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Datasets:
Kevin-Skinner
/
mapofmath-data

Tasks:
Graph Machine Learning
Languages:
English
Size:
100K<n<1M
Tags:
mathematics
lean4
mathlib
dependency-graph
formal-verification
network-analysis
License:
Dataset card Data Studio Files
xet
 Community
mapofmath-data
File size: 286,370 Bytes
ad295e1
1
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{"count":3269,"namespace":"Polynomial","names":["Polynomial.ofFinsupp","Polynomial.coeff","Polynomial.support","Polynomial.degree","Polynomial.natDegree","Polynomial.leadingCoeff","Polynomial.Monic","Polynomial.sum","Polynomial.eval\u2082","Polynomial.instAdd","Polynomial.toFinsupp","Polynomial.toFinsupp_injective","Polynomial.toFinsupp_add","Polynomial.instZero","Polynomial.toFinsupp_zero","Polynomial.instNSMul","Polynomial.toFinsupp_nsmul","Polynomial.instMul","Polynomial.toFinsupp_mul","Polynomial.instOne","Polynomial.instNatCast","Polynomial.toFinsupp_one","Polynomial.pow","Polynomial.ofFinsupp_mul","Polynomial.ofFinsupp_pow","Polynomial.toFinsupp_pow","Polynomial.semiring","Polynomial.smulZeroClass","Polynomial.toFinsupp_smul","Polynomial.distribMulAction","Polynomial.module","Polynomial.ofFinsupp_add","Polynomial.monomial","Polynomial.toFinsupp_monomial","Polynomial.monomial_mul_monomial","Polynomial.monomial_zero_right","Polynomial.C","Polynomial.X","Polynomial.map","Polynomial.eval\u2082_def","Polynomial.coeff_add","Polynomial.coeff_smul","Polynomial.lcoeff","Polynomial.finset_sum_coeff","Polynomial.coeff_sum","Polynomial.ofFinsupp_single","Polynomial.coeff_C_mul","Polynomial.C_mul_X_pow_eq_monomial","Polynomial.coeff_monomial","Polynomial.coeff_C_mul_X_pow","Polynomial.coeff_X_pow","Polynomial.support_ofFinsupp","Polynomial.coeff_ofFinsupp","Polynomial.mem_support_iff","Polynomial.coeff_map","Polynomial.natDegree_eq_of_degree_eq","Polynomial.degree_le_iff_coeff_zero","Polynomial.degree_lt_iff_coeff_zero","Polynomial.degree_map_le","Polynomial.ofFinsupp_zero","Polynomial.ofFinsupp_inj","Polynomial.ofFinsupp_eq_zero","Polynomial.support_eq_empty","Polynomial.degree_eq_bot","Polynomial.degree_eq_natDegree","Polynomial.leadingCoeff_zero","Polynomial.leadingCoeff_eq_zero","Polynomial.leadingCoeff_ne_zero","Polynomial.le_degree_of_ne_zero","Polynomial.degree_map_eq_of_leadingCoeff_ne_zero","Polynomial.natDegree_map_of_leadingCoeff_ne_zero","Polynomial.leadingCoeff_map_of_leadingCoeff_ne_zero","Polynomial.leadingCoeff_map_eq_of_isUnit_leadingCoeff","Polynomial.eval","Polynomial.C_0","Polynomial.toFinsuppIso","Polynomial.ofFinsupp_sum","Polynomial.sum_monomial_eq","Polynomial.sum_C_mul_X_pow_eq","Polynomial.induction_on","Polynomial.induction_on'","Polynomial.eval\u2082_eq_sum","Polynomial.sum_add_index","Polynomial.eval\u2082_add","Polynomial.map_add","Polynomial.eval_add","Polynomial.sum_monomial_index","Polynomial.eval\u2082_monomial","Polynomial.map_monomial","Polynomial.eval_monomial","Polynomial.eval\u2082_eq_eval_map","Polynomial.ext_iff","Polynomial.ext","Polynomial.map_map","Polynomial.eval\u2082_map","Polynomial.eval_eq_sum","Polynomial.eval\u2082_at_apply","Polynomial.eval_map","Polynomial.hom_eval\u2082","Polynomial.toFinsupp_C","Polynomial.algebraOfAlgebra","Polynomial.commSemiring","Polynomial.C_1","Polynomial.sum_C_index","Polynomial.eval\u2082_C","Polynomial.eval\u2082_one","Polynomial.eval\u2082_ofFinsupp","Polynomial.eval\u2082_mul_noncomm","Polynomial.sum_zero_index","Polynomial.eval\u2082_zero","Polynomial.eval\u2082RingHom'","Polynomial.eval\u2082AlgHom'","Polynomial.aevalTower","Polynomial.CAlgHom","Polynomial.ringHom_ext","Polynomial.ringHom_ext'","Polynomial.algHom_ext'","Polynomial.aevalTower_C","Polynomial.sum_X_index","Polynomial.eval\u2082_X","Polynomial.aevalTower_X","Polynomial.degreeLE","Polynomial.C_mul'","Polynomial.instNeg","Polynomial.instSub","Polynomial.instZSMul","Polynomial.instIntCast","Polynomial.toFinsupp_neg","Polynomial.toFinsupp_sub","Polynomial.toFinsupp_zsmul","Polynomial.ring","Polynomial.instDecidableEq","Polynomial.mem_degreeLE","Polynomial.degree_zero","Polynomial.support_monomial","Polynomial.degree_monomial","Polynomial.degree_monomial_le","Polynomial.degree_C_mul_X_pow_le","Polynomial.degree_X_pow_le","Polynomial.degreeLE_eq_span_X_pow","Polynomial.coeff_eq_zero_of_degree_lt","Polynomial.natDegree_le_iff_degree_le","Polynomial.natDegree_le_of_degree_le","Polynomial.support_toFinsupp","Polynomial.degree_mul_le","Polynomial.degree_le_natDegree","Polynomial.coeff_mul","Polynomial.coeff_mul_X_pow","Polynomial.natDegree_eq_of_degree_eq_some","Polynomial.coeff_mul_degree_add_degree","Polynomial.degree_mul'","Polynomial.natDegree_mul'","Polynomial.leadingCoeff_mul'","Polynomial.leadingCoeff_mul_monic","Polynomial.degree_C_mul_X_pow","Polynomial.natDegree_C_mul_X_pow","Polynomial.natDegree_monomial","Polynomial.leadingCoeff_monomial","Polynomial.leadingCoeff_C_mul_X_pow","Polynomial.leadingCoeff_X_pow","Polynomial.monic_X_pow","Polynomial.leadingCoeff_mul_X_pow","Polynomial.monomial_one_one_eq_X","Polynomial.monomial_one_right_eq_X_pow","Polynomial.X_pow_eq_monomial","Polynomial.degree_X_pow","Polynomial.erase","Polynomial.erase_def","Polynomial.toFinsupp_erase","Polynomial.monomial_add_erase","Polynomial.degree_add_le","Polynomial.ofFinsupp_neg","Polynomial.support_neg","Polynomial.degree_neg","Polynomial.degree_erase_le","Polynomial.support_erase","Polynomial.degree_erase_lt","Polynomial.degree_sub_lt","Polynomial.commRing","Polynomial.isNoetherianRing","Polynomial.degree_lt_wf","Polynomial.instWellFoundedRelation","Polynomial.inhabited","Polynomial.unique","Polynomial.leadingCoeff_monic_mul","Polynomial.leadingCoeff_C","Polynomial.div_wf_lemma","Polynomial.divModByMonicAux","Polynomial.modByMonic","Polynomial.divByMonic","Polynomial.modByMonic_eq_sub_mul_div","Polynomial.modByMonic_add_div","Polynomial.degree_modByMonic_lt","Polynomial.modByMonic_eq_zero_iff_dvd","Polynomial.decidableDvdMonic","Polynomial.monic_one","Polynomial.C_neg","Polynomial.monic_of_subsingleton","Polynomial.le_natDegree_of_ne_zero","Polynomial.natDegree_eq_of_le_of_coeff_ne_zero","Polynomial.monic_of_natDegree_le_of_coeff_eq_one","Polynomial.monic_of_degree_le","Polynomial.monic_X_pow_add","Polynomial.monomial_zero_left","Polynomial.degree_C","Polynomial.degree_C_le","Polynomial.monic_X_pow_add_C","Polynomial.monic_X_add_C","Polynomial.monic_X_sub_C","Polynomial.leadingCoeff_pow'","Polynomial.natDegree_C","Polynomial.natDegree_one","Polynomial.degree_pow'","Polynomial.natDegree_pow'","Polynomial.finiteMultiplicity_of_degree_pos_of_monic","Polynomial.degree_X","Polynomial.degree_le_degree","Polynomial.coeff_natDegree_eq_zero_of_degree_lt","Polynomial.ne_zero_of_degree_gt","Polynomial.degree_add_eq_left_of_degree_lt","Polynomial.degree_X_add_C","Polynomial.degree_X_sub_C","Polynomial.finiteMultiplicity_X_sub_C","Polynomial.rootMultiplicity","Polynomial.IsRoot","Polynomial.coeff_C_zero","Polynomial.coeff_C","Polynomial.eq_C_of_degree_le_zero","Polynomial.eval_C","Polynomial.degree_pos_of_root","Polynomial.eval\u2082_mul","Polynomial.eval_mul","Polynomial.eval\u2082_neg","Polynomial.eval\u2082_sub","Polynomial.eval_sub","Polynomial.eval_X","Polynomial.modByMonic_X_sub_C_eq_C_eval","Polynomial.mul_divByMonic_eq_iff_isRoot","Polynomial.modByMonic_eq_self_iff","Polynomial.divByMonic_eq_zero_iff","Polynomial.degree_of_subsingleton","Polynomial.degree_add_eq_right_of_degree_lt","Polynomial.degree_add_divByMonic","Polynomial.degree_divByMonic_lt","Polynomial.rootMultiplicity_eq_multiplicity","Polynomial.instIsLeftCancelMulZeroOfIsCancelAdd","Polynomial.instIsRightCancelMulZeroOfIsCancelAdd","Polynomial.instIsCancelMulZeroOfIsCancelAdd","Polynomial.degree_X_pow_add_C","Polynomial.X_pow_add_C_ne_zero","Polynomial.X_pow_sub_C_ne_zero","Polynomial.X_sub_C_ne_zero","Polynomial.natDegree_mul_le","Polynomial.degree_sub_le","Polynomial.degree_X_le","Polynomial.degree_X_sub_C_le","Polynomial.natDegree_X_sub_C_le","Polynomial.le_natDegree_of_mem_supp","Polynomial.supp_subset_range","Polynomial.sum_over_range'","Polynomial.ofFinsupp_sub","Polynomial.coeff_sub","Polynomial.coeff_mul_X","Polynomial.coeff_mul_C","Polynomial.coeff_mul_X_sub_C","Polynomial.coeff_eq_zero_of_natDegree_lt","Polynomial.coeff_natDegree_succ_eq_zero","Polynomial.mul_coeff_zero","Polynomial.coeff_X_zero","Polynomial.eval_mul_X_sub_C","Polynomial.eval_one","Polynomial.not_isUnit_X_sub_C","Polynomial.monomial_injective","Polynomial.C_injective","Polynomial.C_inj","Polynomial.dvd_iff_isRoot","Polynomial.prime_X_sub_C","Polynomial.rootMultiplicity_mul","Polynomial.instNoZeroDivisors","Polynomial.degree_le_of_natDegree_le","Polynomial.eq_C_of_natDegree_le_zero","Polynomial.eq_C_of_natDegree_eq_zero","Polynomial.eq_one_of_monic_natDegree_zero","Polynomial.natDegree_eq_zero_iff_degree_le_zero","Polynomial.rootMultiplicity_eq_nat_find_of_nonzero","Polynomial.le_rootMultiplicity_iff","Polynomial.rootMultiplicity_le_iff","Polynomial.natDegree_le_natDegree","Polynomial.degree_smul_le","Polynomial.natDegree_smul_le","Polynomial.smul_eq_C_mul","Polynomial.coeff_zero","Polynomial.coeff_natDegree","Polynomial.eq_zero_of_mul_eq_zero_of_smul","Polynomial.C_eq_zero","Polynomial.notMem_nonZeroDivisors_iff","Polynomial.mem_nonZeroDivisors_iff","Polynomial.mem_nonzeroDivisors_of_coeff_mem","Polynomial.pow_rootMultiplicity_not_dvd","Polynomial.rootMultiplicity_zero","Polynomial.pow_rootMultiplicity_dvd","Polynomial.rootMultiplicity_mul_X_sub_C_pow","Polynomial.nontrivial","Polynomial.C_add","Polynomial.natDegree_add_eq_left_of_degree_lt","Polynomial.ne_zero_of_natDegree_gt","Polynomial.degree_lt_degree","Polynomial.natDegree_add_eq_left_of_natDegree_lt","Polynomial.natDegree_add_C","Polynomial.natDegree_sub_C","Polynomial.natDegree_X","Polynomial.rootMultiplicity_C","Polynomial.rootMultiplicity_X_sub_C_pow","Polynomial.rootMultiplicity_X_sub_C_self","Polynomial.rootMultiplicity_eq_zero_iff","Polynomial.rootMultiplicity_eq_zero","Polynomial.root_X_sub_C","Polynomial.rootMultiplicity_X_sub_C","Polynomial.exists_multiset_roots","Polynomial.roots","Polynomial.nthRoots","Polynomial.roots_zero","Polynomial.roots_def","Polynomial.count_roots","Polynomial.rootMultiplicity_pos'","Polynomial.mem_roots'","Polynomial.mem_roots","Polynomial.eval\u2082AddMonoidHom","Polynomial.eval\u2082RingHom","Polynomial.eval\u2082_pow","Polynomial.eval_pow","Polynomial.mem_nthRoots","Polynomial.card_roots","Polynomial.degree_X_pow_sub_C","Polynomial.card_nthRoots","Polynomial.aeval","Polynomial.smul_monomial","Polynomial.smul_X_eq_monomial","Polynomial.adjoin_X","Polynomial.aeval_X","Polynomial.aeval_def","Polynomial.eval\u2082_sum","Polynomial.sum_def","Polynomial.natDegree_zero","Polynomial.natDegree_lt_natDegree","Polynomial.natDegree_modByMonic_lt","Polynomial.monic_multiset_prod_of_monic","Polynomial.monic_prod_of_monic","Polynomial.leadingCoeff_add_of_degree_lt","Polynomial.degree_one","Polynomial.degree_eq_iff_natDegree_eq","Polynomial.degree_eq_iff_natDegree_eq_of_pos","Polynomial.leadingCoeff_multiset_prod'","Polynomial.natDegree_multiset_prod'","Polynomial.natDegree_prod'","Polynomial.natDegree_X_sub_C","Polynomial.degreeLT","Polynomial.mem_degreeLT","Polynomial.C_eq_intCast","Polynomial.natDegree_list_prod_le","Polynomial.natDegree_multiset_prod_le","Polynomial.natDegree_prod_le","Polynomial.natDegree_X_le","Polynomial.natDegree_neg","Polynomial.coeff_one","Polynomial.coeff_