvPolynomial, divRadical_dvd_wronskian_right, Ideal.isPrime_map_C_of_isPrime, Polynomial.div_eq_quo_add_rem_div, PolynomialModule.equivPolynomialSelf_apply_eq, Polynomial.finiteMultiplicity_of_degree_pos_of_monic, MvPolynomial.finSuccEquiv_comp_C_eq_C, Polynomial.irreducible_of_degree_le_three_of_not_isRoot, Polynomial.degree_prod, Polynomial.degreeLT.addLinearEquiv_symm_apply, MulSemiringAction.charpoly_eq, Polynomial.Chebyshev.iterate_derivative_U_eval_one_recurrence, LaurentSeries.LaurentSeries_coe, Polynomial.coe_basisMonomials, PowerSeries.trunc_apply, WeierstrassCurve.Affine.CoordinateRing.C_addPolynomial_slope, Polynomial.degree_zero_le, WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_mul_mk_XYIdeal', IsAdjoinRoot.adjoinRootAlgEquiv_apply_mk, WeierstrassCurve.ψ_odd, Polynomial.isMonicOfDegree_one_iff, root_X_pow_sub_C_pow, WeierstrassCurve.Ψ_even, Polynomial.support_opRingEquiv, Polynomial.IsPrimitive.Int.dvd_iff_map_cast_dvd_map_cast, Polynomial.natDegree_sub, RatFunc.ofFractionRing_neg, bernsteinPolynomial.sum_mul_smul, LinearMap.aeval_self_charpoly, Polynomial.natDegree_X_pow_mul, LaurentSeries.powerSeries_ext_subring, WeierstrassCurve.Φ_four, Mathlib.Tactic.ComputeDegree.natDegree_C_le, LaurentPolynomial.eval₂_toLaurent, Polynomial.coe_mapRingHom, Polynomial.C_mul_dvd, MvPolynomial.finSuccEquiv_eq, Polynomial.eval_listSum, Polynomial.eval_mul_X_pow, Polynomial.isNilpotent_monomial_iff, Polynomial.as_sum_range', Polynomial.Chebyshev.C_add_one, Polynomial.natDegree_monomial, Polynomial.mem_iff_annIdealGenerator_dvd, spectrum.subset_polynomial_aeval, PolyEquivTensor.toFunAlgHom_apply_tmul_eq_smul, Polynomial.factorial_mul_shiftedLegendre_eq, Polynomial.isNilpotent_iff, Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_derivative_T_eq_poly_in_T, Polynomial.C_comp, FunctionField.ringOfIntegers.instIsDedekindDomainSubtypeMemSubalgebraPolynomialOfIsSeparableRatFunc, Polynomial.natDegree_X_pow_le, IsAdjoinRootMonic.map_modByMonicHom, Polynomial.coeff_divModByMonicAux_mem_span_pow_mul_span, WeierstrassCurve.Affine.degree_polynomial, Polynomial.div_C, Polynomial.separable_def, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero, Polynomial.comp_one, Polynomial.coeffs_one, MvPolynomial.image_support_finSuccEquiv, Polynomial.iterate_derivative_smul, Ideal.mem_map_C_iff, Polynomial.natSepDegree_pow_of_ne_zero, Polynomial.natSepDegree_one, Polynomial.Monic.nextCoeff_multiset_prod, LieAlgebra.engel_isBot_of_isMin.lieCharpoly_coeff_natDegree, IsConjRoot.aeval_eq_zero, PowerSeries.IsWeierstrassDivisorAt.mod_smul, IntermediateField.isSplittingField_iSup, Polynomial.Chebyshev.S_neg, Polynomial.sumIDeriv_X, Polynomial.Bivariate.aevalAeval_swap, Polynomial.natTrailingDegree_eq_support_min', Polynomial.natDegree_pow_le, Polynomial.card_support_eq_zero, MulSemiringActionHom.coe_polynomial, Polynomial.coeff_X_pow_self, Polynomial.natDegree_pow, Polynomial.contentIdeal_monomial, Polynomial.dvd_C_mul_X_sub_one_pow_add_one, RatFunc.denom_div_dvd, Polynomial.separable_gcd_right, Polynomial.rootSet_C, Polynomial.injective_ofFn, matPolyEquiv_symm_C, Polynomial.toFinsupp_algebraMap, FixedPoints.smul_polynomial, Polynomial.separable_gcd_left, Polynomial.Bivariate.equivMvPolynomial_C_X, Polynomial.divX_zero, Polynomial.Monic.sub_of_left, isPurelyInseparable_iff_minpoly_eq_X_pow_sub_C, Polynomial.lifts_iff_coeff_lifts, PolyEquivTensor.toFunBilinear_apply_apply, Polynomial.natDegree_mul_C_eq_of_mul_ne_zero, Polynomial.coe_compRingHom, Polynomial.ofMultiset_apply, RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply, Module.AEval.mem_mapSubmodule_symm_apply, PolyEquivTensor.toFunLinear_tmul_apply, RatFunc.rank_ratFunc_ratFunc, Polynomial.ofFinsupp_neg, Polynomial.coeff_iterate_derivative, Cubic.prod_X_sub_C_eq, WeierstrassCurve.ΨSq_one, Polynomial.algHom_ext_iff, Polynomial.trailingDegree_lt_wf, Polynomial.coeToPowerSeries.algHom_apply, Polynomial.Chebyshev.T_neg_two, Polynomial.rootMultiplicity_eq_multiplicity, bernsteinPolynomial.eq_zero_of_lt, Lagrange.degree_interpolate_le, Polynomial.bernoulli_def, Polynomial.X_mul, Module.AEval.X_smul_of, Polynomial.derivative_eval₂_C, LaurentSeries.powerSeriesRingEquiv_coe_apply, Polynomial.multiset_prod_X_sub_C_nextCoeff, Polynomial.splits_of_splits_mul, Polynomial.C_div, Polynomial.isPrimitive_one, Polynomial.Chebyshev.S_two, Polynomial.eval_natCast_mul, RatFunc.instIsScalarTowerOfPolynomial, gal_one_isSolvable, Polynomial.normalize_eq_self_iff_monic, Lagrange.nodal_eq_mul_nodal_erase, Polynomial.lhom_ext'_iff, Polynomial.Monic.irreducible_iff_degree_lt, PowerSeries.derivative_coe, Polynomial.natDegree_X_pow, Polynomial.divX_C_mul_X_pow, MvPolynomial.prod_X_add_C_coeff, Polynomial.sum_add_index, MvPolynomial.degree_finSuccEquiv, Polynomial.Bivariate.Polynomial.Bivariate.pderiv_zero_equivMvPolynomial, Polynomial.X_pow_mul_monomial, Polynomial.roots_expand_pow_map_iterateFrobenius, Polynomial.IsPrimitive.dvd_primPart_iff_dvd, LaurentPolynomial.toLaurent_support, Polynomial.aeval_derivative_of_splits, Polynomial.evalEval_add, MvPolynomial.nonempty_support_optionEquivLeft, Polynomial.map_expand_pow_char, Polynomial.toFinsupp_eq_one, WeierstrassCurve.Affine.CoordinateRing.map_injective, WeierstrassCurve.Ψ_zero, WeierstrassCurve.ψ_three, Polynomial.reflect_neg, Polynomial.lsum_apply, Polynomial.mem_closure_X_union_C, Polynomial.infinite, WeierstrassCurve.ΨSq_zero, Ideal.polynomialQuotientEquivQuotientPolynomial_symm_mk, Matrix.charpoly_isEmpty, WeierstrassCurve.Affine.baseChange_polynomial, Polynomial.coeff_expand_mul, Polynomial.cyclotomic_mul_prime_eq_pow_of_not_dvd, Polynomial.coeff_mul_intCast, Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, Polynomial.derivative_pow, Polynomial.isDomain_iff, Polynomial.C_ofNat, Polynomial.reverse_add_C, Polynomial.wronskian_add_left, Polynomial.derivative_prod, IsPrimitiveRoot.squarefree_minpoly_mod, Polynomial.isSplittingField_C, not_irreducible_expand, AlgebraicClosure.Monics.map_eq_prod, LindemannWeierstrass.integral_exp_mul_eval, WeierstrassCurve.ψ_neg, minpoly.dvd_map_of_isScalarTower', Polynomial.isLocalization, Polynomial.scaleRoots_dvd_iff, Polynomial.contentIdeal_eq_bot_iff, Polynomial.expand_mul, Polynomial.eval_sumIDeriv_of_pos, Polynomial.cyclotomic_one, Polynomial.natDegree_smul_le, Polynomial.coeff_X_mul_zero, Polynomial.aeval_continuousMap_apply, Polynomial.image_comap_C_basicOpen, Polynomial.leadingCoeff_monic_mul, Polynomial.mkDerivation_X, Polynomial.coe_aeval_mk_apply, Polynomial.dickson_one_one_eq_chebyshev_T, Polynomial.leadingCoeff_mul_C_of_isUnit, FunctionField.ringOfIntegers.algebraMap_injective, Polynomial.Monic.sub_of_right, FiniteField.X_pow_card_sub_X_natDegree_eq, Polynomial.IsMonicOfDegree.pow, Polynomial.isRegular_X_pow, Polynomial.prod_cyclotomic_eq_geom_sum, RatFunc.denom_inv_dvd, Polynomial.coeff_zero_eq_aeval_zero, Polynomial.derivation_ext_iff, MvPolynomial.support_optionEquivLeft, Polynomial.map_zero, Polynomial.mahlerMeasure_one, Polynomial.roots_prod, Polynomial.not_isUnit_X_sub_C, PowerSeries.IsWeierstrassDivisionAt.add, Polynomial.Monic.add_of_right, Polynomial.degree_multiset_prod_le, FiniteField.splits_X_pow_card_sub_X, MvPolynomial.finSuccEquiv_X_succ, Polynomial.card_support_eq_two, Polynomial.coeff_sub, Polynomial.Monic.geom_sum, WeierstrassCurve.Affine.Point.toClass_some, Polynomial.coeff_zero_multiset_prod, PowerSeries.add_weierstrassMod, cfc_polynomial, WeierstrassCurve.baseChange_ψ, Polynomial.degree_prod_of_monic, Polynomial.coeffList_eq_nil, polynomial_expand_eq, Polynomial.degree_sub_le, Matrix.charpoly_fromBlocks_zero₁₂, Polynomial.Chebyshev.iterate_derivative_U_eval_one, Polynomial.chebyshev_T_eq_dickson_one_one, Polynomial.span_minpoly_eq_annihilator, Polynomial.toFinsuppIsoAlg_symm_apply_toFinsupp, Polynomial.divByMonic_eq_div, Polynomial.iterate_derivative_C_mul, Polynomial.reflect_C_mul_X_pow, Polynomial.card_support_eq_one, Polynomial.natDegree_add_eq_right_of_degree_lt, Polynomial.Monic.degree_mul, PolyEquivTensor.invFun_monomial, Polynomial.coe_expand, Polynomial.roots_mul, Polynomial.contentIdeal_zero, Polynomial.one_comp, Polynomial.ringKrullDim_le, polynomialFunctions_coe, Polynomial.irreducible_factor, Polynomial.aroots_C_mul_X_pow, Polynomial.mkDerivation_one_eq_derivative, Matrix.charpoly_sub_diagonal_degree_lt, Polynomial.fourierCoeff_toAddCircle_natCast, Polynomial.leadingCoeff_C_mul_X, Polynomial.map_smul, Polynomial.mahlerMeasure_zero, Polynomial.degreeLT.addLinearEquiv_symm_apply', spectrum.map_polynomial_aeval_of_degree_pos, Polynomial.coe_mul, Polynomial.constantCoeff_surjective, Polynomial.eraseLead_C, Polynomial.Splits.X_sub_C, Polynomial.isUnit_primPart_C, Polynomial.degree_smul_le, Polynomial.iterate_derivative_mul_X_pow, Polynomial.sub_modByMonic, MvPolynomial.eval₂_const_pUnitAlgEquiv, Polynomial.eval₂RingHom'_apply, IsAdjoinRootMonic.modByMonicHom_root_pow, Polynomial.annIdealGenerator_aeval_eq_zero, Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_C, Polynomial.coeff_inv_units, Polynomial.eval₂_pow, minpoly.eq_X_sub_C', Polynomial.smeval_pow, Polynomial.taylor_coeff_one, Polynomial.root_gcd_iff_root_left_right, RatFunc.mk_eq_mk, Polynomial.toContinuousMapAlgHom_apply, Polynomial.algebraMap_hahnSeries_apply, Polynomial.sup_ker_aeval_le_ker_aeval_mul, Polynomial.fderivWithin_aeval, PolyEquivTensor.toFunLinear_one_tmul_one, Polynomial.cauchyBound_zero, Polynomial.splits_mul, Polynomial.reverse_mul, Polynomial.fderivWithin, Polynomial.mem_map_range, RatFunc.num_mul_dvd, Cubic.equiv_symm_apply_c, Polynomial.monomial_neg, Polynomial.leadingCoeff_sub_of_degree_eq, Polynomial.hasDerivAt, WeierstrassCurve.Affine.Point.toClass_injective, Polynomial.Monic.comp_X_add_C, Polynomial.divX_C, StandardEtalePresentation.toPresentation_σ', Polynomial.monomial_zero_right, Polynomial.cyclotomic_eq_prod_X_pow_sub_one_pow_moebius, Polynomial.Monic.C_dvd_iff_isUnit, Polynomial.iterate_derivative_sub, Polynomial.coeff_X_add_one_pow, Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_one, Polynomial.signVariations_monomial, Polynomial.natSepDegree_C, Polynomial.mul_X_add_natCast_comp, Derivation.map_aeval, matPolyEquiv_eval_eq_map, Polynomial.monic_mul_leadingCoeff_inv, Polynomial.eq_X_sub_C_of_splits_of_single_root, Polynomial.Splits.aeval_eq_prod_aroots_of_monic, Mathlib.Tactic.ComputeDegree.coeff_sub_of_eq, Polynomial.divByMonic_zero, Polynomial.natDegree_natCast, Polynomial.card_support_C_mul_X_pow_le_one, PolyEquivTensor.left_inv, Polynomial.natTrailingDegree_neg, Polynomial.monomial_mul_X_pow, matPolyEquiv_coeff_apply, Polynomial.discr_C, Polynomial.aeval_neg, Polynomial.coeToPowerSeries.ringHom_apply, Polynomial.support_C_mul_X_pow, aeval_derivative_mem_differentIdeal, MvPolynomial.prod_C_add_X_eq_sum_esymm, Polynomial.modByMonic_X_sub_C_eq_C_eval, denomsClearable_C_mul_X_pow, Polynomial.coeff_opRingEquiv, Polynomial.binomial_eq_binomial, Polynomial.taylorEquiv_symm, Polynomial.iterate_derivative_X_pow_eq_C_mul, Matrix.charpoly_vecMulVec, Polynomial.instIsLeftCancelMulZeroOfIsCancelAdd, Polynomial.derivative_X_pow, Cubic.zero, Polynomial.exists_monic_aeval_eq_zero_forall_mem_pow_of_mem_map, MvPolynomial.optionEquivRight_apply, Polynomial.coe_sub, Polynomial.leadingCoeff_mul', Polynomial.coeff_expand, MvPolynomial.finSuccEquiv_apply, Polynomial.sumIDeriv_derivative, Polynomial.rootsExpandToRoots_apply, Polynomial.degree_C_mul, Polynomial.X_dvd_iff, Polynomial.degree_neg, Polynomial.X_mul_monomial, Polynomial.gaussNorm_C, Lagrange.interpolate_eq_add_interpolate_erase, StandardEtalePair.HasMap.isUnit_derivative_f, Polynomial.Splits.eq_prod_roots_of_monic, PowerBasis.equivOfMinpoly_symm, Polynomial.mul_mod, AdjoinRoot.mk_X, Polynomial.toFinsuppIso_apply, Polynomial.leadingCoeff_expand, Polynomial.isNilpotent_C_mul_pow_X_of_isNilpotent, Polynomial.aeval_sumIDeriv_eq_eval, Polynomial.coe_neg, Polynomial.leadingCoeff_X_sub_C, RatFunc.denom_C, Polynomial.Monic.pow, Matrix.isUnit_charpolyRev_of_isNilpotent, Polynomial.expand_eq_C, RatFunc.num_div_dvd', WeierstrassCurve.