prod_mem_ideal_pow_tsub","Polynomial.coeff_X_mul_zero","Polynomial.aeval_C","Polynomial.aeval_algHom_apply","Polynomial.aeval_subalgebra_coe","Polynomial.smulCommClass","Polynomial.isScalarTower","Polynomial.map_one","Polynomial.X_mul","Polynomial.commute_X","Polynomial.map_mul","Polynomial.map_zero","Polynomial.mapRingHom","Polynomial.map_sum","Polynomial.distribSMul","Polynomial.aeval_one","Polynomial.coeff_X","Polynomial.coeff_neg","Polynomial.sum_smul_index","Polynomial.derivative","Polynomial.Separable","Polynomial.Splits","Polynomial.monic_X_pow_sub_C","Polynomial.eval\u2082_X_pow","Polynomial.algHom_ext","Polynomial.aeval_algHom","Polynomial.leadingCoeff_mul","Polynomial.monic_mul_leadingCoeff_inv","Polynomial.derivative_apply","Polynomial.derivative_monomial","Polynomial.derivative_mul","Polynomial.map_C","Polynomial.map_natCast","Polynomial.map_pow","Polynomial.map_X","Polynomial.derivative_map","Polynomial.degree_mul","Polynomial.degree_mul_C","Polynomial.degree_mul_leadingCoeff_inv","Polynomial.aeval_modByMonic_eq_self_of_root","Polynomial.aeval_zero","Polynomial.aeval_map_algebraMap","Polynomial.coeffs","Polynomial.coeff_mem_coeffs","Polynomial.toSubring","Polynomial.coeff_toSubring","Polynomial.map_toSubring","Polynomial.support_toSubring","Polynomial.degree_toSubring","Polynomial.natDegree_toSubring","Polynomial.monic_toSubring","Polynomial.derivative_zero","Polynomial.not_separable_zero","Polynomial.div","Polynomial.instDiv","Polynomial.monic_zero_iff_subsingleton","Polynomial.divByMonic_zero","Polynomial.mod","Polynomial.instMod","Polynomial.modByMonic_zero","Polynomial.degree_le_mul_left","Polynomial.instEuclideanDomain","Polynomial.mod_def","Polynomial.degree_map_eq_iff","Polynomial.degree_map_eq_of_injective","Polynomial.natDegree_map_eq_of_injective","Polynomial.leadingCoeff_map_of_injective","Polynomial.leadingCoeff_map","Polynomial.div_modByMonic_unique","Polynomial.map_mod_divByMonic","Polynomial.map_modByMonic","Polynomial.map_mod","Polynomial.gcd_map","Polynomial.natDegree_of_subsingleton","Polynomial.natDegree_mul","Polynomial.natDegree_eq_zero_of_isUnit","Polynomial.zero_le_degree_iff","Polynomial.degree_eq_zero_of_isUnit","Polynomial.C_mul","Polynomial.isUnit_iff_degree_eq_zero","Polynomial.degree_map","Polynomial.isUnit_map","Polynomial.isCoprime_map","Polynomial.separable_def","Polynomial.separable_map","Polynomial.factor","Polynomial.isScalarTower_right","Polynomial.smul_C","Polynomial.nnqsmul_eq_C_mul","Polynomial.qsmul_eq_C_mul","Polynomial.prime_X","Polynomial.irreducible_X","Polynomial.irreducible_factor","Polynomial.fact_irreducible_factor","Polynomial.removeFactor","Polynomial.SplittingFieldAuxAux","Polynomial.SplittingFieldAux","Polynomial.SplittingField","Polynomial.instCommRingSplittingField","Polynomial.natDegree_map_le","Polynomial.splits_iff_exists_multiset'","Polynomial.splits_iff_exists_multiset","Polynomial.roots_mul","Polynomial.not_isRoot_C","Polynomial.roots_C","Polynomial.roots_C_mul","Polynomial.roots_one","Polynomial.roots_list_prod","Polynomial.roots_multiset_prod","Polynomial.roots_X_sub_C","Polynomial.roots_multiset_prod_X_sub_C","Polynomial.degree_C_mul","Polynomial.natDegree_C_mul","Polynomial.natDegree_multiset_prod_of_monic","Polynomial.natDegree_multiset_prod_X_sub_C_eq_card","Polynomial.eq_mul_leadingCoeff_of_monic_of_dvd_of_natDegree_le","Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le","Polynomial.monic_multisetProd_X_sub_C","Polynomial.map_injective","Polynomial.map_dvd_map","Polynomial.prod_multiset_root_eq_finset_root","Polynomial.map_prod","Polynomial.map_sub","Polynomial.C_sub","Polynomial.isCoprime_X_sub_C_of_isUnit_sub","Polynomial.pairwise_coprime_X_sub_C","Polynomial.map_dvd","Polynomial.prod_multiset_X_sub_C_dvd","Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_C","Polynomial.splits_iff_card_roots","Polynomial.natDegree_eq_zero","Polynomial.splits_of_natDegree_eq_zero","Polynomial.eval_zero","Polynomial.degree_ne_of_natDegree_ne","Polynomial.natDegree_X_pow","Polynomial.natDegree_X_pow_add_C","Polynomial.coeff_X_pow_self","Polynomial.leadingCoeff_X_pow_add_C","Polynomial.leadingCoeff_X_add_C","Polynomial.leadingCoeff_X_sub_C","Polynomial.splits_X_sub_C_mul_iff","Polynomial.splits_mul_iff","Polynomial.splits_prod_iff","Polynomial.map_eq_zero_iff","Polynomial.map_eq_zero","Polynomial.map_ne_zero","Polynomial.aroots","Polynomial.rootSet","Polynomial.IsSplittingField","Polynomial.map_multiset_prod","Polynomial.count_map_roots","Polynomial.map_roots_le","Polynomial.map_ne_zero_iff","Polynomial.map_roots_le_of_injective","Polynomial.card_roots'","Polynomial.card_roots_map_le_natDegree","Polynomial.roots_map_of_injective_of_card_eq_natDegree","Polynomial.coeff_C_succ","Polynomial.eq_X_add_C_of_degree_le_one","Polynomial.eq_X_add_C_of_natDegree_le_one","Polynomial.exists_eq_X_add_C_of_natDegree_le_one","Polynomial.instIsDomainOfIsCancelAdd","Polynomial.factor_dvd_of_not_isUnit","Polynomial.factor_dvd_of_degree_ne_zero","Polynomial.factor_dvd_of_natDegree_ne_zero","Polynomial.map_id","Polynomial.X_sub_C_mul_removeFactor","Polynomial.zero_divByMonic","Polynomial.natDegree_divByMonic","Polynomial.natDegree_map","Polynomial.natDegree_removeFactor","Polynomial.natDegree_removeFactor'","Polynomial.rootSet_def","Polynomial.aroots_def","Polynomial.aeval_sub","Polynomial.coe_eval\u2082RingHom","Polynomial.natDegree_le_of_dvd","Polynomial.aeval_monomial","Polynomial.degree_sum_le","Polynomial.degree_sum_fin_lt","Polynomial.exists_iff_exists_finsupp","Polynomial.aeval_add","Polynomial.aeval_algebraMap_apply","Polynomial.irreducible_of_monic","Polynomial.aeval_mul","Polynomial.natDegree_pos_iff_degree_pos","Polynomial.as_sum_range'","Polynomial.eval\u2082_eq_sum_range'","Polynomial.aeval_eq_sum_range'","Polynomial.degree_sub_eq_left_of_degree_lt","Polynomial.mem_roots_map_of_injective","Polynomial.mem_roots_iff_aeval_eq_zero","Polynomial.map_monic_eq_zero_iff","Polynomial.map_monic_ne_zero","Polynomial.rootOfSplits","Polynomial.mem_aroots'","Polynomial.mem_aroots","Polynomial.eval_rootOfSplits","Polynomial.coeff_one_zero","Polynomial.constantCoeff","Polynomial.isUnit_C","Polynomial.isUnit_iff","Polynomial.instNormalizationMonoid","Polynomial.coe_normUnit","Polynomial.coe_normUnit_of_ne_zero","Polynomial.map_dvd_map'","Polynomial.aroots_C","Polynomial.rootSet_C","Polynomial.rootSet_zero","Polynomial.ne_zero_of_mem_rootSet","Polynomial.mem_rootSet'","Polynomial.aeval_eq_zero_of_mem_rootSet","Polynomial.mem_rootSet","Polynomial.mem_rootSet_of_ne","Polynomial.natDegree_lt_natDegree_iff","Polynomial.C_ne_zero","Polynomial.instCommSemiringAdjoinSingleton","Polynomial.instCommRingAdjoinSingleton","Polynomial.coe_aeval_mk_apply","Polynomial.lift_of_splits","Polynomial.roots_prod","Polynomial.rootSet_prod","Polynomial.eval_map_algebraMap","Polynomial.irreducible_mul_leadingCoeff_inv","Polynomial.degree_eq_one_of_irreducible_of_root","Polynomial.evalRingHom","Polynomial.eval_prod","Polynomial.integralNormalization","Polynomial.support_integralNormalization_subset","Polynomial.coeff_ne_zero_of_eq_degree","Polynomial.integralNormalization_coeff","Polynomial.integralNormalization_coeff_degree","Polynomial.integralNormalization_coeff_natDegree","Polynomial.monic_integralNormalization","Polynomial.integralNormalization_zero","Polynomial.as_sum_range","Polynomial.eval\u2082_finset_sum","Polynomial.eval\u2082_eq_sum_range","Polynomial.degree_eq_of_le_of_coeff_ne_zero","Polynomial.degree_integralNormalization","Polynomial.coe_lt_degree","Polynomial.integralNormalization_coeff_mul_leadingCoeff_pow","Polynomial.integralNormalization_eval\u2082_leadingCoeff_mul_of_commute","Polynomial.integralNormalization_eval\u2082_eq_zero_of_commute","Polynomial.integralNormalization_aeval_eq_zero","Polynomial.mem_coeffs_iff","Polynomial.support_smul","Polynomial.instIsTorsionFree","Polynomial.exists_eq_pow_rootMultiplicity_mul_and_not_dvd","Polynomial.divX","Polynomial.coeff_divX","Polynomial.coeff_X_mul","Polynomial.X_mul_divX_add","Polynomial.X_dvd_iff","Polynomial.aeval_X_pow","Polynomial.X_pow_mul","Polynomial.X_dvd_sub_C","Polynomial.comp","Polynomial.leadingCoeff_C_mul_X","Polynomial.natDegree_pow_le","Polynomial.coeff_pow_mul_natDegree","Polynomial.coeff_comp_degree_mul_degree","Polynomial.natDegree_C_mul_X","Polynomial.add_comp","Polynomial.monomial_comp","Polynomial.eval\u2082_mul'","Polynomial.eval\u2082_pow'","Polynomial.eval\u2082_comp'","Polynomial.aeval_comp","Polynomial.notMem_support_iff","Polynomial.eval\u2082_smul","Polynomial.rootSet_maps_to'","Polynomial.rootSetFintype","Polynomial.derivative_add","Polynomial.derivative_X","Polynomial.derivative_C","Polynomial.separable_X_add_C","Polynomial.separable_X_sub_C","Polynomial.natSepDegree","Polynomial.natSepDegree_eq_of_splits","Polynomial.natSepDegree_eq_of_isAlgClosed","Polynomial.IsPrimitive","Polynomial.content","Polynomial.C_dvd_iff_dvd_coeff","Polynomial.content_dvd_coeff","Polynomial.dvd_content_iff_C_dvd","Polynomial.C_content_dvd","Polynomial.primPart","Polynomial.normalize_content","Polynomial.isPrimitive_iff_content_eq_one","Polynomial.content_C","Polynomial.content_zero","Polynomial.eq_C_content_mul_primPart","Polynomial.eraseLead","Polynomial.erase_zero","Polynomial.eraseLead_zero","Polynomial.eraseLead_support","Polynomial.coeff_erase","Polynomial.eraseLead_coeff","Polynomial.content_eq_gcd_leadingCoeff_content_eraseLead","Polynomial.content_eq_gcd_range_of_lt","Polynomial.gcd_content_eq_of_dvd_sub","Polynomial.eraseLead_add_monomial_natDegree_leadingCoeff","Polynomial.self_sub_monomial_natDegree_leadingCoeff","Polynomial.self_sub_C_mul_X_pow","Polynomial.content_mul_aux","Polynomial.primPart_zero","Polynomial.isPrimitive_one","Polynomial.content_eq_zero_iff","Polynomial.content_C_mul","Polynomial.isPrimitive_primPart","Polynomial.primPart_ne_zero","Polynomial.natDegree_primPart","Polynomial.content_primPart","Polynomial.content_mul","Polynomial.primPart_mul","Polynomial.cancelLeads","Polynomial.natDegree_add_le","Polynomial.natDegree_add_le_of_le","Polynomial.natDegree_mul_le_of_le","Polynomial.natDegree_neg_le_of_le","Polynomial.natDegree_pow_le_of_le","Polynomial.natDegree_cancelLeads_lt_of_natDegree_le_natDegree_of_comm","Polynomial.natDegree_cancelLeads_lt_of_natDegree_le_natDegree","Polynomial.dvd_cancelLeads_of_dvd_of_dvd","Polynomial.isUnit_primPart_C","Polynomial.exists_primitive_lcm_of_isPrimitive","Polynomial.primPart_dvd","Polynomial.dvd_iff_content_dvd_content_and_primPart_dvd_primPart","Polynomial.normalizedGcdMonoid","Polynomial.derivative_one","Polynomial.derivative_pow_succ","Polynomial.derivative_pow","Polynomial.pow_sub_one_dvd_derivative_of_pow_dvd","Polynomial.pow_sub_dvd_iterate_derivative_of_pow_dvd","Polynomial.isRoot_iterate_derivative_of_lt_rootMultiplicity","Polynomial.pow_mul_divByMonic_rootMultiplicity_eq","Polynomial.eval_divByMonic_pow_rootMultiplicity_ne_zero","Polynomial.derivative_sum","Polynomial.derivative_smul","Polynomial.iterate_derivative_mul","Polynomial.eval_finset_sum","Polynomial.derivative_X_add_C","Polynomial.derivative_X_add_C_pow","Polynomial.iterate_derivative_X_add_pow","Polynomial.iterate_derivative_X_sub_pow","Polynomial.eval\u2082_id","Polynomial.eval_smul","Polynomial.iterate_derivative_X_sub_pow_self","Polynomial.C_eq_natCast","Polynomial.eval_natCast","Polynomial.eval_iterate_derivative_rootMultiplicity","Polynomial.lt_rootMultiplicity_of_isRoot_iterate_derivative_of_mem_nonZeroDivisors","Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative_of_mem_nonZeroDivisors","Polynomial.one_lt_rootMultiplicity_iff_isRoot_iterate_derivative","Polynomial.one_lt_rootMultiplicity_iff_isRoot","Polynomial.one_lt_rootMultiplicity_iff_isRoot_gcd","Polynomial.isUnit_of_self_mul_dvd_separable","Polynomial.emultiplicity_le_one_of_separable","Polynomial.rootMultiplicity_le_one_of_separable","Polynomial.count_roots_le_one","Polynomial.nodup_roots","Polynomial.nodup_roots_iff_of_splits","Polynomial.nodup_aroots_iff_of_splits","Polynomial.card_rootSet_eq_natDegree_iff_of_splits","Polynomial.natSepDegree_eq_natDegree_iff","Polynomial.expand","Polynomial.IsSeparableContraction","Polynomial.HasSeparableContraction","Polynomial.coeff_derivative","Polynomial.of_mem_support_derivative","Polynomial.degree_derivative_lt","Polynomial.natDegree_derivative_lt","Polynomial.derivative_of_natDegree_zero","Polynomial.separable_iff_derivative_ne_zero","Polynomial.mem_support_derivative","Polynomial.degree_derivative_eq","Polynomial.expand_C","Polynomial.expand_X","Polynomial.expand_one","Polynomial.natDegree_eq_zero_of_derivative_eq_zero","Polynomial.not_irreducible_C","Polynomial.degree_pos_of_irreducible","Polynomial.contract","Polynomial.eq_C_of_degree_eq_zero","Polynomial.expand_eq_sum","Polynomial.coeff_expand","Polynomial.coeff_expand_mul","Polynomial.expand_injective","Polynomial.expand_inj","Polynomial.expand_eq_C","Polynomial.isLocalHom_expand","Polynomial.coeff_contract","Polynomial.expand_contract","Polynomial.separable_or","Polynomial.separable_C","Polynomial.degree_le_zero_iff","Polynomial.coe_expand","Polynomial.eval\u2082_hom","Polynomial.expand_eq_zero","Polynomial.natDegree_expand","Polynomial.expand_expand","Polynomial.exists_separable_of_irreducible","Polynomial.eval\u2082_at_one","Polynomial.expand_zero","Polynomial.eval_one_map","Polynomial.map_expand","Polynomial.coeff_natCast_ite","Polynomial.natCast_inj","Polynomial.charZero","Polynomial.instCharP","Polynomial.instExpChar","Polynomial.expand_ne_zero","Polynomial.expand_eq_comp_X_pow","Polynomial.eval_comp","Polynomial.isRoot_comp","Polynomial.rootMultiplicity_expand_pow","Polynomial.roots_expand_pow","Polynomial.roots_expand_pow_map_iterateFrobenius","Polynomial.roots_expand_image_iterateFrobenius","Polynomial.rootsExpandPowEquivRoots","Polynomial.eval\u2082_dvd","Polynomial.eval\u2082_eq_zero_of_dvd_of_eval\u2082_eq_zero","Polynomial.natDegree_X_pow_sub_C","Polynomial.eq_of_dvd_of_natDegree_le_of_leadingCoeff","Polynomial.natDegree_mul_C","Polynomial.associated_of_dvd_of_natDegree_le_of_leadingCoeff","Polynomial.associated_of_dvd_of_natDegree_le","Polynomial.derivative_sub","Polynomial.derivative_C_mul_X_pow","Polynomial.derivative_X_pow","Polynomial.expand_monomial","Polynomial.map_frobenius_expand","Polynomial.natSepDegree_expand","Polynomial.natSepDegree_eq_natDegree_of_separable","Polynomial.mem_roots_map","Polynomial.aeval_algebraMap_eq_zero_iff","Polynomial.not_isUnit_of_degree_pos","Polynomial.not_isUnit_of_natDegree_pos","Polynomial.leadingCoeffHom","Polynomial.leadingCoeff_pow","Polynomial.natDegree_pow","Polynomial.separable_of_subsingleton","Polynomial.separable_def'","Polynomial.separable_X_pow_sub_C_unit","Polynomial.separable_X_pow_sub_C","Polynomial.X_pow_sub_C_separable_iff","Polynomial.X_pow_sub_one_separable_iff","Polynomial.eq_X_add_C_of_degree_eq_one","Polynomial.natDegree_X_add_C","Polynomial.not_isUnit_X_add_C","Polynomial.aeval_eq_sum_range","Polynomial.lifts","Polynomial.lifts_iff_ringHom_rangeS","Polynomial.coe_mapRingHom","Polynomial.as_sum_range_C_mul_X_pow'","Polynomial.as_sum_range_C_mul_X_pow","Polynomial.mem_map_rangeS","Polynomial.lifts_iff_coeff_lifts","Polynomial.lifts_and_degree_eq_and_monic","Polynomial.lifts_and_natDegree_eq_and_monic","Polynomial.smul_eq_map","Polynomial.smul_X","Polynomial.instMulSemiringAction","Polynomial.algebraMap_apply","Polynomial.coeff_monomial_same","Polynomial.as_sum_support","Polynomial.scaleRoots","Polynomial.coeff_scaleRoots","Polynomial.coeff_scaleRoots_natDegree","Polynomial.dvd_term_of_dvd_eval_of_dvd_terms","Polynomial.dvd_term_of_isRoot_of_dvd_terms","Polynomial.isRoot_of_eval\u2082_map_eq_zero","Polynomial.support_scaleRoots_le","Polynomial.scaleRoots_eval\u2082_mul_of_commute","Polynomial.scaleRoots_eval\u2082_mul","Polynomial.scaleRoots_eval\u2082_eq_zero","Polynomial.zero_scaleRoots","Polynomial.degree_scaleRoots","Polynomial.natDegree_scaleRoots","Polynomial.leadingCoeff_X","Polynomial.monic_X","Polynomial.leadingCoeff_scaleRoots","Polynomial.monic_scaleRoots_iff","Polynomial.coeff_X_one","Polynomial.X_ne_zero","Polynomial.separable_gcd_right","Polynomial.eval\u2082_gcd_eq_zero","Polynomial.eval_gcd_eq_zero","Polynomial.root_left_of_root_gcd","Polynomial.eval\u2082_comp","Polynomial.root_right_of_root_gcd","Polynomial.eq_X_sub_C_of_separable_of_root_eq","Polynomial.C_comp","Polynomial.coeff_X_of_ne_one","Polynomial.eval\u2082_mul_X","Polynomial.map_comp","Polynomial.nextCoeff","Polynomial.nextCoeff_C_eq_zero","Polynomial.revAtFun","Polynomial.revAtFun_invol","Polynomial.revAtFun_inj","Polynomial.revAt","Polynomial.reflect","Polynomial.reverse","Polynomial.revAt_invol","Polynomial.coeff_reflect","Polynomial.coeff_reverse","Polynomial.revAt_le","Polynomial.coeff_one_reverse","Polynomial.support_monomial'","Polynomial.card_support_le_one_iff_monomial","Polynomial.monomial_natDegree_leadingCoeff_eq_self","Polynomial.C_mul_X_pow_eq_self","Polynomial.reflect_C_mul","Polynomial.reflect_C_mul_X_pow","Polynomial.reflect_monomial","Polynomial.revAt_add","Polynomial.reflect_zero","Polynomial.eraseLead_add_C_mul_X_pow","Polynomial.reflect_add","Polynomial.natDegree_mem_support_of_nonzero","Polynomial.eraseLead_support_card_lt","Polynomial.eraseLead_degree_le","Polynomial.eraseLead_natDegree_le_aux","Polynomial.support_C_mul_X_pow'","Polynomial.card_support_C_mul_X_pow_le_one","Polynomial.natDegree_C_mul_X_pow_le","Polynomial.reflect_mul_induction","Polynomial.reflect_mul","Polynomial.reverse_mul","Polynomial.mul_coeff_one","Polynomial.coeff_zero_reverse","Polynomial.nextCoeff_of_natDegree_pos","Polynomial.nextCoeff_X_add_C","Polynomial.nextCoeff_X_sub_C","Polynomial.multiset_prod_X_sub_C_nextCoeff","Polynomial.multiset_prod_X_sub_C_coeff_card_pred","Polynomial.prod_X_sub_C_coeff_card_pred","Polynomial.nextCoeff_map","Polynomial.nextCoeff_map_eq","Polynomial.nextCoeff_C_mul","Polynomial.divX_C","Polynomial.divX_mul_X_add","Polynomial.divX_eq_zero_iff","Polynomial.degree_lt_degree_mul_X","Polynomial.degree_divX_lt","Polynomial.coeff_mul_X_zero","Polynomial.recOnHorner","Polynomial.eq_of_monic_of_associated","Polynomial.eval_X_pow","Polynomial.smul_eval_smul","Polynomial.eval_smul'","Polynomial.separable_one","Polynomial.separable_prod'","Polynomial.separable_prod_X_sub_C_iff'","Polynomial.separable_prod_X_sub_C_iff","Polynomial.separable_X","Polynomial.aroots_zero","Polynomial.cyclotomic'","Polynomial.nthRoots_zero","Polynomial.cyclotomic'_zero","Polynomial.nthRootsFinset","Polynomial.roots_pow","Polynomial.roots_X","Polynomial.nthRoots_zero_right","Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq","Polynomial.X_pow_sub_one_eq_prod","Polynomial.nthRootsFinset_def","Polynomial.nthRootsFinset_zero","Polynomial.mem_nthRootsFinset","Polynomial.prod_cyclotomic'_eq_X_pow_sub_one","Polynomial.map_divByMonic","Polynomial.int_coeff_of_cyclotomic'","Polynomial.cyclotomic","Polynomial.int_cyclotomic_rw","Polynomial.int_cyclotomic_spec","Polynomial.map_cyclotomic_int","Polynomial.prod_cyclotomic_eq_X_pow_sub_one","Polynomial.isRoot_prod","Polynomial.map_cyclotomic","Polynomial.cyclotomic_ne_zero","Polynomial.cyclotomic_zero","Polynomial.cyclotomic_eq_X_pow_sub_one_div","Polynomial.cyclotomic'_eq_X_pow_sub_one_div","Polynomial.cyclotomic_eq_prod_X_sub_primitiveRoots","Polynomial.roots_prod_X_sub_C","Polynomial.isRoot_map_iff","Polynomial.isRoot_cyclotomic_iff","Polynomial.cyclotomic'_ne_zero","Polynomial.natDegree_prod","Polynomial.natDegree_cyclotomic'","Polynomial.degree_cyclotomic'","Polynomial.degree_cyclotomic","Polynomial.natDegree_cyclotomic","Polynomial.isPrimitive_iff_isUnit_of_C_dvd","Polynomial.isUnit_or_eq_zero_of_isUnit_integerNormalization_primPart","Polynomial.isPrimitive_of_dvd","Polynomial.eq_of_monic_of_dvd_of_natDegree_le","Polynomial.map_aeval_eq_aeval_map","Polynomial.mem_lifts","Polynomial.liftsRing","Polynomial.lifts_iff_liftsRing","Polynomial.X_mem_lifts","Polynomial.C'_mem_lifts","Polynomial.degree_le_of_dvd","Polynomial.eq_zero_of_dvd_of_degree_lt","Polynomial.IsWeaklyEisensteinAt","Polynomial.sum_over_range","Polynomial.eval_eq_sum_range","Polynomial.dvd_pow_natDegree_of_eval\u2082_eq_zero","Polynomial.expand_mul","Polynomial.map_iterateFrobenius_expand","Polynomial.cyclotomic_eq_minpoly","Polynomial.eq_cyclotomic_iff","Polynomial.cyclotomic'_one","Polynomial.int_cyclotomic_unique","Polynomial.cyclotomic_one","Polynomial.prod_cyclotomic_eq_geom_sum","Polynomial.cyclotomic_prime","Polynomial.cyclotomic_prime_pow_eq_geom_sum","Polynomial.eval_one_cyclotomic_prime_pow","Polynomial.degree_cyclotomic_pos","Polynomial.coe_evalRingHom","Polynomial.coeff_zero_eq_eval_zero","Polynomial.eval_multiset_prod","Polynomial.eval_intCast_map","Polynomial.irreducible_X_sub_C","Polynomial.of_irreducible_expand","Polynomial.leadingCoeff_expand","Polynomial.monic_expand_iff","Polynomial.expand_eval","Polynomial.cyclotomic_expand_eq_cyclotomic","Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow","Polynomial.mapRingHom_comp","Polynomial.mapRingHom_id","Polynomial.mapEquiv","Polynomial.mapEquiv_apply","Polynomial.reflect_eq_zero_iff","Polynomial.reverse_eq_zero","Polynomial.card_support_eq_zero","Polynomial.support_zero","Polynomial.card_support_eraseLead_add_one","Polynomial.card_support_eraseLead","Polynomial.card_support_eraseLead'","Polynomial.lt_natDegree_of_mem_eraseLead_support","Polynomial.ne_natDegree_of_mem_eraseLead_support","Polynomial.eraseLead_ne_zero","Polynomial.eraseLead_natDegree_lt","Polynomial.induction_with_natDegree_le","Polynomial.eval\u2082_reflect_mul_pow","Polynomial.eval\u2082_reflect_eq_zero_iff","Polynomial.eval\u2082_reverse_eq_zero_iff","Polynomial.aeval_X_left","Polynomial.eval_unique","Polynomial.support_nonempty","Polynomial.coeff_C_mul_X","Polynomial.degree_add_le_of_degree_le","Polynomial.degree_C_mul_X_le","Polynomial.degree_linear_le","Polynomial.degree_quadratic_le","Polynomial.degree_quadratic_lt","Polynomial.degree_quadratic_lt_degree_C_mul_X_cb","Polynomial.degree_cubic","Polynomial.leadingCoeff_cubic","Polynomial.degree_modByMonic_le","Polynomial.mem_image_comap_C_basicOpen","Polynomial.image_comap_C_basicOpen","Polynomial.modByMonic_eq_of_not_monic","Polynomial.add_modByMonic","Polynomial.smul_modByMonic","Polynomial.modByMonicHom","Polynomial.mem_ker_modByMonic","Polynomial.natDegree_lt_iff_degree_lt","Polynomial.sum_fin","Polynomial.sum_modByMonic_coeff","Polynomial.algebraMap_eq","Polynomial.modByMonic_X","Polynomial.X_mul_C","Polynomial.eval_neg","Polynomial.coeff_isUnit_isNilpotent_of_isUnit","Polynomial.erase_monomial","Polynomial.eraseLead_monomial","Polynomial.eraseLead_C_mul_X_pow","Polynomial.eraseLead_natDegree_lt_or_eraseLead_eq_zero","Polynomial.eraseLead_natDegree_le","Polynomial.eraseLead_coeff_of_ne","Polynomial.commute_X_pow","Polynomial.C_pow","Polynomial.isNilpotent_C_mul_pow_