Φ_two, Polynomial.aeval_C, PowerBasis.exists_eq_aeval', Polynomial.evalEval_neg, Polynomial.IsMonicOfDegree.eq_isMonicOfDegree_two_mul_isMonicOfDegree, Polynomial.aeval_eq_prod_aroots_sub_of_splits, Polynomial.Chebyshev.C_comp_two_mul_X, KaehlerDifferential.polynomial_D_apply, PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_2, Polynomial.eval_add, Polynomial.toLaurent_inj, Polynomial.leval_apply, Polynomial.instNoZeroDivisors, Polynomial.eval₂_X_mul, Polynomial.X_pow_mem_lifts, AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_symm_mk_mk, MvPolynomial.rename_polynomial_aeval_X, Polynomial.ofFn_degree_lt, Polynomial.taylor_monomial, Polynomial.comp_eq_aeval, Lagrange.interpolate_apply, IsPurelyInseparable.minpoly_eq_X_pow_sub_C, Polynomial.C_mul, Polynomial.valuation_aeval_monomial_eq_valuation_pow, LinearMap.charpoly_one, Lagrange.interpolate_eq_iff_values_eq_on, Polynomial.natDegree_X_sub_C_le, Polynomial.splits_X_sub_C_mul_iff, WeierstrassCurve.preΨ_neg, Polynomial.coeff_ofNat_mul, Polynomial.factorial_smul_hasseDeriv, Polynomial.toMvPolynomial_X, RatFunc.natDegree_num_mul_right_sub_natDegree_denom_mul_left_eq_intDegree, FiniteField.minpoly_frobeniusAlgHom, Polynomial.mem_ker_modByMonic, Polynomial.dickson_of_two_le, Matrix.charmatrix_one, Matrix.coeff_det_one_add_X_smul_one, Polynomial.aeval_ofReal, Polynomial.leadingCoeff_add_of_degree_lt, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eq_poly_in_T, Polynomial.degree_add_degree_leadingCoeff_inv, Polynomial.toFinsupp_sum, Polynomial.resultant_prod_right, Polynomial.Chebyshev.U_add_one, Polynomial.eval₂AddMonoidHom_apply, Polynomial.trinomial_def, Polynomial.hasDerivAt_aeval, Polynomial.coe_algebraMap_eq_CC, Polynomial.coeffList_zero, Polynomial.aeval_root_derivative_of_splits, Polynomial.X_sub_C_scaleRoots, FunctionField.ringOfIntegers.instIsFractionRingSubtypeMemSubalgebraPolynomial, Polynomial.Chebyshev.aeval_C, PerfectField.separable_iff_squarefree, Polynomial.iterate_derivative_neg, Polynomial.aeval_eq_sum_range, Polynomial.Chebyshev.C_mul_C, polyEquivTensor_apply, Polynomial.resultant_C_zero_left, Polynomial.C_eq_or_isOpenQuotientMap_eval, PolyEquivTensor.toFunBilinear_apply_eq_smul, MvPolynomial.eval_toMvPolynomial, Polynomial.X_pow_sub_X_sub_one_irreducible_rat, Polynomial.instFree, Polynomial.sum_taylor_eq, Polynomial.ofNat_comp, Polynomial.taylor_eval_sub, Polynomial.Chebyshev.aeval_U, Polynomial.trailingDegree_one, Polynomial.algebraMap_hahnSeries_injective, Polynomial.derivative_prod_finset, Polynomial.mem_normalizedFactors_iff, LaurentSeries.valuation_coe_ratFunc, Polynomial.isNilpotent_C_iff, gal_mul_isSolvable, Polynomial.cyclotomic'_two, Polynomial.disc_C, Polynomial.IsMonicOfDegree.eq_isMonicOfDegree_one_mul_isMonicOfDegree, Polynomial.MonicDegreeEq.mk_coe, Polynomial.X_mem_nonzeroDivisors, Differential.deriv_aeval_eq, MvPolynomial.irreducible_toPolynomialAdjoinImageCompl, Polynomial.hasseDeriv_C, Algebra.exists_aeval_invOf_eq_zero_of_idealMap_adjoin_sup_span_eq_top, Polynomial.degree_sub_eq_left_of_degree_lt, Polynomial.natDegree_linear_le, MvPolynomial.toMvPowerSeries_pUnitAlgEquiv, Polynomial.root_mul_left_of_isRoot, Polynomial.coeff_list_sum, Ideal.factors_span_eq, Polynomial.derivation_C, minpoly_algEquiv_toLinearMap, Polynomial.sum_zero_index, Polynomial.degree_div_lt, Polynomial.smeval_monomial, PowerSeries.IsWeierstrassDivisorAt.mod_zero, Polynomial.natDegree_det_X_add_C_le, Polynomial.modByMonic_add_div, Polynomial.eval_C_X_comp_eval₂_map_C_X, AdjoinRoot.algHom_subsingleton, Polynomial.toLaurent_one, Polynomial.natCast_comp, Polynomial.homogenize_monomial_of_lt, Polynomial.mod_X_sub_C_eq_C_eval, Polynomial.degree_map_eq_iff, StandardEtalePair.cond, Polynomial.splits_prod_iff, Polynomial.prod_comp, Polynomial.toSubring_zero, Polynomial.Chebyshev.one_sub_X_sq_mul_U_eq_pol_in_T, minpoly.one, StandardEtalePresentation.aeval_val_equivMvPolynomial, Polynomial.toFinsupp_add, PolynomialModule.eval_smul, instIsPushoutFractionRingPolynomial, Polynomial.smul_C, Polynomial.derivative_sub, Polynomial.degree_comp_neg_X, Polynomial.mem_rootSet', Polynomial.root_mul, Polynomial.uniqueFactorizationMonoid, AdjoinRoot.Polynomial.quotQuotEquivComm_symm_mk_mk, LaurentSeries.valuation_compare, Polynomial.geom_sum_X_comp_X_add_one_eq_sum, Polynomial.Chebyshev.U_neg_one, Polynomial.hasStrictDerivAt, LinearMap.charpoly_prodMap, LinearMap.charpoly_sub_smul, RatFunc.ofFractionRing_inv, Polynomial.Bivariate.swap_C, minpoly.neg, Polynomial.cyclotomic.irreducible_rat, Polynomial.natSepDegree_X_sub_C, Polynomial.coe_normUnit, Polynomial.MonicDegreeEq.natDegree, RatFunc.algebraMap_apply, Algebraic.cardinalMk_le_mul, instFaithfulSMulPolynomial, Polynomial.aroots_monomial, Polynomial.Chebyshev.T_mul_T, Polynomial.reverse_neg, Polynomial.det_taylorLinearEquiv, WeierstrassCurve.Affine.CoordinateRing.coe_norm_smul_basis, PowerSeries.trunc_one, Polynomial.aroots_X_pow, Polynomial.toFinsupp_neg, Polynomial.derivative_monomial_succ, NormedAlgebra.Real.exists_isMonicOfDegree_two_and_aeval_eq_zero, Polynomial.resultant_deriv, Polynomial.logMahlerMeasure_zero, Polynomial.Chebyshev.T_sub_one, Polynomial.degree_le_zero_iff, Polynomial.roots_one, Polynomial.toFinsupp_smul, Polynomial.rootSet_one, IsAdjoinRoot.algebraMap_apply, Polynomial.support_X_pow, spectralValue_X_sub_C, StandardEtalePair.aeval_X_g_mul_mk_X, Transcendental.aeval, Polynomial.map_sub, PowerSeries.trunc_succ, Polynomial.roots_C_mul_X_sub_C, Polynomial.isIntegral_iff_isIntegral_coeff, MvPolynomial.eval₂_pUnitAlgEquiv_symm, Polynomial.isJacobsonRing_polynomial_of_isJacobsonRing, Polynomial.monomial_one_right_eq_X_pow, Polynomial.degree_add_le, Derivation.compAEval_eq, LaurentSeries.tendsto_valuation, Polynomial.eval₂_mul_eq_zero_of_right, Polynomial.aroots_neg, Polynomial.hasseDeriv_apply_one, Polynomial.aeval_endomorphism, Polynomial.ofFinsupp_mul, WeierstrassCurve.Affine.CoordinateRing.mk_ψ₂_sq, IntermediateField.mem_adjoin_simple_iff, Polynomial.eval₂_neg, Polynomial.rootMultiplicity_le_iff, Polynomial.eraseLead_mul_eq_mul_eraseLead_of_nextCoeff_zero, RatFunc.mk_one, Polynomial.eval_one, Polynomial.isUnit_iff_degree_eq_zero, RatFunc.algebraMap_injective, Matrix.charmatrix_map, Polynomial.surjective_toFn, Polynomial.modByMonic_X, IsPurelyInseparable.minpoly_eq_X_sub_C_pow, WeierstrassCurve.Affine.CoordinateRing.basis_zero, Module.AEval.of_aeval_smul, Polynomial.map_sum, Algebra.mem_ideal_map_adjoin, Lagrange.interpolate_empty, LaurentSeries.coe_range_dense, X_pow_sub_C_irreducible_of_prime_pow, minpoly.not_isUnit, Polynomial.mem_aroots, Polynomial.integralNormalization_mul_C_leadingCoeff, Polynomial.eval_sum, bernsteinPolynomial.derivative_succ, ZMod.expand_card, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero', PowerSeries.IsWeierstrassDivision.isWeierstrassFactorization, RatFunc.finrank_ratFunc_ratFunc, RatFunc.neg_def, Polynomial.coeff_zero, Polynomial.lifts_iff_liftsRing, Polynomial.coeff_mul_natCast, Polynomial.Splits.dvd_of_roots_le_roots, Polynomial.iterate_derivative_X_sub_pow_self, Polynomial.derivativeFinsupp_one, Polynomial.X_dvd_sub_C, IsAdjoinRoot.map_self, Polynomial.degreeLT_eq_span_X_pow, Polynomial.eval_mul_X_sub_C, MvPolynomial.polynomial_eval_eval₂, WeierstrassCurve.Affine.map_polynomialX, minpolyDiv_spec, Polynomial.isNilpotent_mul_X_iff, Polynomial.reverse_C, Lagrange.eq_interpolate_of_eval_eq, Polynomial.Splits.C_mul, Polynomial.cardPowDegree_nonzero, Polynomial.toFinsuppIsoAlg_apply, Polynomial.reflect_C, Polynomial.eval₂_C, Polynomial.coeffList_neg, Cubic.equiv_apply_coe, Polynomial.taylor_zero, Ideal.jacobson_bot_polynomial_of_jacobson_bot, Polynomial.comp_zero, Polynomial.toMatrix_sylvesterMap, PowerSeries.coeff_mul_eq_coeff_trunc_mul_trunc, Cubic.of_d_eq_zero', MvPolynomial.optionEquivLeft_monomial, IsAdjoinRootMonic.modByMonicHom_root, RatFunc.ofFractionRing_eq, Polynomial.Chebyshev.C_zero, Polynomial.reflect_C_mul, Polynomial.coeff_neg, Polynomial.derivative_neg, Polynomial.dvd_comp_neg_X_iff, Polynomial.aeval_algEquiv, Matrix.charpoly_inv, Polynomial.deriv, Polynomial.resultant_prod_left, Polynomial.eval₂_pow', support_subset_support_matPolyEquiv, Polynomial.algEquivAevalNegX_apply, Polynomial.natDegree_sub_C, Polynomial.leadingCoeff_mul_monic, Polynomial.toFinsupp_sub, Module.End.ker_aeval_ring_hom'_unit_polynomial, PowerSeries.trunc_coe_eq_self, PrimeSpectrum.range_comap_algebraMap_localization_compl_eq_range_comap_quotientMk, StandardEtalePresentation.toPresentation_algebra_algebraMap_apply, Derivation.mapCoeffs_apply, MvPolynomial.optionEquivLeft_symm_apply, RatFunc.denom_algebraMap, Algebra.FinitePresentation.polynomial, Polynomial.hasseDeriv_natDegree_eq_C, Polynomial.hasFDerivWithinAt_aeval, RatFunc.mk_zero, Polynomial.as_sum_range_C_mul_X_pow, Submodule.IsPrincipal.contentIdeal_generator_dvd, Polynomial.contDiff_aeval, Polynomial.content_mul, IsAdjoinRoot.ofAlgEquiv_map_apply, Polynomial.degree_mul_X, Polynomial.isNilpotent_reflect_iff, Mathlib.Tactic.ComputeDegree.natDegree_one_le, matPolyEquiv_symm_map_eval, AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_mk, mem_reesAlgebra_iff, Polynomial.dickson_zero, Polynomial.derivative_C_mul_X_pow, Polynomial.signVariations_X_sub_C_mul_eraseLead_le, Polynomial.support_binomial, MvPolynomial.mem_support_coeff_finSuccEquiv, Polynomial.derivative_C, FunctionField.ringOfIntegers.instIsNoetherianPolynomialSubtypeMemSubalgebraOfIsSeparableRatFunc, Polynomial.roots_X_pow_char_sub_C, Polynomial.degree_mul_C_of_isUnit, Polynomial.mem_rootSet, AdjoinRoot.minpoly_powerBasis_gen, AdjoinRoot.aeval_algHom_eq_zero, Polynomial.derivative_bernoulli_add_one, Polynomial.hasseDeriv_apply, Polynomial.addSubmonoid_closure_setOf_eq_monomial, Polynomial.map_under_lt_comap_of_quasiFiniteAt, Polynomial.dickson_two_one_eq_chebyshev_U, Lagrange.sum_basis, Polynomial.eval₂_derivative_of_splits, Polynomial.natTrailingDegree_X_pow, Polynomial.Separable.squarefree, Polynomial.intCast_coeff_zero, Polynomial.C_mul_comp, IsAdjoinRoot.map_eq_zero_iff, Algebra.FiniteType.instPolynomial, Polynomial.isRoot_prod, Polynomial.mul_X_comp, Module.End.IsSemisimple.minpoly_squarefree, Polynomial.roots_expand_image_iterateFrobenius, Polynomial.support_eq_empty, Polynomial.sum_modByMonic_coeff, Polynomial.Chebyshev.iterate_derivative_U_eval_one_eq_div, RatFunc.num_mul_eq_mul_denom_iff, Polynomial.aeval_monomial, Polynomial.eval_map_algebraMap, Algebra.Norm.Transitivity.eval_zero_det_det, Polynomial.mapAlgEquiv_coe_ringHom, Polynomial.leadingCoeff_multiset_prod, AdjoinRoot.quotEquivQuotMap_symm_apply, Polynomial.bernoulli_one, Polynomial.Chebyshev.iterate_derivative_T_eval_one, Polynomial.degree_sub_lt, Lagrange.eval_interpolate_at_node, StandardEtalePresentation.toPresentation_val, Polynomial.algEquivOfCompEqX_apply, Ideal.isDomain_map_C_quotient, matPolyEquiv_eval, Polynomial.isIntegrallyClosed_iff', Polynomial.mem_rootSet_of_ne, Polynomial.mapAlg_comp, Polynomial.sylvesterMap_apply_coe, Polynomial.Chebyshev.T_zero, IsAdjoinRoot.aeval_root_self, Differential.implicitDeriv_X, Polynomial.natDegree_mul_C_le, Polynomial.natTrailingDegree_mul, Polynomial.aeval_eq_sum_range', Polynomial.degreeLT.addLinearEquiv_natAdd, Polynomial.contentIdeal_mul_eq_top_of_contentIdeal_eq_top, Polynomial.expand_char, Polynomial.Chebyshev.U_sub_two, Polynomial.aeval_zero, PowerSeries.IsWeierstrassDivisorAt.eq_zero_of_mul_eq, Polynomial.Monic.natDegree_mul, Polynomial.eval_smul, Polynomial.leadingCoeff_X_pow_sub_one, Polynomial.Chebyshev.C_eq_two_mul_T_comp_half_mul_X, MvPolynomial.pUnitAlgEquiv_monomial, conductor_mul_differentIdeal, Polynomial.support_derivativeFinsupp_subset_range, Polynomial.homogenize_sub, Polynomial.mapRingHom_id, Polynomial.ofFn_comp_toFn_eq_id_of_natDegree_lt, Polynomial.monomial_zero_left, Polynomial.mirror_eq_zero, Polynomial.natDegree_mul_C, Module.AEval.annihilator_top_eq_ker_aeval, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_mk, FiniteField.X_pow_card_pow_sub_X_natDegree_eq, gal_zero_isSolvable, Polynomial.coe_injective, Polynomial.iterate_comp_eval₂, Polynomial.rootMultiplicity_mul', WeierstrassCurve.φ_four, Polynomial.roots_expand_pow_image_iterateFrobenius_subset, Lagrange.interpolate_poly_eq_self, Polynomial.rootMultiplicity_X_sub_C_self, Polynomial.natDegree_mul_le_of_le, Polynomial.taylor_coeff, minpoly.eq_iff_aeval_minpoly_eq_zero, Polynomial.roots_neg, Polynomial.splits_X_sub_C, Polynomial.algEquivCMulXAddC_symm_apply, Polynomial.taylor_inj, Polynomial.Chebyshev.T_eq_half_mul_C_comp_two_mul_X, Polynomial.derivative_zero, Polynomial.opRingEquiv_symm_C, Polynomial.UniversalFactorizationRing.factor₁_mul_factor₂, Polynomial.evalEval_zero, Polynomial.resultant_add_mul_left, Polynomial.aroots_one, Polynomial.signVariations_neg, IsAlgClosed.roots_eq_zero_iff, Polynomial.faithfulSMul, Polynomial.exists_irreducible_of_natDegree_ne_zero, Polynomial.natDegree_cubic, KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map, Polynomial.coe_zero, Polynomial.degree_leadingCoeff_inv, Polynomial.irreducible_X, Polynomial.IsMonicOfDegree.aeval_sub, Polynomial.eval_neg, MvPolynomial.finSuccEquiv_rename_finSuccEquiv, Polynomial.roots_eq_zero_iff_eq_zero_or_isRoot_eq_bot, Polynomial.map_neg, Polynomial.ofFinsupp_zsmul, Polynomial.not_isUnit_X_pow_sub_one, Polynomial.UniversalCoprimeFactorizationRing.factor₁_mul_factor₂, ContinuousMap.polynomial_comp_attachBound, Polynomial.Sequence.degree_strictMono, Polynomial.toFinsupp_C_mul_X_pow, Polynomial.expand_eval, Polynomial.logMahlerMeasure_const, Polynomial.mul_comp, Polynomial.natDegree_C_mul_of_isUnit, Polynomial.hermite_zero, Polynomial.instIsJacobsonRing, Polynomial.Monic.not_irreducible_iff_exists_add_mul_eq_coeff, Polynomial.Monic.irreducible_iff_natDegree', isAlgebraic_iff_not_injective, AdjoinRoot.powerBasisAux'_repr_apply_to_fun, Polynomial.dickson_two, Polynomial.succ_signVariations_X_sub_C_mul_monomial, Polynomial.derivative