X_of_isNilpotent","Polynomial.isUnit_of_coeff_isUnit_isNilpotent","Polynomial.isUnit_iff_coeff_isUnit_isNilpotent","Polynomial.coeff_zero_eq_aeval_zero","Polynomial.isNilpotent_C_iff","Polynomial.coeff_X_pow_mul","Polynomial.isRegular_X_pow","Polynomial.isRegular_X","Polynomial.isNilpotent_X_mul_iff","Polynomial.isNilpotent_mul_X_iff","Polynomial.monomial_pow","Polynomial.monomial_eq_zero_iff","Polynomial.isNilpotent_monomial_iff","Polynomial.isNilpotent_iff","Polynomial.isUnit_C_add_X_mul_iff","Polynomial.isUnit_iff'","Polynomial.natDegree_sub_le","Polynomial.revAt_eq_self_of_lt","Polynomial.isNilpotent_reflect_iff","Polynomial.reflect_neg","Polynomial.reflect_sub","Polynomial.toFinsuppIsoAlg","Polynomial.toLaurentAlg","Polynomial.toLaurent","Polynomial.toLaurent_C_mul_T","Polynomial.toLaurent_X","Polynomial.toLaurent_C","Polynomial.toLaurent_comp_C","Polynomial.toLaurent_one","Polynomial.toFinsupp_inj","Polynomial.toLaurent_injective","Polynomial.revAt_zero","Polynomial.reflect_C","Polynomial.reverse_add_C","Polynomial.toLaurent_C_mul_eq","Polynomial.toLaurent_X_pow","Polynomial.reverse_zero","Polynomial.reverse_mul_of_domain","Polynomial.natDegree_mul_X","Polynomial.reflect_one_X","Polynomial.reverse_mul_X","Polynomial.coe_toLaurentAlg","Polynomial.map_neg","Polynomial.idealSpan_range_update_divByMonic","Polynomial.not_monic_zero_iff","Polynomial.not_monic_zero","Polynomial.coeff_mul_X_pow'","Polynomial.coeff_divModByMonicAux_mem_span_pow_mul_span","Polynomial.coeff_modByMonic_mem_pow_natDegree_mul","Polynomial.modByMonic_one","Polynomial.natDegree_eq_natDegree","Polynomial.degree_map_lt","Polynomial.isLocalization","Polynomial.map_surjective","Polynomial.ker_mapRingHom","Polynomial.coeff_map_eq_comp","Polynomial.coeff_C_ne_zero","Polynomial.evalEval","Polynomial.continuous_eval\u2082","Polynomial.continuous","Polynomial.toContinuousMap","Polynomial.toContinuousMapOn","Polynomial.toContinuousMapOnAlgHom","Polynomial.natCast_mul","Polynomial.aeval_continuousMap_apply","Polynomial.C_eq_algebraMap","Polynomial.toContinuousMapOn_X_eq_restrict_id","Polynomial.toContinuousMapOnAlgHom_apply","Polynomial.expand_aeval","Polynomial.natSepDegree_le_natDegree","Polynomial.natSepDegree_eq_zero","Polynomial.natSepDegree_C","Polynomial.natSepDegree_zero","Polynomial.aroots_X_sub_C","Polynomial.natSepDegree_X_sub_C","Polynomial.natSepDegree_le_of_dvd","Polynomial.natSepDegree_X_pow_char_pow_sub_C","Polynomial.natSepDegree_ne_zero","Polynomial.natSepDegree_eq_zero_iff","Polynomial.natSepDegree_ne_zero_iff","Polynomial.hasStrictDerivAt","Polynomial.hasDerivAt","Polynomial.differentiableAt","Polynomial.differentiable","Polynomial.degree_pos_induction_on","Polynomial.leadingCoeff_mul_X","Polynomial.tendsto_abv_eval\u2082_atTop","Polynomial.tendsto_abv_atTop","Polynomial.tendsto_norm_atTop","Polynomial.zero_of_eval_zero","Polynomial.funext","Polynomial.ext_iff_natDegree_le","Polynomial.bUnion_roots_finite","Polynomial.eq_one_of_roots_le","Polynomial.X_pow_mul_C","Polynomial.coeff_eq_esymm_roots_of_card","Polynomial.coeff_eq_esymm_roots_of_splits","Polynomial.coeff_le_of_roots_le","Polynomial.coeff_bdd_of_roots_le","Polynomial.sylvester","Polynomial.resultant","Polynomial.sylvester_zero_left_deg","Polynomial.resultant_zero_left_deg","Polynomial.sylvester_comm","Polynomial.resultant_comm","Polynomial.resultant_zero_right_deg","Polynomial.induction_of_Splits_of_injective_of_surjective","Polynomial.resultant_zero_right","Polynomial.sum_eq_of_subset","Polynomial.resultant_add_mul_right","Polynomial.resultant_add_mul_left","Polynomial.resultant_zero_left","Polynomial.resultant_succ_left_deg","Polynomial.resultant_add_left_deg","Polynomial.resultant_C_mul_right","Polynomial.sylvester_map_map","Polynomial.resultant_map_map","Polynomial.map_sub_sprod_roots_eq_prod_map_eval","Polynomial.map_sub_roots_sprod_eq_prod_map_eval","Polynomial.resultant_eq_prod_roots_sub","Polynomial.resultant_add_right_deg","Polynomial.resultant_C_mul_left","Polynomial.resultant_eq_prod_eval","Polynomial.mem_lifts_and_degree_eq","Polynomial.resultant_mul_right","Polynomial.resultant_C_right","Polynomial.resultant_one_right","Polynomial.resultant_dvd_leadingCoeff_pow","Polynomial.resultant_ne_zero","Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity_of_ne_zero","Polynomial.sylvesterDeriv","Polynomial.discr","Polynomial.evalEvalRingHom","Polynomial.coe_evalEvalRingHom","Polynomial.evalEvalRingHom_eq","Polynomial.eval\u2082_evalRingHom","Polynomial.coe_aeval_eq_eval","Polynomial.rootSet_finite","Polynomial.Gal","Polynomial.instGroupGal","Polynomial.trinomial","Polynomial.trinomial_def","Polynomial.trinomial_middle_coeff","Polynomial.comp_eq_sum_left","Polynomial.degree_one_le","Polynomial.degree_pow_le","Polynomial.natDegree_comp_le","Polynomial.natDegree_comp_eq_of_mul_ne_zero","Polynomial.comp_C","Polynomial.zero_comp","Polynomial.natDegree_comp","Polynomial.leadingCoeff_comp","Polynomial.one_comp","Polynomial.charP","Polynomial.mul_comp","Polynomial.X_comp","Polynomial.natCast_comp","Polynomial.eval_geom_sum","Polynomial.instIsLocalHomRingHomC","Polynomial.wfDvdMonoid","Polynomial.uniqueFactorizationMonoid","Polynomial.cyclotomic_three","Polynomial.divByMonic_eq_div","Polynomial.mul_div_eq_iff_isRoot","Polynomial.derivative_sq","Polynomial.derivative_X_sub_C","Polynomial.derivative_X_sub_C_sq","Polynomial.idealX","Polynomial.toPowerSeries","Polynomial.coeff_coe","Polynomial.coe_monomial","Polynomial.coe_one","Polynomial.coe_mul","Polynomial.coe_zero","Polynomial.coe_add","Polynomial.coe_C","Polynomial.coe_injective","Polynomial.algebraMap_hahnSeries_injective","Polynomial.coe_X","Polynomial.coe_inj","Polynomial.coe_eq_zero_iff","Polynomial.normUnit_X","Polynomial.X_eq_normalize","Polynomial.coeff_X_pow_mul'","Polynomial.X_pow_dvd_iff","Polynomial.idealX_span","Polynomial.valuation_of_mk","Polynomial.sub_comp","Polynomial.card_le_degree_of_subset_roots","Polynomial.dickson","Polynomial.dickson_add_two","Polynomial.irreducible_of_degree_eq_one_of_isRelPrime_coeff","Polynomial.degree_add_le_of_le","Polynomial.degree_mul_le_of_le","Polynomial.coeff_mul_add_eq_of_natDegree_le","Polynomial.irreducible_C_mul_X_add_C","Polynomial.smul_pow","Polynomial.smeval","Polynomial.continuousAt","Polynomial.eval\u2082_at_natCast","Polynomial.smeval_def","Polynomial.smeval_eq_sum","Polynomial.eval_eq_smeval","Polynomial.smeval_C","Polynomial.smeval_one","Polynomial.smeval_add","Polynomial.smeval_monomial","Polynomial.smeval_mul_X","Polynomial.C_mul_monomial","Polynomial.smeval_C_mul","Polynomial.ascPochhammer_smeval_cast","Polynomial.integralNormalization_eval\u2082_leadingCoeff_mul","Polynomial.degreeLTEquiv","Polynomial.degreeLTEquiv_eq_zero_iff_eq_zero","Polynomial.eval_eq_sum_degreeLTEquiv","Polynomial.eq_zero_of_degree_lt_of_eval_finset_eq_zero","Polynomial.eq_of_degree_sub_lt_of_eval_finset_eq","Polynomial.eq_of_degrees_lt_of_eval_finset_eq","Polynomial.card_rootSet_eq_natDegree","Polynomial.eval\u2082_at_zero","Polynomial.coeff_zero_eq_aeval_zero'","Polynomial.eval\u2082_smulOneHom_eq_smeval","Polynomial.finite_setOf_isRoot","Polynomial.eq_zero_of_infinite_isRoot","Polynomial.algHom_ext_iff","Polynomial.coeff_expand_mul'","Polynomial.derivative'","Polynomial.derivation_ext","Polynomial.mkDerivation","Polynomial.mkDerivation_apply","Polynomial.discr_of_degree_eq_two","Polynomial.coeff_zero_multiset_prod","Polynomial.coeff_zero_prod","Polynomial.cyclotomic_coeff_zero","Polynomial.cyclotomic_two","Polynomial.cyclotomic_pos","Polynomial.cyclotomic_pos_and_nonneg","Polynomial.cyclotomic_pos'","Polynomial.cyclotomic_nonneg","Polynomial.sub_one_pow_totient_lt_cyclotomic_eval","Polynomial.sub_one_pow_totient_lt_natAbs_cyclotomic_eval","Polynomial.sub_one_lt_natAbs_cyclotomic_eval","Polynomial.aeval_algebraMap_apply_eq_algebraMap_eval","Polynomial.coeff_det_X_add_C_zero","Polynomial.isProperMap_eval","Polynomial.isClosedMap_eval","Polynomial.aeval_apply_smul_mem_of_le_comap'","Polynomial.newtonMap","Polynomial.newtonMap_apply","Polynomial.powSubPowFactor","Polynomial.evalSubFactor","Polynomial.isNilpotent_aeval_sub_of_isNilpotent_sub","Polynomial.isNilpotent_iterate_newtonMap_sub_of_isNilpotent","Polynomial.powAddExpansion","Polynomial.sum_add'","Polynomial.sum_add","Polynomial.eval_sum","Polynomial.eval_mul_X","Polynomial.eval_mul_X_pow","Polynomial.derivative_eval","Polynomial.binomExpansion","Polynomial.isUnit_aeval_of_isUnit_aeval_of_isNilpotent_sub","Polynomial.aeval_pow_two_pow_dvd_aeval_iterate_newtonMap","Polynomial.existsUnique_nilpotent_sub_and_aeval_eq_zero","Polynomial.piEquiv","Polynomial.derivative_natCast","Polynomial.natDegree_add_eq_right_of_degree_lt","Polynomial.natDegree_add_eq_right_of_natDegree_lt","Polynomial.tendsto_div_exp_atTop","Polynomial.eval_eq_zero_of_dvd_of_eval_eq_zero","Polynomial.aeval_eq_zero_of_dvd_aeval_eq_zero","Polynomial.lcoeff_apply","Polynomial.coeff_X_add_C_pow","Polynomial.coeff_X_add_one_pow","Polynomial.coeff_mul_natCast","Polynomial.natDegree_quadratic_le","Polynomial.eq_neg_mul_add_of_roots_quadratic_eq_pair","Polynomial.natDegree_map_eq_iff","Polynomial.integralNormalization_map","Polynomial.bernoulli","Polynomial.bernoulli_def","Polynomial.IsMonicOfDegree","Polynomial.isMonicOfDegree_iff'","Polynomial.isMonicOfDegree_zero_iff","Polynomial.isMonicOfDegree_iff_of_subsingleton","Polynomial.update","Polynomial.support_update","Polynomial.degree_update_le","Polynomial.degree_linear_lt","Polynomial.degree_linear_lt_degree_C_mul_X_sq","Polynomial.leadingCoeff_quadratic","Polynomial.degree_quadratic","Polynomial.natDegree_quadratic","Polynomial.MonicDegreeEq","Polynomial.freeMonic","Polynomial.coeff_freeMonic","Polynomial.degree_freeMonic","Polynomial.natDegree_freeMonic","Polynomial.monic_freeMonic","Polynomial.UniversalFactorizationRing","Polynomial.instCommRingUniversalFactorizationRing","Polynomial.instAlgebraUniversalFactorizationRing","Polynomial.UniversalCoprimeFactorizationRing","Polynomial.adjSylvester","Polynomial.sylvesterMap","Polynomial.toMatrix_sylvesterMap","Polynomial.toMatrix_sylvesterMap'","Polynomial.sylveserMap_comp_adjSylvester","Polynomial.exists_mul_add_mul_eq_C_resultant","Polynomial.isUnit_resultant_iff_isCoprime","Polynomial.natDegree_le_iff_coeff_eq_zero","Polynomial.instEtaleUniversalCoprimeFactorizationRing","Polynomial.natDegree_pos_of_nextCoeff_ne_zero","Polynomial.natDegree_eraseLead","Polynomial.degree_gcd_le_left","Polynomial.degree_gcd_le_right","Polynomial.C_mul_dvd","Polynomial.div_def","Polynomial.leadingCoeff_divByMonic_of_monic","Polynomial.leadingCoeff_div","Polynomial.div_C_mul","Polynomial.natDegree_sub_eq_of_prod_eq","Polynomial.trailingDegree","Polynomial.natTrailingDegree","Polynomial.contract_mul_expand","Polynomial.contract_add","Polynomial.contract_C","Polynomial.isCoprime_expand","Polynomial.wronskian","Polynomial.wronskianBilin","Polynomial.wronskian_add_right","Polynomial.eval_C_mul","Polynomial.natDegree_pos_of_eval\u2082_root","Polynomial.natDegree_pos_of_aeval_root","Polynomial.natDegree_pos_of_monic_of_aeval_eq_zero","Polynomial.map_ofNat","Polynomial.eval_ofNat","Polynomial.logMahlerMeasure","Polynomial.mahlerMeasure","Polynomial.cardinalMk_eq_max","Polynomial.cardinalMk_le_max","Polynomial.natTrailingDegree_le_trailingDegree","Polynomial.eq_zero_of_natDegree_lt_card_of_eval_eq_zero","Polynomial.eq_of_natDegree_lt_card_of_eval_eq","Polynomial.preHilbertPoly","Polynomial.natDegree_smul","Polynomial.natDegree_preHilbertPoly","Polynomial.coeff_list_prod_of_natDegree_le","Polynomial.coeff_multiset_prod_of_natDegree_le","Polynomial.coeff_prod_of_natDegree_le","Polynomial.coeff_det_X_add_C_card","Polynomial.natDegree_list_sum_le","Polynomial.natDegree_multiset_sum_le","Polynomial.natDegree_sum_le","Polynomial.natDegree_det_X_add_C_le","Polynomial.leadingCoeff_det_X_one_add_C","Polynomial.modByMonic_eq_of_dvd_sub","Polynomial.toFinsupp_apply","Polynomial.eta","Polynomial.toFinsupp_X_pow","Polynomial.splits_mul","Polynomial.eval\u2082_C_X","Polynomial.degree_C_mul_X","Polynomial.degree_C_lt","Polynomial.degree_C_lt_degree_C_mul_X","Polynomial.leadingCoeff_linear","Polynomial.eval_multiset_prod_X_sub_C_derivative","Polynomial.cyclotomic_prime_pow_mul_X_pow_sub_one","Polynomial.aeval_natCast","Polynomial.IsEisensteinAt","Polynomial.monomial_mul_X","Polynomial.mul_X_comp","Polynomial.X_pow_comp","Polynomial.geom_sum_X_comp_X_add_one_eq_sum","Polynomial.cyclotomic_mul_prime_dvd_eq_pow","Polynomial.pow_comp","Polynomial.ofMultiset","Polynomial.roots_ofMultiset","Polynomial.rightInverse_ofMultiset_roots","Polynomial.aeval_prod","Polynomial.aeval_prod_apply","Polynomial.comp_assoc","Polynomial.smeval_X_mul","Polynomial.smeval_X_pow_assoc","Polynomial.smeval_X_pow_mul","Polynomial.smeval_monomial_mul","Polynomial.smeval_mul","Polynomial.smeval_pow","Polynomial.smeval_comp","Polynomial.smeval_X","Polynomial.smeval_zero","Polynomial.smeval_neg","Polynomial.smeval_sub","Polynomial.smeval_natCast","Polynomial.descPochhammer_smeval_eq_descFactorial","Polynomial.descPochhammer_smeval_eq_ascPochhammer","Polynomial.ascPochhammer_smeval_neg_eq_descPochhammer","Polynomial.ascPochhammer_smeval_eq_eval","Polynomial.eval_natCast_mul","Polynomial.mahlerMeasure_zero","Polynomial.logMahlerMeasure_zero","Polynomial.logMahlerMeasure_eq_log_MahlerMeasure","Polynomial.mahlerMeasure_def_of_ne_zero","Polynomial.mahlerMeasure_eq_zero_iff","Polynomial.intervalIntegrable_mahlerMeasure","Polynomial.mahlerMeasure_mul","Polynomial.logMahlerMeasure_mul_eq_add_logMahlerMeasure","Polynomial.logMahlerMeasure_const","Polynomial.mahlerMeasure_const","Polynomial.logMahlerMeasure_one","Polynomial.mahlerMeasure_one","Polynomial.prod_mahlerMeasure_eq_mahlerMeasure_prod","Polynomial.logMahlerMeasure_X_sub_C","Polynomial.mahlerMeasure_pos_of_ne_zero","Polynomial.mahlerMeasure_X_sub_C","Polynomial.logMahlerMeasure_eq_log_leadingCoeff_add_sum_log_roots","Polynomial.mahlerMeasure_eq_leadingCoeff_mul_prod_roots","Polynomial.norm_coeff_le_choose_mul_mahlerMeasure","Polynomial.mirror","Polynomial.natTrailingDegree_eq_of_trailingDegree_eq_some","Polynomial.support_add","Polynomial.support_trinomial'","Polynomial.trailingDegree_le_of_ne_zero","Polynomial.trinomial_trailing_coeff'","Polynomial.trinomial_natTrailingDegree","Polynomial.trinomial_leading_coeff'","Polynomial.trinomial_natDegree","Polynomial.trinomial_mirror","Polynomial.binomial_eq_binomial","Polynomial.mirror_zero","Polynomial.trailingCoeff","Polynomial.natTrailingDegree_zero","Polynomial.trailingDegree_eq_top","Polynomial.trailingDegree_eq_natTrailingDegree","Polynomial.trailingCoeff_eq_zero","Polynomial.natTrailingDegree_le_natDegree","Polynomial.trailingCoeff_nonzero_iff_nonzero","Polynomial.reverse_natDegree_le","Polynomial.natTrailingDegree_le_of_ne_zero","Polynomial.natDegree_eq_reverse_natDegree_add_natTrailingDegree","Polynomial.reverse_natDegree","Polynomial.reverse_leadingCoeff","Polynomial.mirror_natDegree","Polynomial.coeff_eq_zero_of_lt_trailingDegree","Polynomial.trailingDegree_zero","Polynomial.coeff_eq_zero_of_lt_natTrailingDegree","Polynomial.revAtFun_eq","Polynomial.nonempty_support_iff","Polynomial.mul_X_pow_eq_zero","Polynomial.natTrailingDegree_eq_support_min'","Polynomial.natTrailingDegree_mul_X_pow","Polynomial.trailingDegree_eq_zero","Polynomial.natTrailingDegree_eq_zero","Polynomial.natTrailingDegree_reverse","Polynomial.mirror_natTrailingDegree","Polynomial.coeff_mirror","Polynomial.mirror_mirror","Polynomial.mirror_involutive","Polynomial.mirror_eq_iff","Polynomial.mapAlgHom","Polynomial.mapAlgHom_comp","Polynomial.mapAlgHom_id","Polynomial.mapAlgEquiv","Polynomial.rootSet_mapsTo","Polynomial.card_support_eq'","Polynomial.card_support_eq","Polynomial.X_pow_sub_one_splits","Polynomial.aeval_eq_prod_aroots_sub_of_splits","Polynomial.exists_monic_irreducible_factor","Polynomial.aroots_pow","Polynomial.natSepDegree_pow","Polynomial.natSepDegree_pow_of_ne_zero","Polynomial.aroots_mul","Polynomial.natSepDegree_mul_eq_iff","Polynomial.natSepDegree_mul_of_isCoprime","Polynomial.derivative_neg","Polynomial.natDegree_C_mul_le","Polynomial.lifts_iff_set_range","Polynomial.support_binomial'","Polynomial.support_binomial","Polynomial.card_support_binomial","Polynomial.card_support_eq_two","Polynomial.hermite","Polynomial.eval_eq_sum_range'","Polynomial.eq_zero_of_forall_eval_zero_of_natDegree_lt_card","Polynomial.exists_eval_ne_zero_of_natDegree_lt_card","Polynomial.mahlerMeasure_le_sum_norm_coeff","Polynomial.comp_X","Polynomial.algEquivOfCompEqX","Polynomial.neg_comp","Polynomial.algEquivAevalNegX","Polynomial.algEquivAevalNegX_symm_apply","Polynomial.X_pow_mul_assoc","Polynomial.X_pow_mul_assoc_C","Polynomial.scaleRoots_ne_zero","Polynomial.scaleRoots_aeval_eq_zero","Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero","Polynomial.eq_of_degree_sub_lt_of_eval_index_eq","Polynomial.coeff_pow_of_natDegree_le","Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_C","Polynomial.C_mul_comp","Polynomial.natCast_mul_comp","Polynomial.aeval_X_left_apply","Polynomial.derivative_X_pow_succ","Polynomial.iterate_derivative_zero","Polynomial.iterate_derivative_eq_zero","Polynomial.iterate_derivative_smul","Polynomial.derivativeFinsupp","Polynomial.sumIDeriv","Polynomial.support_derivativeFinsupp_subset_range","Polynomial.sumIDeriv_apply","Polynomial.sumIDeriv_eq_self_add","Polynomial.annIdeal","Polynomial.annIdealGenerator","Polynomial.annIdealGenerator_eq_zero_iff","Polynomial.mem_annIdeal_iff_aeval_eq_zero","Polynomial.monic_annIdealGenerator","Polynomial.annIdealGenerator_mem","Polynomial.annIdealGenerator_aeval_eq_zero","Polynomial.span_singleton_annIdealGenerator","Polynomial.mem_iff_annIdealGenerator_dvd","Polynomial.degree_annIdealGenerator_le_of_mem","Polynomial.annIdealGenerator_eq_minpoly","Polynomial.rootMultiplicity_pos","Polynomial.derivative_X_sub_C_pow","Polynomial.derivative_rootMultiplicity_of_root_of_mem_nonZeroDivisors","Polynomial.derivative_rootMultiplicity_of_root","Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_one","Polynomial.eval\u2082_mul_eq_zero_of_left","Polynomial.mapRingHom_comp_C","Polynomial.residueFieldMapCAlgEquiv","Polynomial.residueFieldMapCAlgEquiv_symm_C","Polynomial.natDegree_natCast","Polynomial.natDegree_sub_le_of_le","Polynomial.X_pow_sub_X_sub_one_irreducible_aux","Polynomial.eq_of_degrees_lt_of_eval_index_eq","Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity","Polynomial.toFinsupp_algebraMap","Polynomial.ofFinsupp_algebraMap","Polynomial.toMvPolynomial","Polynomial.toMvPolynomial_X","Polynomial.degree_list_prod_le","Polynomial.degree_multiset_prod_le","Polynomial.degree_prod_le","Polynomial.jacobson_bot_of_integral_localization","Polynomial.mem_closure_X_union_C","Polynomial.isIntegral_isLocalization_polynomial_quotient","Polynomial.isJacobsonRing_polynomial_of_isJacobsonRing","Polynomial.isJacobsonRing_polynomial_iff_isJacobsonRing","Polynomial.isMaximal_comap_C_of_isMaximal","Polynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRing","Polynomial.isMaximal_comap_C_of_isJacobsonRing","Polynomial.transcendental_X","Polynomial.monomial_one_eq_iff","Polynomial.infinite","Polynomial.map_normalize","Polynomial.toFinsuppIsoLinear","Polynomial.instFree","Polynomial.exists_degree_le_of_mem_span","Polynomial.exists_degree_le_of_mem_span_of_finite","Polynomial.span_le_degreeLE_of_finite","Polynomial.not_finite","Polynomial.leadingCoeff_normalize","Polynomial.monic_normalize","Polynomial.normalize_eq_self_iff_monic","Polynomial.mem_normalizedFactors_iff","Polynomial.degree_mul_leadingCoeff_self_inv","Polynomial.natDegree_mul_leadingCoeff_self_inv","Polynomial.natDegree_of_dvd_cyclotomic_of_irreducible","Polynomial.mul_scaleRoots","Polynomial.mul_scaleRoots'","Polynomial.mul_scaleRoots_of_noZeroDivisors","Polynomial.scaleRoots_dvd","Polynomial.prime_C_iff","Polynomial.integralNormalization_degree","Polynomial.natDegree_add_le_of_degree_le","Polynomial.coprime_of_root_cyclotomic","Polynomial.IsDistinguishedAt","Polynomial.coe_sub","Polynomial.polynomial_map_coe","Polynomial.coe_pow","Polynomial.algebra","Polynomial.aevalAeval","Polynomial.taylor","Polynomial.taylor_eval","Polynomial.mono_map_natDegree_eq","Polynomial.map_natDegree_eq_sub","Polynomial.map_natDegree_eq_natDegree","Polynomial.taylor_monomial","Polynomial.eq_natDegree_of_le_mem_support","Polynomial.natDegree_C_mul_of_mul_ne_zero","Polynomial.leadingCoeff_pow_X_add_C","Polynomial.natDegree_pow_X_add_C","Polynomial.natDegree_taylor","Polynomial.lsum","Polynomial.hasseDeriv","Polynomial.leval","Polynomial.addSubmonoid_closure_setOf_eq_monomial","Polynomial.addHom_ext","Polynomial.lhom_ext'","Polynomial.hasseDeriv_apply","Polynomial.hasseDeriv_coeff","Polynomial.hasseDeriv_monomial","Polynomial.taylor_coeff","Polynomial.hasseDeriv_one'","Polynomial.hasseDeriv_one","Polynomial.taylor_coeff_one","Polynomial.hasseDeriv_zero'","Polynomial.hasseDeriv_zero","Polynomial.taylor_coeff_zero","Polynomial.eval_add_of_sq_eq_zero","Polynomial.aeval_add_of_sq_eq_zero","Polynomial.eq_X_sub_C_of_splits_of_single_root","Polynomial.algEquivCMulXAddC","Polynomial.dvd_comp_C_mul_X_add_C_iff","Polynomial.IsUnitTrinomial","Polynomial.support_trinomial","Polynomial.card_support_trinomial","Polynomial.aeval_mem_adjoin_singleton","Polynomial.leadingCoeffHom_apply","Polynomial.leadingCoeff_multiset_prod","Polynomial.leadingCoeff_prod","Polynomial.degree_smul_of_smul_regular","Polynomial.natDegree_smul_of_smul_regular","Polynomial.leadingCoeff_smul_of_smul_regular","Polynomial.monic_of_isUnit_leadingCoeff_inv_smul","Polynomial.isUnit_leadingCoeff_mul_left_eq_zero_iff","Polynomial.separable_cyclotomic","Polynomial.natDegree_linear_le","Polynomial.reflect_map","Polynomial.reflect_one","Polynomial.monic_of_injective","Polynomial.monic_map_iff","Polynomial.instEquivLikeGalSplittingField","Polynomial.derivative_natCast_mul","Polynomial.eq_zero_of_dvd_of_natDegree_lt","Polynomial.not_dvd_of_natDegree_lt","Polynomial.derivation_C","Polynomial.Sequence","Polynomial.divX_one","Polynomial.divX_X_pow","Polynomial.resultant_self","Polynomial.isEquivalent_atTop_lead","Polynomial.isEquivalent_atTop_div","Polynomial.div_tendsto_zero_of_degree_lt","Polynomial.div_tendsto_zero_iff_degree_lt","Polynomial.trailingCoeff_eq_coeff_zero","Polynomial.le_degree_of_mem_supp","Polynomial.degree_eraseLead_lt","Polynomial.eraseLead_coeff_natDegree","Polynomial.eraseLead_add_of_degree_lt_left","Polynomial.eraseLead_X_pow","Polynomial.monicEquivDegreeLT","Polynomial.cyclotomic_injective","Polynomial.cyclotomic_eq_minpoly_rat","Polynomial.cyclotomic_expand_eq_cyclotomic_mul","Polynomial.cyclotomic_mul_prime_eq_pow_of_not_dvd","Polynomial.isMonicOfDegree_iff","Polynomial.coeff_add_eq_left_of_lt","Polynomial.roots_eq_of_degree_le_card_of_ne_zero","Polynomial.roots_eq_of_degree_eq_card","Polynomial.C_ofNat","Polynomial