_X_add_C_sq, Polynomial.one_lt_rootMultiplicity_iff_isRoot_iterate_derivative, Polynomial.span_le_degreeLE_of_finite, Polynomial.cyclotomic_three, Polynomial.map_eq_zero_iff, Polynomial.as_sum_support, FiniteField.expand_card, Polynomial.taylorLinearEquiv_symm, RatFunc.mk_one', Polynomial.coeff_expand_mul', Polynomial.comp_eq_sum_left, Polynomial.differentiableWithinAt_aeval, Polynomial.Monic.mul_natDegree_lt_iff, Polynomial.rootMultiplicity_X_sub_C, Polynomial.prime_X, AdjoinRoot.coe_algEquivOfEq, Polynomial.natTrailingDegree_monomial_le, Polynomial.zero_scaleRoots, Polynomial.Monic.natDegree_mul_comm, AdjoinRoot.aeval_eq, Matrix.charpoly_mul_comm', Polynomial.eval₂_multiset_sum, Polynomial.coeff_zero_eq_aeval_zero', PowerSeries.eval₂_trunc_eq_sum_range, Polynomial.Chebyshev.U_neg_two, Polynomial.eval₂_gcd_eq_zero, IsLocalization.adjoin_inv, Polynomial.degreeLT.addLinearEquiv_symm_apply_inl_basis, Polynomial.Chebyshev.S_neg_sub_one, Polynomial.not_monic_zero_iff, PowerSeries.trunc_one_X, Polynomial.leval_coe_eq_smeval, Polynomial.map_dvd_map, Polynomial.dvd_comp_X_sub_C_iff, LaurentPolynomial.leftInverse_trunc_toLaurent, Polynomial.Monic.mul_left_eq_zero_iff, Polynomial.aroots_mul, Polynomial.roots_expand_pow, MvPolynomial.universalFactorizationMap_freeMonic, RatFunc.liftOn_def, AnalyticOnNhd.aeval_polynomial, Polynomial.homogenize_zero, Polynomial.reverse_zero, Polynomial.natDegree_mul_le, Polynomial.leadingCoeff_div, Polynomial.evalEval_map_C, Polynomial.pow_mul_divByMonic_rootMultiplicity_eq, Polynomial.cardinalMk_le_max, Polynomial.Chebyshev.C_sub_two, Polynomial.contract_mul_expand, Polynomial.monic_one, Polynomial.algEquivAevalXAddC_apply, Polynomial.leadingCoeff_C, Polynomial.eval_mul_X, PolynomialModule.monomial_smul_apply, Polynomial.map_frobenius_expand, Polynomial.smeval_add, Polynomial.natDegree_coe_units, Module.AEval.instFinitePolynomial, PowerSeries.IsWeierstrassDivisorAt.mk_mod'_eq_self, Polynomial.toFinsuppIso_symm_apply, RatFunc.isScalarTower_liftAlgebra, Polynomial.logMahlerMeasure_monomial, Polynomial.cauchyBound_X_add_C, Polynomial.degree_cubic_le, PowerSeries.trunc_trunc, Polynomial.map_eq_zero, WeierstrassCurve.Ψ_four, Polynomial.mul_coeff_zero, cyclotomic_comp_X_add_one_isEisensteinAt, Polynomial.leadingCoeff_X_pow_add_one, Polynomial.natDegree_neg, Polynomial.rootSet_monomial, matPolyEquiv_symm_X, Polynomial.monomial_left_inj, Polynomial.evalEval_list_prod, Polynomial.isCoprime_map, Polynomial.aeval_pi, Cubic.equiv_symm_apply_d, Polynomial.newtonMap_apply, Derivation.apply_aeval_eq', Polynomial.toLaurent_C_mul_eq, Polynomial.natDegree_intCast, Polynomial.X_sub_C_mul_removeFactor, Polynomial.aevalTower_comp_C, Polynomial.logMahlerMeasure_C_mul_X_add_C, Polynomial.not_isUnit_X, Cubic.eq_prod_three_roots, FiniteField.isSplittingField_sub, Polynomial.coe_aeval_eq_eval, Matrix.aeval_self_charpoly, Polynomial.leadingCoeff_pow, Polynomial.exists_irreducible_of_natDegree_pos, Multiset.prod_X_add_C_eq_sum_esymm, Polynomial.degree_div_le, Polynomial.leadingCoeff_sub_of_degree_lt', Polynomial.coeff_C_zero, Polynomial.natDegree_iterate_derivative, Polynomial.Monic.nextCoeff_pow, Polynomial.exists_prod_multiset_X_sub_C_mul, Polynomial.degree_linear_le, Polynomial.smul_modByMonic, divRadical_dvd_wronskian_left, IsAdjoinRoot.algEquiv_map, Polynomial.mapAlgHom_comp, Matrix.charmatrix_apply, instFiniteTypeSubtypePolynomialMemSubalgebraReesAlgebraOfIsNoetherianRing, Polynomial.eval_add_of_sq_eq_zero, Polynomial.scaleRoots_zero, Polynomial.derivative_X_add_C_pow, Polynomial.homogenize_C, RatFunc.sub_def, Polynomial.natDegree_opRingEquiv, PowerSeries.aeval_coe, Polynomial.cyclotomic_prime, WeierstrassCurve.Affine.Point.toClass_eq_zero, Polynomial.mul_X_sub_intCast_comp, LaurentSeries.ratfuncAdicComplRingEquiv_apply, Polynomial.content_C, Polynomial.resultant_mul_right, Polynomial.smul_eval, Polynomial.Monic.dvd_iff_fraction_map_dvd_fraction_map, RatFunc.div_def, Polynomial.eval_multisetSum, Polynomial.degree_add_le_of_degree_le, Polynomial.natDegree_multiset_prod', Polynomial.natDegree_prod_of_monic, Polynomial.Chebyshev.T_sub_two, Polynomial.splits_iff_exists_multiset', Polynomial.toFinsupp_C_mul_X, Polynomial.natDegree_monomial_eq, Matrix.charmatrix_ofNat, minpoly.natSepDegree_eq_one_iff_eq_expand_X_sub_C, Polynomial.Monic.expand, Polynomial.dvd_iff_isRoot, RatFunc.add_def, Polynomial.smulCommClass, Polynomial.isUnitTrinomial_iff', Polynomial.iterate_derivative_mul, minpolyDiv_eq_zero, Polynomial.mapRingHom_comp, Polynomial.Chebyshev.T_eq_X_mul_T_sub_pol_U, Polynomial.qsmul_eq_C_mul, Polynomial.derivative_map, Polynomial.Gal.restrictProd_injective, Multiset.prod_X_add_C_coeff', Polynomial.splits_X_pow, PowerSeries.substAlgHom_coe, Polynomial.degree_linear_lt_degree_C_mul_X_sq, LinearMap.charpoly_zero, Polynomial.eq_zero_of_infinite_isRoot, Polynomial.cauchyBound_X_sub_C, Cubic.toPoly_eq_zero_iff, Polynomial.splits_of_exists_multiset, Polynomial.map_C, Polynomial.rootSet_X_pow, RatFunc.denom_add_dvd, Polynomial.iterate_derivative_intCast_mul, Polynomial.taylor_mem_degreeLT, Polynomial.C_neg, Polynomial.leadingCoeff_monomial, Lagrange.eval_nodal_derivative_eval_node_eq, MvPolynomial.rename_toMvPolynomial, Polynomial.ofFinsupp_eq_zero, Polynomial.natDegree_expand, Polynomial.rootSet_prod, Module.Basis.traceDual_powerBasis_eq, Polynomial.isNilpotent_pow_X_mul_C_of_isNilpotent, Polynomial.prod_X_sub_C_coeff_card_pred, Polynomial.evalEval_smul, Polynomial.card_support_le_one_iff_monomial, Polynomial.resultant_one_left, MvPolynomial.optionEquivLeft_symm_C_X, Polynomial.not_irreducible_C, Polynomial.mirror_smul, Polynomial.coeff_mul_monomial, Polynomial.degree_quadratic_lt_degree_C_mul_X_cb, Polynomial.Chebyshev.S_add_two, Polynomial.coeffs_zero, Polynomial.coeff_C_mul_X_pow, LaurentPolynomial.trunc_C_mul_T, Polynomial.aeval_pi_apply₂, Polynomial.Chebyshev.C_add_two, RatFunc.num_div_denom, Polynomial.add_modByMonic, Polynomial.neg_comp, Polynomial.derivative_natCast, WeierstrassCurve.