.degree_mul_X","Polynomial.natDegree_of_mem_normalizedFactors_cyclotomic","Polynomial.degree_coe_units","Polynomial.degree_eq_degree_of_associated","Polynomial.natDegree_multiset_prod","Polynomial.squarefree_cyclotomic","Polynomial.normalizedFactors_cyclotomic_card","Polynomial.X_pow_sub_one_mul_prod_cyclotomic_eq_X_pow_sub_one_of_dvd","Polynomial.X_pow_sub_one_mul_cyclotomic_dvd_X_pow_sub_one_of_dvd","Polynomial.eval_dvd","Polynomial.degreeLT_succ_eq_degreeLE","Polynomial.span_of_finite_le_degreeLT","Polynomial.sumIDeriv_apply_of_le","Polynomial.natDegree_derivative_le","Polynomial.sumIDeriv_derivative","Polynomial.smeval_at_natCast","Polynomial.mul_X_sub_intCast_comp","Polynomial.divX_zero","Polynomial.not_isUnit_of_natDegree_pos_of_isReduced","Polynomial.continuous_aeval","Polynomial.continuousOn_aeval","Polynomial.restriction","Polynomial.natDegree_coe_units","Polynomial.coeff_coe_units_zero_ne_zero","Polynomial.coeff_inv_units","Polynomial.mahlerMeasure_X_add_C","Polynomial.mahlerMeasure_C_mul_X_add_C","Polynomial.mahlerMeasure_of_degree_eq_one","Polynomial.map_mem_nthRootsFinset","Polynomial.map_mem_nthRootsFinset_one","Polynomial.roots_X_pow_char_pow_sub_C","Polynomial.logMahlerMeasure_def","Polynomial.trailingCoeff_zero","Polynomial.coeff_mul_natTrailingDegree_add_natTrailingDegree","Polynomial.le_trailingDegree_mul","Polynomial.trailingDegree_mul'","Polynomial.natTrailingDegree_mul'","Polynomial.eval_zero_map","Polynomial.bernoulli_eval_zero","Polynomial.bernoulli_eval_one","Polynomial.bernoulli_zero","Polynomial.derivative_bernoulli_add_one","Polynomial.derivative_bernoulli","Polynomial.derivative_C_mul_X_sq","Polynomial.C_mul_X_eq_monomial","Polynomial.toFinsupp_C_mul_X","Polynomial.one_le_prod_max_one_norm_roots","Polynomial.natDegree_X_pow_le","Polynomial.isMonicOfDegree_X_pow","Polynomial.isIntegral_coeff_prod","Polynomial.ofNat_comp","Polynomial.tendsto_abv_aeval_atTop","Polynomial.mkDerivation_X","Polynomial.mkDerivationEquiv","Polynomial.evalEval_mul","Polynomial.toLaurent_inj","Polynomial.eq_C_of_derivative_eq_zero","Polynomial.continuousOn","Polynomial.deriv","Polynomial.card_roots_toFinset_le_card_roots_derivative_diff_roots_succ","Polynomial.card_roots_toFinset_le_derivative","Polynomial.card_rootSet_le_derivative","Polynomial.mapEquiv_symm_apply","Polynomial.degree_mul_C_of_isUnit","Polynomial.natDegree_mul_C_of_isUnit","Polynomial.mirror_eq_zero","Polynomial.natDegree_mul_mirror","Polynomial.constantCoeff_apply","Polynomial.cauchyBound","Polynomial.cauchyBound_C","Polynomial.natSepDegree_mul","Polynomial.faithfulSMul","Polynomial.map_injective_iff","Polynomial.splits_of_natDegree_eq_one","Polynomial.separable_X_pow_sub_C_of_irreducible","Polynomial.comp_eq_zero_iff","Polynomial.compRingHom","Polynomial.multiset_prod_comp","Polynomial.leadingCoeff_X_pow_sub_C","Polynomial.leadingCoeff_X_pow_sub_one","Polynomial.instAlgEquivClassGalSplittingField","Polynomial.cardPowDegree","Polynomial.exists_eq_polynomial","Polynomial.exists_approx_polynomial_aux","Polynomial.cardPowDegree_nonzero","Polynomial.exists_approx_polynomial","Polynomial.nextCoeffUp","Polynomial.nextCoeffUp_zero","Polynomial.fintypeSubtypeMonicDvd","Polynomial.algEquivAevalXAddC","Polynomial.comp_X_add_C_eq_zero_iff","Polynomial.comp_X_add_C_ne_zero_iff","Polynomial.leval_apply","Polynomial.degree_sub_le_of_le","Polynomial.bernoulli_three_eval_one_quarter","Polynomial.degree_ne_bot","Polynomial.iterate_derivative_map","Polynomial.derivativeFinsupp_map","Polynomial.instInhabitedSplittingField","Polynomial.sumIDeriv_map","Polynomial.leadingCoeff_neg","Polynomial.comp_neg_X_leadingCoeff_eq","Polynomial.aeval_neg","Polynomial.div_tendsto_atTop_of_degree_gt'","Polynomial.div_tendsto_atTop_of_degree_gt","Polynomial.div_tendsto_atBot_of_degree_gt'","Polynomial.div_tendsto_atBot_of_degree_gt","Polynomial.abs_div_tendsto_atTop_of_degree_gt","Polynomial.hermite_succ","Polynomial.coeff_hermite_succ_succ","Polynomial.coeff_hermite_of_lt","Polynomial.coeff_hermite_self","Polynomial.degree_hermite","Polynomial.derivative_eval\u2082_C","Polynomial.derivative_expand","Polynomial.isUnit_or_eq_zero_of_separable_expand","Polynomial.derivative_prod","Polynomial.derivative_prod_finset","Polynomial.isMonicOfDegree_X","Polynomial.isMonicOfDegree_X_add_one","Polynomial.roots_C_mul_X_sub_C_of_IsUnit","Polynomial.roots_C_mul_X_add_C_of_IsUnit","Polynomial.sum_comp","Polynomial.smul_comp","Polynomial.prod_comp","Polynomial.coeff_injective","Polynomial.comp_C_mul_X_coeff","Polynomial.comp_C_mul_X_eq_zero_iff","Polynomial.toLaurentAlg_apply","Polynomial.toFn","Polynomial.zero_isRoot_iff_coeff_zero_eq_zero","Polynomial.zero_isRoot_of_coeff_zero_eq_zero","Polynomial.exists_prod_multiset_X_sub_C_mul","Polynomial.eq_C_coeff_zero_iff_natDegree_eq_zero","Polynomial.mul_comp_neg_X","Polynomial.transcendental","Polynomial.trailingDegree_monomial","Polynomial.trailingDegree_C","Polynomial.trailingDegree_one","Polynomial.contentIdeal","Polynomial.contentIdeal_def","Polynomial.contentIdeal_le_span_content","Polynomial.coeff_mem_contentIdeal","Polynomial.degreeMonoidHom","Polynomial.degree_pow","Polynomial.degree_list_sum_le_of_forall_degree_le","Polynomial.coe_mapAlgHom","Polynomial.cyclotomic_mul_prime_pow_eq","Polynomial.taylor_C","Polynomial.taylor_one","Polynomial.taylor_mul","Polynomial.taylorAlgHom","Polynomial.coe_taylorAlgHom","Polynomial.roots_expand_pow_map_iterateFrobenius_le","Polynomial.roots_expand_pow_image_iterateFrobenius_subset","Polynomial.rootsExpandPowToRoots","Polynomial.eq_mul_mul_of_roots_quadratic_eq_pair","Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero","Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero","Polynomial.tendsto_atTop_of_leadingCoeff_nonneg","Polynomial.tendsto_atTop_iff_leadingCoeff_nonneg","Polynomial.tendsto_atBot_iff_leadingCoeff_nonpos","Polynomial.tendsto_atBot_of_leadingCoeff_nonpos","Polynomial.map_taylor","Polynomial.sub_dvd_eval_sub","Polynomial.isIntegral_coeff_of_factors","Polynomial.isIntegral_coeff_of_dvd","Polynomial.ne_zero_of_ne_zero_of_monic","Polynomial.aeval_pi","Polynomial.map_rootOfSplits","Polynomial.natDegree_sum_le_of_forall_le","Polynomial.coeff_mem_pow_of_mem_adjoin_C_mul_X","Polynomial.exists_monic_aeval_eq_zero_forall_mem_pow_of_isIntegral","Polynomial.exists_monic_aeval_eq_zero_forall_mem_pow_of_mem_map","Polynomial.exists_monic_aeval_eq_zero_forall_mem_of_mem_map","Polynomial.coeffs_empty_iff","Polynomial.coeffs_nonempty_iff","Polynomial.homogenize","Polynomial.homogenize_zero","Polynomial.homogenize_smul","Polynomial.homogenize_C_mul","Polynomial.homogenize_monomial","Polynomial.homogenize_X_pow","Polynomial.homogenize_add","Polynomial.eval\u2082_homogenize_of_eq_one","Polynomial.aeval_homogenize_of_eq_one","Polynomial.aeval_homogenize_X_one","Polynomial.splits_of_natDegree_le_one_of_invertible","Polynomial.eval\u2082_mul_C'","Polynomial.hasseDeriv_comp","Polynomial.span_minpoly_eq_annihilator","Polynomial.eraseLead_add_of_degree_lt_right","Polynomial.eraseLead_add_of_natDegree_lt_right","Polynomial.cyclotomic_irreducible_of_irreducible_pow","Polynomial.natDegree_mul_C_le","Polynomial.natDegree_mul_C_eq_of_mul_eq_one","Polynomial.natDegree_mod_lt","Polynomial.dvd_pow_natDegree_of_aeval_eq_zero","Polynomial.wronskian_zero_right","Polynomial.cardPowDegree_apply","Polynomial.derivative_comp","Polynomial.comp_eq_aeval","Polynomial.eval\u2082_algebraMap_X","Polynomial.scaleRoots_zero","Polynomial.scaleRoots_eval\u2082_eq_zero_of_eval\u2082_div_eq_zero","Polynomial.trailingDegree_X","Polynomial.map_smul","Polynomial.natDegree_le_pred","Polynomial.nextCoeff_eq_zero","Polynomial.eraseLead_C","Polynomial.natDegree_eraseLead_le_of_nextCoeff_eq_zero","Polynomial.toFinsuppIso_symm_apply","Polynomial.mem_roots_sub_C'","Polynomial.mem_roots_sub_C","Polynomial.degree_add_C","Polynomial.card_roots_sub_C","Polynomial.card_roots_sub_C'","Polynomial.monomial_mul_C","Polynomial.toMvPolynomial_eq_rename_comp","Polynomial.mem_map_range","Polynomial.splits_id_of_splits","Polynomial.mapAlg","Polynomial.mapAlg_eq_map","Polynomial.mapAlg_comp","Polynomial.coeffList","Polynomial.signVariations","Polynomial.coeffList_zero","Polynomial.signVariations_zero","Polynomial.coeffList_C","Polynomial.withBotSucc_degree_eq_natDegree_add_one","Polynomial.length_coeffList_eq_ite","Polynomial.coeffList_eq_cons_leadingCoeff","Polynomial.natDegree_monomial_eq","Polynomial.coeff_monomial_of_ne","Polynomial.coeffList_monomial","Polynomial.coeffList_eraseLead","Polynomial.coeffList_eq_nil","Polynomial.signVariations_eq_eraseLead_add_ite","Polynomial.signVariations_le_eraseLead_succ","Polynomial.valuation_monomial_eq_valuation_X_pow","Polynomial.valuation_inv_monomial_eq_valuation_X_zpow","Polynomial.natSepDegree_map","Polynomial.natTrailingDegree_mem_support_of_nonzero","Polynomial.iterate_derivative_C","Polynomial.degree_pos_of_eval\u2082_root","Polynomial.aeval_primPart_eq_zero","Polynomial.div_tendsto_leadingCoeff_div_of_degree_eq","Polynomial.dickson_one","Polynomial.dickson_two_one_eq_chebyshev_S","Polynomial.card_support_eq_one_of_eraseLead_eq_zero","Polynomial.card_support_le_one_of_eraseLead_eq_zero","Polynomial.taylor_apply","Polynomial.taylor_zero","Polynomial.taylor_zero'","Polynomial.natDegree_hasseDeriv_le","Polynomial.hasseDeriv_natDegree_eq_C","Polynomial.coeff_taylor_natDegree","Polynomial.leadingCoeff_taylor","Polynomial.taylor_eq_zero","Polynomial.taylor_injective","Polynomial.taylor_taylor","Polynomial.map_mapRingHom_eval_map","Polynomial.map_mapRingHom_eval_map_eval","Polynomial.map_mapRingHom_evalEval","Polynomial.div_eq_quo_add_rem_div","Polynomial.natTrailingDegree_mul","Polynomial.mirror_mul_of_domain","Polynomial.reverse_neg","Polynomial.trailingDegree_neg","Polynomial.natTrailingDegree_neg","Polynomial.mirror_neg","Polynomial.irreducible_of_mirror","Polynomial.natTrailingDegree_mul_mirror","Polynomial.coeff_mul_mirror","Polynomial.trinomial_support","Polynomial.card_support_eq_three","Polynomial.isUnitTrinomial_iff","Polynomial.isUnitTrinomial_iff'","Polynomial.isUnitTrinomial_iff''","Polynomial.trinomial_trailingCoeff","Polynomial.trinomial_leadingCoeff","Polynomial.mirror_trailingCoeff","Polynomial.mirror_leadingCoeff","Polynomial.mirror_eval_one","Polynomial.mirror_inj","Polynomial.X_pow_sub_X_sub_one_irreducible","Polynomial.hilbertPoly","Polynomial.smul_sum","Polynomial.sum_smul_index'","Polynomial.hilbertPoly_smul","Polynomial.coeffs_monomial","Polynomial.contentIdeal_monomial","Polynomial.contentIdeal_C","Polynomial.contentIdeal_mul_le_mul_contentIdeal","Polynomial.contentIdeal_le_contentIdeal_of_dvd","Polynomial.isPrimitive_of_contentIdeal_eq_top","Polynomial.roots_X_add_C","Polynomial.eq_quadratic_of_degree_le_two","Polynomial.preHilbertPoly_eq_choose_sub_add","Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval","Polynomial.eq_of_infinite_eval_eq","Polynomial.existsUnique_hilbertPoly","Polynomial.eq_hilbertPoly_of_forall_coeff_eq_eval","Polynomial.hilbertPoly_mul_one_sub_succ","Polynomial.hilbertPoly_mul_one_sub_pow_add","Polynomial.coeff_preHilbertPoly_self","Polynomial.natDegree_hilbertPoly_of_ne_zero_of_rootMultiplicity_lt","Polynomial.derivative_ofNat","Polynomial.derivative_intCast","Polynomial.iterate_derivative_X_pow_eq_natCast_mul","Polynomial.iterate_derivative_X_pow_eq_C_mul","Polynomial.iterate_derivative_X_pow_eq_smul","Polynomial.iterate_derivative_mul_X_pow","Polynomial.iterate_derivative_derivative_mul_X","Polynomial.iterate_derivative_derivative_mul_X_sq","Polynomial.iterate_derivative_intCast_mul","Polynomial.iterate_derivative_natCast_mul","Polynomial.iterate_derivative_sub","Polynomial.eval_intCast","Polynomial.instInhabitedSplittingFieldAux","Polynomial.toSubring_zero","Polynomial.natDegree_eq_of_natDegree_add_lt_left","Polynomial.natDegree_eq_of_natDegree_add_lt_right","Polynomial.natDegree_eq_of_natDegree_add_eq_zero","Polynomial.mem_nonZeroDivisors_of_trailingCoeff","Polynomial.degree_add_degree_leadingCoeff_inv","Polynomial.degree_mod_lt","Polynomial.cardPowDegree_isEuclidean","Polynomial.cardPowDegree_anti_archimedean","Polynomial.exists_partition_polynomial_aux","Polynomial.exists_partition_polynomial","Polynomial.cardPowDegreeIsAdmissible","Polynomial.support_C_mul_X_pow","Polynomial.card_support_eq_one","Polynomial.natDegree_finset_prod_X_sub_C_eq_card","Polynomial.monic_prod_X_sub_C","Polynomial.gaussNorm","Polynomial.gaussNorm_zero","Polynomial.exists_eq_gaussNorm","Polynomial.gaussNorm_coe_powerSeries","Polynomial.aeval_ofReal","Polynomial.degree_taylor","Polynomial.ne_zero_of_degree_ge_degree","Polynomial.eventually_no_roots","Polynomial.isBigO_of_degree_le","Polynomial.aeval_root_of_mapAlg_eq_multiset_prod_X_sub_C","Polynomial.monic_of_monic_mapAlg","Polynomial.cyclotomic_eval_lt_add_one_pow_totient","Polynomial.natDegree_iterate_comp","Polynomial.one_scaleRoots","Polynomial.pow_scaleRoots'","Polynomial.X_sub_C_scaleRoots","Polynomial.scaleRoots_eval_mul","Polynomial.rootMultiplicity_scaleRoots","Polynomial.support_map_subset","Polynomial.sum_bernoulli","Polynomial.bernoulli_generating_function","Polynomial.coeff_restriction","Polynomial.support_restriction","Polynomial.eval\u2082_restriction","Polynomial.fwdDiff_iter_degree_eq_factorial","Polynomial.aeval_conj","Polynomial.mul_star_dvd_of_aeval_eq_zero_im_ne_zero","Polynomial.quadratic_dvd_of_aeval_eq_zero_im_ne_zero","Polynomial.degree_C_mul_of_mul_ne_zero","Polynomial.integralNormalization_coeff_degree_ne","Polynomial.integralNormalization_coeff_ne_natDegree","Polynomial.trailingDegree_mul","Polynomial.comp_zero","Polynomial.eval\u2082AlgHom'_apply","Polynomial.hasSMulPi'","Polynomial.algebraPi","Polynomial.algebraMap_pi_eq_aeval","Polynomial.natDegree_prod_of_monic","Polynomial.count_map_roots_of_injective","Polynomial.intCast_coeff_zero","Polynomial.intCast_inj","Polynomial.coeff_intCast_mul","Polynomial.map_rootOfSplits'","Polynomial.coeff_natTrailingDegree_pred_eq_zero","Polynomial.natDegree_ne_zero_induction_on","Polynomial.isRoot_of_mem_roots","Polynomial.ne_zero_of_mem_roots","Polynomial.coeff_X_sub_C_mul","Polynomial.leadingCoeff_eraseLead_eq_nextCoeff","Polynomial.nextCoeff_eq_zero_of_eraseLead_eq_zero","Polynomial.natDegree_eraseLead_add_one","Polynomial.X_mul_monomial","Polynomial.monomial_neg","Polynomial.monomial_sub","Polynomial.signVariations_eraseLead_mul_X_sub_C","Polynomial.coeff_mul_monomial","Polynomial.leadingCoeff_cons_eraseLead","Polynomial.succ_signVariations_X_sub_C_mul_monomial","Polynomial.signVariations_eraseLead_le","Polynomial.card_support_mul_le","Polynomial.natDegree_eq_one","Polynomial.eraseLead_C_mul_X","Polynomial.nextCoeff_C_mul_X_add_C","Polynomial.two_le_natDegree_of_nextCoeff_eraseLead","Polynomial.eraseLead_mul_eq_mul_eraseLead_of_nextCoeff_zero","Polynomial.signVariations_X_sub_C_mul_eraseLead_le","Polynomial.coeffList_neg","Polynomial.signVariations_neg","Polynomial.succ_signVariations_le_X_sub_C_mul","Polynomial.roots_countP_pos_le_signVariations","Polynomial.aeval_smul","Polynomial.smul_mem_rootSet","Polynomial.instMulActionElemRootSetOfSMulCommClass","Polynomial.X_sub_C_mul_divByMonic_eq_sub_modByMonic","Polynomial.divByMonic_add_X_sub_C_mul_derivative_divByMonic_eq_derivative","Polynomial.X_sub_C_dvd_derivative_of_X_sub_C_dvd_divByMonic","Polynomial.adjSylvester_comp_sylveserMap","Polynomial.coeff_list_sum","Polynomial.coeff_list_sum_map","Polynomial.roots_X_pow_char_sub_C","Polynomial.reflect_support","Polynomial.noZeroDivisors_iff","Polynomial.aeval_root_derivative_of_splits","Polynomial.isWeaklyEisensteinAt_iff","Polynomial.algEquivAevalXAddC_symm","Polynomial.coeff_monomial_succ","Polynomial.not_isUnit_X","Polynomial.leval_coe_eq_smeval","Polynomial.taylor_eval_sub","Polynomial.natTrailingDegree_monomial","Polynomial.natTrailingDegree_X_pow","Polynomial.ofSubring","Polynomial.irreducible_of_dvd_cyclotomic_of_natDegree","Polynomial.degree_sub_eq_right_of_degree_lt","Polynomial.eval\u2082_at_intCast","Polynomial.roots_map","Polynomial.mapAlgEquiv_toAlgHom","Polynomial.shiftedLegendre","Polynomial.coeff_shiftedLegendre","Polynomial.degree_shiftedLegendre","Polynomial.natDegree_shiftedLegendre","Polynomial.coeff_update","Polynomial.natDegree_intCast","Polynomial.basisMonomials","Polynomial.mem_rootSet_of_injective","Polynomial.ofFn","Polynomial.toFn_comp_ofFn_eq_id","Polynomial.isSplittingField_C","Polynomial.eval\u2082_multiset_sum","Polynomial.eval_multisetSum","Polynomial.evalEval_intCast","Polynomial.aroots_X","Polynomial.aroots_X_pow","Polynomial.one_le_cauchyBound","Polynomial.reverse_mul_X_pow","Polynomial.homogenizeLM","Polynomial.homogenize_finsetSum","Polynomial.homogenize_eq_of_isHomogeneous","Polynomial.isHomogeneous_homogenize","Polynomial.homogenize_mul","Polynomial.homogenize_dvd","Polynomial.evalEval_multiset_prod","Polynomial.splits_of_algHom","Polynomial.taylor_X","Polynomial.ofFinsupp_zsmul","Polynomial.degree_cubic_le","Polynomial.root_mul_left_of_isRoot","Polynomial.coeff_ofNat_zero","Polynomial.natTrailingDegree_le_of_trailingDegree_le","Polynomial.nextCoeff_eq_neg_sum_roots_mul_leadingCoeff_of_splits","Polynomial.preimage_eval_singleton","Polynomial.toPowerSeries_toMvPowerSeries","Polynomial.ofFinsupp_one","Polynomial.ofFinsupp_eq_one","Polynomial.natTrailingDegree_eq_zero_of_constantCoeff_ne_zero","Polynomial.sumIDeriv_X","Polynomial.divByMonic_eq_of_not_monic","Polynomial.degree_divByMonic_le","Polynomial.degree_div_le","Polynomial.smeval_neg_nat","Polynomial.natDegree_ofNat","Polynomial.mul_X_add_natCast_comp","Polynomial.wronskian_add_left","Polynomial.natDegree_iterate_derivative","Polynomial.as_sum_support_C_mul_X_pow","Polynomial.coeff_iterate_derivative","Polynomial.iterate_derivative_eq_sum","Polynomial.iterate_derivative_eq_factorial_smul_sum","Polynomial.exists_iterate_derivative_eq_factorial_smul","Polynomial.aeval_iterate_derivative_of_ge","Polynomial.aeval_iterate_derivative_of_lt","Polynomial.aeval_iterate_derivative_self","Polynomial.aeval_sumIDeriv_of_pos","Polynomial.eval_sumIDeriv_of_pos","Polynomial.aeval_sumIDeriv","Polynomial.aeval_sumIDeriv_eq_eval","Polynomial.derivative_monomial_succ","Polynomial.eval\u2082_primPart_eq_zero","Polynomial.roots_smul_nonzero","Polynomial.roots_neg","Polynomial.aroots_neg","Polynomial.rootSet_neg","Polynomial.taylorEquiv","Polynomial.nthRootsFinset_toSet","Polynomial.splits_iff_splits","Polynomial.mem_nonZeroDivisors_of_leadingCoeff","Polynomial.taylor_mem_degreeLT","Polynomial.comap_taylorEquiv_degreeLT","Polynomial.map_taylorEquiv_degreeLT","Polynomial.taylorLinearEquiv","Polynomial.support_integralNormalization","Polynomial.lifts_iff_coeffs_subset_range","Polynomial.gaussNorm_eq_zero_iff","Polynomial.roots_expand_image_frobenius_subset","Polynomial.rootsExpandToRoots","Polynomial.cyclotomic'_two","Polynomial.roots_eq_zero_of_irreducible_of_natDegree_ne_one","Polynomial.mirror_monomial","Polynomial.mirror_X","Polynomial.coeff_natTrailingDegree_eq_zero_of_trailingDegree_lt","Polynomial.iterate_comp_eval\u2082","Polynomial.iterate_comp_eval","Polynomial.X_pow_add_C_ne_one","Polynomial.X_add_C_ne_one","Polynomial.divX_add","Polynomial.divX_hom","Polynomial.divX_hom_toFun","Polynomial.smeval_commute_left","Polynomial.smeval_commute","Polynomial.supp_subset_range_natDegree_succ","Polynomial.card_supp_le_succ_natDegree","Polynomial.degree_linear","Polynomial.cauchyBound_X_sub_C","Polynomial.nextCoeff_eq_neg_sum_roots_of_monic_of_splits","Polynomial.sum_roots_eq_nextCoeff_of_monic_of_split","Polynomial.roots_map_of_map_ne_zero_of_card_eq_natDegree","Polynomial.coeff_zero_eq_prod_roots_of_monic_of_splits","Polynomial.eval\u2082_X_mul","Polynomial.int","Polynomial.int_leadingCoeff_eq","Polynomial.derivativeFinsupp_apply_apply","Polynomial.derivativeFinsupp_apply_toFun","Polynomial.factorial_smul_hasseDeriv","Polynomial.leadingCoeff_mul_prod_normalizedFactors","Polynomial.eval_one_cyclotomic_not_prime_pow","Polynomial.hasStrictDerivAt_aeval","Polynomial.hasDerivAt_aeval","Polynomial.differentiableAt_aeval","Polynomial.differentiable_aeval","Polynomial.opRingEquiv","Polynomial.opRingEquiv_op_monomial","Polynomial.opRingEquiv_symm_monomial","Polynomial.opRingEquiv_symm_C_mul_X_pow","Polynomial.isNilpotent_pow_X_mul_C_of_isNilpotent","Polynomial.aroots_C_mul","Polynomial.aroots_C_mul_X_pow","Polynomial.aroots_monomial","Polynomial.rootSet_monomial","Polynomial.rootSet_C_mul_X_pow","Polynomial.rootSet_X_pow","Polynomial.coe_def","Polynomial.toContinuousMapAlgHom","Polynomial.aeval_ne_zero_of_isCoprime","Polynomial.degree_pos_of_ne_zero_of_nonunit","Polynomial.isCoprime_iff_aeval_ne_zero_of_isAlgClosed","Polynomial.ncard_rootSet_le","Polynomial.coeToPowerSeries","Polynomial.natDegree_add_coeff_mul","Polynomial.coeff_zero_of_isScalarTower","Polynomial.monic_mapAlg_iff","Polynomial.isRoot_cyclotomic_prime_pow_mul_iff_of_charP","Polynomial.support_X_pow","Polynomial.coeff_natCast_mul","Polynomial.derivativeFinsupp_C","Polynomial.resultant_eq_zero_iff","Polynomial.modByMonic_eq_mod","Polynomial.mod_X_sub_C_eq_C_eval","Polynomial.homogenizeLM_apply","Polynomial.eval_list_prod","Polynomial.evalEval_list_prod","Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero","Polynomial.discr_C","Polynomial.rootMultiplicity_eq_rootMultiplicity","Polynomial.rootMultiplicity_eq_natTrailingDegree'","Polynomial.rootMultiplicity_eq_natTrailingDegree","Polynomial.reverse_X_pow_mul","Polynomial.eval_divByMonic_eq_trailingCoeff_comp","Polynomial.rootMultiplicity_mul'","Polynomial.isRoot_of_unity_of_root_cyclotomic","Polynomial.leadingCoeff_eq_zero_iff_deg_eq_bot","Polynomial.le_trailingDegree_monomial","Polynomial.le_trailingDegree_C","Polynomial.coeff_one_add_X_pow","Polynomial.trailingDegree_eq_iff_natTrailingDegree_eq","Polynomial.coeff_natTrailingDegree_eq_zero","Polynomial.roots_C_mul_X_sub_C","Polynomial.coeff_monomial_mul","Polynomial.coeff_monomial_zero_mul","Polynomial.exists_forall_norm_le","Polynomial.sylvesterDeriv_updateRow","Polynomial.resultant_deriv","Polynomial.separable_gcd_left","Polynomial.splits_iff_comp_splits_of_natDegree_eq_one","Polynomial.splits_iff_comp_splits_of_degree_eq_one","Polynomial.dickson_zero","Polynomial.rootOfSplits'","Polynomial.aevalTower_comp_C","Polynomial.sylvesterMap_apply_coe","Polynomial.smeval_at_zero","Polynomial.TrailingMonic","Polynomial.evalEval_finset_sum","Polynomial.degree_smul_of_isRightRegular_leadingCoeff","Polynomial.degree_sum_eq_of_disjoint","Polynomial.degree_eq_card_roots'","Polynomial.mem_lift_of_splits_of_roots_mem_range","Polynomial.one_add_X_pow_sub_X_pow","Polynomial.hilbertPoly_succ","Polynomial.mem_support_C_mul_X_pow","Polynomial.degree_mul_X_pow","Polynomial.roots_X_pow_char_pow_sub_C_pow","Polynomial.det_taylorLinearEquiv_toLinearMap","Polynomial.det_taylorLinearEquiv","Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_one","Polynomial.ker