φ_two, Cubic.equiv_symm_apply_a, Polynomial.eval₂_mul_eq_zero_of_left, Polynomial.degree_C_mul_X, PowerSeries.IsWeierstrassFactorizationAt.mul, MvPolynomial.finSuccEquiv_X_zero, Polynomial.comp_X_add_C_eq_zero_iff, MvPolynomial.degreeOf_eq_natDegree, Polynomial.resultant_X_sub_C_left, Polynomial.natTrailingDegree_zero, Polynomial.hasseDeriv_X, Polynomial.lifts_iff_set_range, IsGalois.tfae, PowerSeries.weierstrassMod_zero_right, Polynomial.monic_zero_iff_subsingleton', Polynomial.aeval_mem_adjoin_singleton, spectralValue_eq_zero_iff, Polynomial.rootMultiplicity_zero, Polynomial.toLaurent_X, Polynomial.derivative_bernoulli, Polynomial.scaleRoots_C, Polynomial.eval₂AlgHom'_apply, Polynomial.integralNormalization_zero, Polynomial.natDegree_multiset_prod_le, LieAlgebra.engel_isBot_of_isMin.lieCharpoly_natDegree, Polynomial.toAddCircle_X_eq_fourier_one, bernsteinPolynomial.sum, AdjoinRoot.mk_self, Polynomial.natSepDegree_mul, LaurentPolynomial.isLocalization, WeierstrassCurve.ΨSq_three, Polynomial.ofFn_coeff_eq_val_of_lt, Polynomial.map_monic_eq_zero_iff, Polynomial.coeff_mul_X_pow', Polynomial.evalEval_surjective, Polynomial.coeff_mul_mirror, Polynomial.degree_pow', PolynomialModule.monomial_smul_lsingle, Polynomial.tendsto_abv_aeval_atTop, Polynomial.map_multiset_prod, Polynomial.natDegree_mod_lt, Lagrange.nodal_subgroup_eq_X_pow_card_sub_one, Polynomial.degree_mul_C, LinearMap.not_hasEigenvalue_zero_tfae, MvPolynomial.transcendental_supported_polynomial_aeval_X_iff, Polynomial.div_C_mul, Polynomial.resultant_C_mul_left, Polynomial.Chebyshev.T_add_two, Polynomial.resultant_pow_left, PowerSeries.weierstrassMod_zero, StandardEtalePresentation.toPresentation_relation, Polynomial.cyclotomic_expand_eq_cyclotomic, Polynomial.map_mapRingHom_eval_map, Polynomial.ringKrullDim_of_isNoetherianRing, Polynomial.toMvPolynomial_injective, WeierstrassCurve.preΨ_two, Polynomial.roots_X_pow, Polynomial.opRingEquiv_op_C_mul_X_pow, Polynomial.degreeLT.basisProd_natAdd, Ideal.polynomialQuotientEquivQuotientPolynomial_map_mk, Polynomial.eval₂_smul, PowerSeries.WithPiTopology.tendsto_trunc_atTop, Polynomial.roots_X_add_C, Polynomial.Sequence.linearIndependent, WeierstrassCurve.Affine.baseChange_polynomialY, Polynomial.eq_one_of_monic_natDegree_zero, Polynomial.map_surjective_iff, Polynomial.monomial_natDegree_leadingCoeff_eq_self, Polynomial.contentIdeal_mul_le_mul_contentIdeal, Polynomial.degree_mod_lt, Polynomial.degreeLE_mono, Polynomial.aeval_algHom_apply, Polynomial.coe_toLaurentAlg, WeierstrassCurve.ΨSq_four, PowerSeries.IsWeierstrassDivisionAt.smul, Polynomial.leadingCoeff_prod', Polynomial.natCast_mul_comp, Polynomial.hilbertPoly_mul_one_sub_pow_add, Ideal.quotient_mk_maps_eq, Polynomial.divX_one, RatFunc.toFractionRingRingEquiv_symm_eq, Polynomial.degree_multiset_prod, bernsteinPolynomial.linearIndependent, Polynomial.shiftedLegendre_eval_symm, bernsteinPolynomial.derivative_zero, Polynomial.iterate_derivative_map, Polynomial.sumIDeriv_apply_of_le, Polynomial.splits_of_splits_mul', RatFunc.aeval_X_left_eq_algebraMap, Polynomial.Splits.comp_neg_X, Polynomial.IsMonicOfDegree.add_right, Polynomial.Bivariate.pderiv_one_equivMvPolynomial, Polynomial.support_monomial', WeierstrassCurve.map_ψ, Polynomial.le_rootMultiplicity_mul, Polynomial.mem_degreeLE, Polynomial.isScalarTower_right, Polynomial.X_pow_sub_one_mul_cyclotomic_dvd_X_pow_sub_one_of_dvd, Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_C, Polynomial.reflect_eq_zero_iff, Polynomial.splits_iff_splits, Polynomial.Monic.irreducible_iff_irreducible_map_fraction_map, Matrix.IsHermitian.charpoly_eq, RatFunc.associated_num_inv, bernsteinPolynomial.iterate_derivative_at_0_eq_zero_of_lt, Polynomial.taylor_X, Polynomial.multiset_prod_X_sub_C_coeff_card_pred, Polynomial.map_natCast, Polynomial.separable_X_sub_C, Polynomial.mapAlgHom_coe_ringHom, bernsteinPolynomial.iterate_derivative_at_0, Polynomial.finiteMultiplicity_X_sub_C, Polynomial.eraseLead_add_of_natDegree_lt_left, Polynomial.natDegree_add_le_of_le, Polynomial.Chebyshev.derivative_U_eval_one_eq_div, WeierstrassCurve.Affine.CoordinateRing.XYIdeal'_eq, Polynomial.hasFDerivWithinAt, Algebra.IsInvariant.charpoly_mem_lifts, MvPolynomial.optionEquivLeft_elim_eval, Algebra.FormallySmooth.polynomial, MvPolynomial.optionEquivLeft_symm_X, Polynomial.leadingCoeff_X_add_C, Polynomial.degree_sum_fin_lt, PowerSeries.algebraMap_apply', RatFunc.toFractionRingRingEquiv_apply, minpoly.irreducible, Polynomial.IsEisensteinAt.irreducible, Polynomial.expand_aeval, Polynomial.ringHom_ext'_iff, Polynomial.Monic.mul, Polynomial.irreducible_X_sub_C, Polynomial.not_dvd_of_natDegree_lt, Polynomial.Monic.as_sum, Polynomial.ofFinsupp_sum, Polynomial.degreeLE_eq_span_X_pow, Polynomial.zero_modByMonic, matPolyEquiv_coeff_apply_aux_2, Polynomial.aeval_natCast, Polynomial.aevalTower_comp_toAlgHom, Polynomial.iterate_derivative_one, Polynomial.preimage_eval_singleton, Polynomial.mem_nonzeroDivisors_of_coeff_mem, Polynomial.IsMonicOfDegree.sub, Polynomial.trailingDegree_mul', LaurentSeries.mem_integers_of_powerSeries, Polynomial.IsPrimitive.isUnit_iff_isUnit_map, Polynomial.natDegree_derivative_lt, Polynomial.mapEquiv_apply, MvPolynomial.aeval_comp_toMvPolynomial, Cubic.C_mul_prod_X_sub_C_eq, IsPrimitiveRoot.minpoly_dvd_cyclotomic, Polynomial.aeval_algHom, Polynomial.coe_aevalAeval_eq_evalEval, Polynomial.map_mapRingHom_eval_map_eval, Polynomial.toLaurent_C, Polynomial.ofMultiset_injective, Polynomial.toFinsupp_intCast, Polynomial.IsSplittingField.IsScalarTower.splits, PowerBasis.aeval_minpolyGen, Polynomial.X_pow_comp, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_eq_poly_in_U, Polynomial.exists_primitive_lcm_of_isPrimitive, Polynomial.coe_aeval_eq_evalRingHom, RatFunc.algebraMap_monomial, instFiniteDimensionalQuotientPolynomialIdealSpanSingletonSetSmithCoeffs, polynomial_smul_apply, Polynomial.hilbertPoly_zero_right, RatFunc.denom_dvd, Polynomial.bernoulli_comp_one_sub_X, Polynomial.finite_mahlerMeasure_le, Polynomial.natDegree_lt_coeff_mul, Polynomial.toLaurentAlg_apply, Polynomial.taylor_pow, Polynomial.evalEval_natCast, Polynomial.eval_sub, Polynomial.isUnit_leadingCoeff_mul_right_eq_zero_iff, Polynomial.irreducible_C_mul_X_add_C, Polynomial.smul_X_eq_monomial, Polynomial.commute_X_pow, Polynomial.natDegree_multiset_prod_of_monic, Polynomial.Sequence.basis_degree_strictMono, Polynomial.Chebyshev.C_two, Polynomial.resultant_X_pow_left, Polynomial.succ_signVariations_le_X_sub_C_mul, Polynomial.one_lt_rootMultiplicity_iff_isRoot, Polynomial.not_weaklyQuasiFiniteAt, Polynomial.monomial_sub, Polynomial.coeff_monomial_succ, Polynomial.Splits.C, MvPolynomial.eval₂_pUnitAlgEquiv, WeierstrassCurve.Affine.CoordinateRing.map_smul, PowerSeries.trunc_sub, Polynomial.degree_sub_le_of_le, Polynomial.annIdealGenerator_eq_zero_iff, Polynomial.le_trailingDegree_X_pow, Polynomial.reverse_C_add, Polynomial.normUnit_X, Polynomial.degree_add_eq_of_leadingCoeff_add_ne_zero, Polynomial.natDegree_linear, matPolyEquiv_smul_one, autAdjoinRootXPowSubC_root, Polynomial.Splits.neg, Polynomial.degree_monomial, spectrum.map_polynomial_aeval, Polynomial.toLaurent_C_mul_X_pow, Polynomial.trailingCoeff_eq_zero, Polynomial.isUnit_leadingCoeff_mul_left_eq_zero_iff, Polynomial.coeff_intCast_mul, Polynomial.natDegree_X_mul, Polynomial.Splits.mul, Ideal.isPrime_map_C_iff_isPrime, Polynomial.pow_scaleRoots', PowerSeries.trunc_derivativeFun, Matrix.charpoly_diagonal, Polynomial.degree_mul_X_pow, Polynomial.degree_add_C, Polynomial.sylveserMap_comp_adjSylvester, Polynomial.toAddCircle_C_eq_smul_fourier_zero, Polynomial.le_natTrailingDegree_mul, Polynomial.evalEval_C, AdjoinRoot.algEquivOfEq_symm, Polynomial.natDegree_sub_le, Polynomial.algHom_ext'_iff, Polynomial.isLocalHom_expand, Polynomial.coe_eval₂RingHom, Polynomial.natDegree_pow_X_add_C, LaurentPolynomial.toLaurent_reverse, Polynomial.leadingCoeff_eq_zero, PowerSeries.trunc_map, Polynomial.natDegree_eq_zero, Polynomial.ker_modByMonicHom, Polynomial.monic_zero_iff_subsingleton, Polynomial.monic_normalize, Polynomial.map_dvd_map', Polynomial.Monic.irreducible_of_degree_eq_one, Mathlib.Tactic.ComputeDegree.coeff_pow_of_natDegree_le_of_eq_ite', Polynomial.map_evalRingHom_eval, Polynomial.isNilpotent_reverse_iff, WeierstrassCurve.preΨ_one, PowerSeries.coeff_coe_trunc_of_lt, Polynomial.coeff_prod_of_natDegree_le, Polynomial.IsUnitTrinomial.irreducible_aux1, Polynomial.coeff_X_mul, Polynomial.roots_C_mul_X_add_C_of_IsUnit, MvPolynomial.aeval_natDegree_le, Polynomial.isMonicOfDegree_monomial_one, Polynomial.smeval_neg, Polynomial.wronskian_neg_left, PowerSeries.trunc_zero', Polynomial.mirror_C, Polynomial.mul_modByMonic, Polynomial.trailingDegree_neg, Polynomial.bernoulli_comp_neg_X, MvPolynomial.optionEquivLeft_symm_C_C, Derivation.compAEval_apply, Cubic.of_c_eq_zero, Matrix.charmatrix_transpose, RatFunc.mul_def, matPolyEquiv_eq_X_pow_sub_C, Polynomial.cyclotomic_eq_X_pow_sub_one_div, Polynomial.hasseDeriv_eq_zero_of_lt_natDegree, spectralValue_X_pow, Polynomial.coeff_divByMonic_X_sub_C, Polynomial.ofFn_coeff_eq_zero_of_ge, Polynomial.resultant_eq_zero_iff, Polynomial.degreeLT.basisProd_castAdd, Matrix.derivative_det_one_add_X_smul_aux, Polynomial.degree_C_mul_X_pow, Polynomial.trailingDegree_monomial, Polynomial.C_pow, Polynomial.C_add, Polynomial.coe_taylorEquiv, Polynomial.hasDerivWithinAt, Polynomial.zero_notMem_multiset_map_X_add_C, Matrix.charpoly_ofNat, Matrix.aeval_eq_aeval_mod_charpoly, Polynomial.mod_def, IsAdjoinRootMonic.liftPolyₗ_apply, Polynomial.aeval_algebraMap_apply, Polynomial.Monic.degree_mul_comm, Polynomial.primPart_mul, PowerSeries.trunc_derivative, AdjoinRoot.algEquivOfEq_toAlgHom, Polynomial.leadingCoeff_divByMonic_X_sub_C, bernsteinPolynomial.derivative_succ_aux, Polynomial.pairwise_coprime_X_sub_C, WeierstrassCurve.φ_zero, Polynomial.mul_contentIdeal_le_radical_contentIdeal_mul, transcendental_iff, Polynomial.derivative_X_sub_C, MvPolynomial.IsHomogeneous.finSuccEquiv_coeff_isHomogeneous, Polynomial.Chebyshev.T_eq_U_sub_X_mul_U, Polynomial.comp_neg_X_comp_neg_X, Polynomial.fourierCoeff_toAddCircle, Polynomial.IsDistinguishedAt.algEquivQuotient_apply, Polynomial.natSepDegree_X_pow, Polynomial.coeff_multiset_prod_of_natDegree_le, Module.AEval.mem_mapSubmodule_apply, Polynomial.aroots_C, Polynomial.coeff_one_zero, Polynomial.trailingDegree_eq_top, Polynomial.isMonicOfDegree_X_pow, minpoly.ker_eval, minpoly.eq_X_sub_C, Polynomial.cyclotomic_prime_mul_X_sub_one, ascPochhammer_succ_left, Polynomial.roots_C, Polynomial.eval_gcd_eq_zero, Polynomial.Chebyshev.C_neg_two, Polynomial.mapAlgHom_id, Matrix.charmatrix_diagonal, Lagrange.nodal_erase_eq_nodal_div, Polynomial.monic_prod_X_sub_C, Polynomial.wronskian_zero_right, LaurentPolynomial.instIsScalarTowerPolynomial, Polynomial.natDegree_cubic_le, Polynomial.Monic.nextCoeff_prod, Polynomial.coeff_mul_degree_add_degree, Polynomial.mul_coeff_one, ConjRootClass.irreducible_minpoly, Polynomial.eraseLead_add_of_natDegree_lt_right, Polynomial.card_roots_toFinset_le_derivative, Polynomial.map_aeval_eq_aeval_map, Polynomial.adjoin_X, IsAlgClosed.associated_iff_roots_eq_roots, Polynomial.UniversalCoprimeFactorizationRing.isCoprime_factor₁_factor₂, Polynomial.iterate_derivative_sum, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eval, Polynomial.toFinsupp_zero, WeierstrassCurve.ψ_four, AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_mk_of, Module.AEval.annihilator_eq_ker_aeval, Polynomial.Bivariate.equivMvPolynomial_C_C, WeierstrassCurve.Ψ_odd, RatFunc.toFractionRingAlgEquiv_apply, Polynomial.natDegree_quadratic, Polynomial.isCoprime_iff_aeval_ne_zero, Polynomial.ofFinsupp_nsmul, RatFunc.laurentAux_ofFractionRing_mk, Polynomial.natDegree_C_mul_X_pow_le, WeierstrassCurve.Φ_zero, Polynomial.aeval_add, Polynomial.instIsLocalHomRingHomAlgebraMap, Polynomial.continuousOn_aeval, Polynomial.aeval_sub, Polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero, Polynomial.coe_pow, Polynomial.mul_scaleRoots', IsTranscendenceBasis.polynomial, Polynomial.eval_smul', Polynomial.support_zero, Polynomial.leadingCoeff_neg, Polynomial.trailingDegree_one_le, IsAdjoinRoot.map_surjective, Polynomial.homogenize_one, Algebra.IsAlgebraic.rank_fractionRing_polynomial, Polynomial.sumIDeriv_apply_of_lt, Polynomial.mem_lift_of_splits_of_roots_mem_range, Polynomial.erase_monomial, Polynomial.continuousAt_aeval, IsSepClosed.exists_aeval_eq_zero, Polynomial.card_roots_sub_C, Polynomial.homogenizeLM_apply, Polynomial.degree_derivative_le, Module.End.eigenspace_aeval_polynomial_degree_1, inv_eq_of_aeval_divX_ne_zero, Polynomial.Chebyshev.iterate_derivative_T_eval_one_eq_div, Polynomial.lifts_iff_coeffs_subset_range, Polynomial.isRoot_of_isRoot_iff_dvd_derivative_mul, Polynomial.exists_monic_aeval_eq_zero_forall_mem_of_mem_map, Polynomial.resultant_C_mul_right, Polynomial.smeval_zero, Polynomial.derivative_one, Polynomial.taylorLinearEquiv_apply_coe, PowerSeries.natDegree_trunc_lt, Polynomial.homogenize_mul, Polynomial.irreducible_of_degree_eq_one, Polynomial.coe_evalEvalRingHom, Polynomial.degree_linear, Polynomial.Chebyshev.derivative_T_eval_one, WeierstrassCurve.Affine.CoordinateRing.basis_apply, Polynomial.taylor_C, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, Polynomial.supNorm_eq_zero_iff, Polynomial.eval₂_list_prod_noncomm, Polynomial.wfDvdMonoid, Polynomial.mem_degreeLT, Polynomial.derivative_apply, PowerSeries.trunc_X, Polynomial.mem_map_rangeS, Polynomial.C_injective, Polynomial.Splits.prod, Polynomial.aeval_X, WeierstrassCurve.Affine.Point.toClass_apply, Polynomial.Monic.degree_le_zero_iff_eq_one, Polynomial.normalizedFactors_cyclotomic_card, Polynomial.smul_comp, Polynomial.natTrailingDegree_intCast, Polynomial.degreeLT.basis_repr, LaurentPolynomial.exists_T_pow, polyEquivTensor_symm_apply_tmul_eq_smul, Polynomial.nextCoeff_C_mul, PowerSeries.isWeierstrassDivisionAt_zero, AdjoinRoot.mkₐ_toRingHom, Polynomial.self_sub_C_mul_X_pow, Polynomial.monomial_comp, Polynomial.comap_C_surjective, descPochhammer_zero, Polynomial.natDegree_add_C, IsAdjoinRoot.algEquiv_apply_map, Polynomial.coe_evalRingHom, Polynomial.eval_C_mul, Polynomial.divByMonic_one, Polynomial.natTrailingDegree_mul', Polynomial.roots_expand_map_frobenius_le, Polynomial.isCoprime_X_sub_C_of_isUnit_sub, Matrix.BlockTriangular.charpoly, irreducible_X_pow_sub_C_of_root_adjoin_eq_top, Polynomial.eval₂_eval₂RingHom_apply, Polynomial.ofFn_natDegree_lt, Polynomial.isNoetherianRing, Polynomial.aeval_homogenize_of_eq_one, Polynomial.IsPrimitive.dvd_iff_fraction_map_dvd_fraction_map, Polynomial.toContinuousMapOnAlgHom_apply, Polynomial.degree_eq_bot, Polynomial.evalEval_one, Polynomial.neg_one_pow_mul_shiftedLegendre_comp_one_sub_X_eq, RatFunc.denom_zero, IsAdjoinRoot.ker_map, Polynomial.subsingleton_iff_subsingleton, Polynomial.monomial_mul_monomial, Polynomial.coe_mapAlgHom, Polynomial.content_X_pow, RatFunc.associated_denom_inv, Polynomial.signVariations_C_mul, MvPolynomial.totalDegree_coeff_optionEquivLeft_le, Polynomial.Monic.irreducible_iff_roots_eq_zero_of_degree_le_three, DenomsClearable.add, Polynomial.opRingEquiv_symm_X, Polynomial.trailingDegree_X_pow, Polynomial.mkDerivation_apply, Polynomial.not_finite, Polynomial.coeff_monomial_mul, IsAlgClosed.dvd_iff_roots_le_roots, Polynomial.card_mahlerMeasure_le_prod, Polynomial.homogenize_neg, Polynomial.degree_list_sum_le, Module.instFinitePolynomialAEval', Polynomial.reflect_mul_induction, Polynomial.Chebyshev.S_sub_two, Lagrange.interpolate_singleton, Polynomial.isCoprime_iff_aeval_ne_zero_of_isAlgClosed, Polynomial.C_content_dvd, WeierstrassCurve.preΨ'_two, Polynomial.Chebyshev.S_neg_one, galois_poly_separable, Polynomial.ofFinsupp_intCast, Ideal.Filtration.submodule_fg_iff_stable, Polynomial.coeff_X_add_C_pow, WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_Y, Polynomial.resultant_zero_zero, Polynomial.degree_linear_lt, WeierstrassCurve.preΨ_even, Polynomial.coeff_list_prod_of_natDegree_le, ascPochhammer_succ_right, PowerSeries.trunc_C_mul, Polynomial.X_eq_normalize, Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_U, Polynomial.coeffList_monomial, Polynomial.algEquivAevalXAddC_symm, Polynomial.evalEval_mul, Polynomial.degree_natCast_le, Polynomial.degree_coe_units, Polynomial.eval₂_mul_noncomm, IsAlgClosed.exists_aeval_eq_zero, Polynomial.expand_injective, Polynomial.natDegree_list_prod_le, Polynomial.natDegree_pow', Polynomial.coeff_det_X_add_C_zero, Polynomial.derivative_C_mul_X_sq, Polynomial.content_monomial, Lagrange.nodal_eq, Polynomial.derivativeFinsupp_C, Polynomial.card_support_trinomial, Polynomial.trailingCoeff_mul, LieAlgebra.engel_isBot_of_isMin.lieCharpoly_monic, Polynomial.taylor_one, X_pow_sub_C_irreducible_iff_of_prime, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_mul_XYIdeal, Polynomial.cyclotomic'_zero, AdjoinRoot.mk_C, Polynomial.map_iterateFrobenius_expand, Polynomial.derivativeFinsupp_X, Polynomial.map_normalize, Polynomial.roots_X_pow_char_pow_sub_C, Polynomial.Splits.listProd, RatFunc.algebraMap_comp_C, Polynomial.leadingCoeff_add_of_degree_lt', RatFunc.ofFractionRing_algebraMap, RatFunc.eval_algebraMap, Polynomial.sub_comp, Polynomial.exists_irreducible_of_degree_pos, Polynomial.eval₂_algebraMap_X, LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul, Polynomial.toMvPolynomial_C, Polynomial.exists_mul_add_mul_eq_C_resultant, Matrix.charpoly_of_card_eq_two, Polynomial.eval_multiset_prod_X_sub_C_derivative, Polynomial.toFinsupp_C, Polynomial.Chebyshev.U_neg_sub_two, FixedPoints.minpoly.of_eval₂, Polynomial.erase_def, Polynomial.roots_def, Polynomial.smeval_mul_X_pow, Polynomial.X_sub_C_pow_dvd_iff, Polynomial.trailingDegree_mul, FunctionField.ringOfIntegers.not_isField, Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative_of_mem_nonZeroDivisors', Polynomial.aroots_pow, Matrix.charmatrix_zero, Polynomial.Splits.one, Polynomial.natDegree_multiset_sum_le, isCyclic_tfae, Polynomial.erase_zero, Polynomial.roots_prod_X_sub_C, Polynomial.add_scaleRoots_of_natDegree_eq, bernsteinPolynomial.iterate_derivative_at_1, cfc_comp_polynomial, Lagrange.nodalWeight_eq_eval_derivative_nodal, Polynomial.derivative_intCast, Polynomial.C_smul_derivation_apply, Polynomial.leadingCoeff_taylor, Polynomial.homogenize_monomial, Polynomial.X_pow_mul_C, AdjoinRoot.evalEval_mk, Polynomial.derivative_add, Polynomial.expand_pow, Polynomial.degree_sub_C, Polynomial.map_taylorEquiv_degreeLT, Polynomial.monic_finprod_of_monic, PowerBasis.liftEquiv_apply_coe, Multiset.prod_X_sub_C_coeff, IsPrimitiveRoot.minpoly_dvd_x_pow_sub_one, RatFunc.num_denom_neg, Polynomial.degree_X_add_C, Polynomial.eval_geom_sum, Polynomial.eval₂_add, degree_radical_le, Polynomial.monomial_add_erase, Polynomial.degree_mul, Polynomial.isMonicOfDegree_sub_add_two, Polynomial.algebraMap_eq, Polynomial.degree_gcd_le_right, Polynomial.valuation_X_eq_neg_one, Polynomial.coe_mapAlgEquiv, Polynomial.cyclotomic'_eq_X_pow_sub_one_div, Polynomial.X_pow_mul, Polynomial.degree_sub_eq_right_of_degree_lt, Polynomial.rootSet_neg, Polynomial.degree_C_le, Polynomial.eval_monomial, Polynomial.Monic.neg_one_pow_natDegree_mul_comp_neg_X, IsAdjoinRootMonic.modByMonic_repr_map, Polynomial.trdeg_of_isDomain, Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, MvPolynomial.coe_mapEquivMonic_comp, GaloisField.splits_zmod_X_pow_sub_X, Polynomial.Monic.natDegree_mul', RatFunc.ofFractionRing_mul, Polynomial.natDegree_add_le, Polynomial.aeval_sumIDeriv_of_pos, MvPolynomial.eval_polynomial_eval_finSuccEquiv, Polynomial.monic_X_pow_sub, Polynomial.continuousWithinAt_aeval, Mathlib.Tactic.ComputeDegree.coeff_smul, Polynomial.Monic.eq_X_sub_C_pow_of_natSepDegree_eq_one_of_splits, Derivation.apply_aeval_eq, Polynomial.toSubring_one, PowerSeries.trunc_derivative', KummerDedekind.quotMapEquivQuotQuotMap_symm_apply, RatFunc.toFractionRing_eq, Polynomial.modByMonic_eq_mod, Matrix.isNilpotent_charpoly_sub_pow_of_isNilpotent

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