_evalRingHom","Polynomial.quotientSpanXSubCAlgEquiv","Polynomial.quotientSpanXSubCAlgEquiv_symm_apply","Polynomial.coeff_ofSubring","Polynomial.coeffs_ofSubring","Polynomial.CC","Polynomial.coe_algebraMap_eq_CC","Polynomial.dickson_one_one_eq_chebyshev_C","Polynomial.chebyshev_T_eq_dickson_one_one","Polynomial.coeff_update_apply","Polynomial.update_zero_eq_erase","Polynomial.roots_cyclotomic_nodup","Polynomial.ne_zero_of_coe_le_degree","Polynomial.X_pow_mem_lifts","Polynomial.coeff_update_ne","Polynomial.leading_coeff_le_mahlerMeasure","Polynomial.norm_leadingCoeff_eq_one_of_mahlerMeasure_eq_one","Polynomial.abs_leadingCoeff_eq_one_of_mahlerMeasure_eq_one","Polynomial.isIntegral_of_mahlerMeasure_eq_one","Polynomial.prod_max_one_norm_roots_le_mahlerMeasure_of_one_le_leadingCoeff","Polynomial.norm_root_le_one_of_mahlerMeasure_eq_one","Polynomial.pow_eq_one_of_mahlerMeasure_eq_one","Polynomial.isPrimitiveRoot_of_mahlerMeasure_eq_one","Polynomial.cyclotomic_dvd_of_mahlerMeasure_eq_one","Polynomial.evalEval_prod","Polynomial.ker_modByMonicHom","Polynomial.X_sub_C_dvd_sub_C_eval","Polynomial.mem_span_C_X_sub_C_X_sub_C_iff_eval_eval_eq_zero","Polynomial.quotientSpanCXSubCAlgEquiv","Polynomial.quotientSpanCXSubCXSubCAlgEquiv","Polynomial.ofFinsupp_smul","Polynomial.leadingCoeff_preHilbertPoly","Polynomial.dvd_derivative_iff","Polynomial.iterate_derivative_X","Polynomial.derivativeFinsupp_X","Polynomial.evalEval_neg","Polynomial.algEquivOfCompEqX_apply","Polynomial.algEquivCMulXAddC_symm_eq","Polynomial.associated_map_map","Polynomial.splits_C","Polynomial.splits_of_map_degree_eq_one","Polynomial.natDegree_linear","Polynomial.resultant_X_sub_C_left","Polynomial.resultant_X_add_C_left","Polynomial.coe_basisMonomials","Polynomial.degree_map_eq_of_isUnit_leadingCoeff","Polynomial.natDegree_map_eq_of_isUnit_leadingCoeff","Polynomial.cauchyBound_smul","Polynomial.cardPowDegree_zero","Polynomial.content_one","Polynomial.content_X_mul","Polynomial.content_X_pow","Polynomial.reverse_C","Polynomial.eval\u2082_reverse_mul_pow","Polynomial.mahlerMeasure_nonneg","Polynomial.content_eq_gcd_range_succ","Polynomial.smeval_assoc_X_pow","Polynomial.leadingCoeff_prod'","Polynomial.resultant_mul_left","Polynomial.resultant_prod_left","Polynomial.resultant_pow_left","Polynomial.resultant_X_sub_C_pow_left","Polynomial.resultant_X_sub_C_pow_right","Polynomial.resultant_X_pow_right","Polynomial.splits_of_isScalarTower","Polynomial.isMonicOfDegree_X_sub_one","Polynomial.isMonicOfDegree_one_iff","Polynomial.not_quasiFiniteAt","Polynomial.lhom_ext'_iff","Polynomial.list_prod_comp","Polynomial.map_expand_pow_char","Polynomial.degree_normalize","Polynomial.prime_of_degree_eq_one","Polynomial.irreducible_of_degree_eq_one","Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero","Polynomial.derivWithin","Polynomial.derivative_X_add_C_sq","Polynomial.coeff_bernoulli","Polynomial.bernoulli_comp_neg_X","Polynomial.natDegree_mul_leadingCoeff_inv","Polynomial.irreducible_iff_lt_natDegree_lt","Polynomial.monic_of_degree_le_of_coeff_eq_one","Polynomial.differentiableOn","Polynomial.pow_sub_dvd_iterate_derivative_pow","Polynomial.natDegree_cubic","Polynomial.taylorLinearEquiv_apply_coe","Polynomial.discr_of_degree_eq_one","Polynomial.exists_min_root","Polynomial.natDegree_sub_eq_right_of_natDegree_lt","Polynomial.degree_multiset_prod_of_monic","Polynomial.isNilpotent_reverse_iff","Polynomial.toLaurent_eq_zero","Polynomial.coe_compRingHom","Polynomial.X_sub_C_pow_dvd_iff","Polynomial.mem_lifts_iff_mem_alg","Polynomial.smul_mem_lifts","Polynomial.bernoulli_eq_sub_sum","Polynomial.bernoulli_comp_one_add_X","Polynomial.bernoulli_comp_one_sub_X","Polynomial.isCentralScalar","Polynomial.eq_zero_of_natDegree_lt_card_of_eval_eq_zero'","Polynomial.le_natTrailingDegree","Polynomial.iterate_derivative_sum","Polynomial.roots_eq_zero_iff_isRoot_eq_bot","Polynomial.roots_eq_zero_iff_eq_zero_or_isRoot_eq_bot","Polynomial.hasseDeriv_eq_zero_of_lt_natDegree","Polynomial.iterate_derivative_comp_one_sub_X","Polynomial.map_map_freeMonic","Polynomial.instFiniteUniversalFactorizationRing","Polynomial.natTrailingDegree_ne_zero","Polynomial.disjoint_ker_aeval_of_isCoprime","Polynomial.contract_one","Polynomial.expand_contract'","Polynomial.map_scaleRoots","Polynomial.derivative_pow_eq_zero","Polynomial.opRingEquiv_op_C","Polynomial.wronskianBilin_apply","Polynomial.mod_eq_of_dvd_sub","Polynomial.toMvPolynomial_C","Polynomial.degree_div_lt","Polynomial.isCoveringMapOn_eval","Polynomial.support_C","Polynomial.gaussNorm_C","Polynomial.differentiableWithinAt_aeval","Polynomial.derivative_X_sq","Polynomial.scaleRoots_C","Polynomial.X_add_C_scaleRoots","Polynomial.splits_neg_iff","Polynomial.exists_image_comap_of_monic","Polynomial.isOpen_image_comap_of_monic","Polynomial.coeffs_zero","Polynomial.ofFn_coeff_eq_zero_of_ge","Polynomial.ofFn_natDegree_lt","Polynomial.leadingCoeff_add_of_degree_lt'","Polynomial.leadingCoeff_sub_of_degree_lt","Polynomial.natDegree_mul_X_pow","Polynomial.roots_scaleRoots","Polynomial.resultant_scaleRoots","Polynomial.toContinuousMapOn_apply","Polynomial.natDegree_hasseDeriv","Polynomial.evalEval_one","Polynomial.signVariations_monomial","Polynomial.newtonMap_apply_of_not_isUnit","Polynomial.splits_of_splits_of_dvd","Polynomial.natDegree_reflect_le","Polynomial.reflect_reflect","Polynomial.irreducible_comp","Polynomial.X_add_C_ne_zero","Polynomial.lt_rootMultiplicity_of_isRoot_iterate_derivative","Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative","Polynomial.ofFinsupp_ofNat","Polynomial.contentIdeal_map_eq_map_contentIdeal","Polynomial.contentIdeal_eq_bot_iff","Polynomial.mul_contentIdeal_le_radical_contentIdeal_mul","Polynomial.contentIdeal_mul_eq_top_of_contentIdeal_eq_top","Polynomial.eq_mul_mul_of_aroots_quadratic_eq_pair","Polynomial.trailingDegree_eq_iff_natTrailingDegree_eq_of_pos","Polynomial.bernoulli_eval_one_sub","Polynomial.degree_pow_le_of_le","Polynomial.coeffList_C_mul","Polynomial.signVariations_C_mul","Polynomial.natTrailingDegree_monomial_le","Polynomial.natTrailingDegree_C","Polynomial.natTrailingDegree_intCast","Polynomial.derivRootWeight","Polynomial.derivRootWeight_nonneg","Polynomial.algEquivCMulXAddC_symm_apply","Polynomial.one_mem_nthRootsFinset","Polynomial.eval\u2082_natCast","Polynomial.eval\u2082_ofNat","Polynomial.eval\u2082_one_cyclotomic_prime_pow","Polynomial.wronskian_self_eq_zero","Polynomial.isAlt_wronskianBilin","Polynomial.wronskian_neg_eq","Polynomial.roots_C_mul_X_add_C","Polynomial.roots_degree_eq_one","Polynomial.wronskian_eq_of_sum_zero","Polynomial.wronskian_zero_left","Polynomial.degree_wronskian_lt_add","Polynomial.natDegree_wronskian_lt_add","Polynomial.abc","Polynomial.iterate_derivative_C_mul","Polynomial.derivative_C_mul","Polynomial.flt_catalan","Polynomial.splits_prod","Polynomial.zero_modByMonic","Polynomial.neg_modByMonic","Polynomial.sub_modByMonic","Polynomial.sub_mod","Polynomial.sum_derivRootWeight_pos","Polynomial.toContinuousMap_X_eq_id","Polynomial.algebraMap_def","Polynomial.contentIdeal_one","Polynomial.roots_expand","Polynomial.roots_expand_map_frobenius","Polynomial.roots_expand_image_frobenius","Polynomial.rootsExpandEquivRoots","Polynomial.toContinuousMap_apply","Polynomial.opRingEquiv_symm_C","Polynomial.continuousWithinAt","Polynomial.degree_pos_of_not_isUnit_of_dvd_monic","Polynomial.leadingCoeff_dvd_leadingCoeff","Polynomial.irreducible_iff_degree_lt","Polynomial.evalEvalRingHom_apply","Polynomial.degree_modByMonic_le_left","Polynomial.natDegree_modByMonic_le_left","Polynomial.splits_zero","Polynomial.aroots_map","Polynomial.cyclotomic_six","Polynomial.algebraMap_pi_self_eq_eval","Polynomial.valuation_X_eq_neg_one","Polynomial.scaleRoots_one","Polynomial.evalEval_zero","Polynomial.splits_X_pow","Polynomial.isMonicOfDegree_add_add_two","Polynomial.ofFn_zero","Polynomial.card_roots_le_derivative","Polynomial.root_gcd_iff_root_left_right","Polynomial.isRoot_gcd_iff_isRoot_left_right","Polynomial.map_list_prod","Polynomial.isMonicOfDegree_sub_add_two","Polynomial.support_update_ne_zero","Polynomial.degree_natCast_le","Polynomial.rootsExpandEquivRoots_apply","Polynomial.smul_eval","Polynomial.rootSet_one","Polynomial.ite_le_natDegree_coeff","Polynomial.smeval_smul","Polynomial.coeff_update_same","Polynomial.degreeLT_mono","Polynomial.coeff_restriction'","Polynomial.ne_zero_of_ofFn_ne_zero","Polynomial.cyclotomic'_splits","Polynomial.isIntegrallyClosed_iff'","Polynomial.bernoulli_eval_one_add","Polynomial.image_rootSet","Polynomial.coeff_add_eq_right_of_lt","Polynomial.coeff_sub_eq_neg_right_of_lt","Polynomial.trailingDegree_C_mul_X_pow","Polynomial.sum_taylor_eq","Polynomial.splits_pow","Polynomial.derivative_comp_one_sub_X","Polynomial.hermite_zero","Polynomial.deriv_aeval","Polynomial.deriv_gaussian_eq_hermite_mul_gaussian","Polynomial.hermite_eq_deriv_gaussian","Polynomial.leadingCoeff_map'","Polynomial.ofFinsupp_intCast","Polynomial.smul_mem_rootSet_iff_of_isUnit","Polynomial.ext_iff_degree_le","Polynomial.dvd_comp_neg_X_iff","Polynomial.evalEval_C","Polynomial.evalEval_CC","Polynomial.evalEval_surjective","Polynomial.coeff_mem_radical_span_coeff_of_dvd","Polynomial.homogenize_X","Polynomial.one_le_mahlerMeasure_of_ne_zero","Polynomial.scaleRoots_mul","Polynomial.scaleRoots_dvd'","Polynomial.scaleRoots_dvd_iff","Polynomial.aevalTower_ofId","Polynomial.wronskian_neg_left","Polynomial.divX_C_mul","Polynomial.natDegree_divX_eq_natDegree_tsub_one","Polynomial.coeff_ofNat_succ","Polynomial.taylorLinearEquiv_symm","Polynomial.eval\u2082_congr","Polynomial.leadingCoeff_divByMonic_X_sub_C","Polynomial.natTrailingDegree_eq_of_trailingDegree_eq","Polynomial.degree_multiset_prod","Polynomial.trunc_toLaurent","Polynomial.natDegree_X_pow_mul","Polynomial.hasseDeriv_X","Polynomial.monic_finprod_of_monic","Polynomial.monic_finprod_X_sub_C","Polynomial.degree_intCast_le","Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_C'","Polynomial.cauchyBound_X_add_C","Polynomial.rootsExpandPowEquivRoots_apply","Polynomial.splits_of_degree_le_one_of_invertible","Polynomial.int_monic_iff","Polynomial.content_monomial","Polynomial.nontrivial_iff","Polynomial.isLeftCancelMulZero_iff","Polynomial.isRightCancelMulZero_iff","Polynomial.isCancelMulZero_iff","Polynomial.isDomain_iff","Polynomial.toAlgHom_taylorEquiv","Polynomial.eval_derivative_eq_eval_mul_sum_of_splits","Polynomial.trinomial_monic","Polynomial.X_pow_sub_X_sub_one_irreducible_rat","Polynomial.natTrailingDegree_natCast","Polynomial.aroots_smul_nonzero","Polynomial.isEisensteinAt_iff","Polynomial.fiberEquivQuotient","Polynomial.not_ker_le_map_C_of_surjective_of_quasiFiniteAt","Polynomial.coeff_opRingEquiv","Polynomial.support_opRingEquiv","Polynomial.natDegree_eq_support_max'","Polynomial.natDegree_opRingEquiv","Polynomial.monomial_left_inj","Polynomial.toFinsupp_eq_one","Polynomial.mkDerivation_one_eq_derivative'","Polynomial.cyclotomic_mahlerMeasure_eq_one","Polynomial.roots_X_pow_char_sub_C_pow","Polynomial.natSepDegree_X","Polynomial.eq_zero_of_eq_zero","Polynomial.monomial_mem_lifts","Polynomial.contentIdeal_FG","Polynomial.isPrimitive_iff_contentIdeal_eq_top","Polynomial.erase_same","Polynomial.erase_ne","Polynomial.erase_mem_lifts","Polynomial.root_mul","Polynomial.toFinsupp_intCast","Polynomial.evalEval_smul","Polynomial.degree_list_sum_le","Polynomial.map_dickson","Polynomial.splits_one","Polynomial.map_intCast","Polynomial.eval\u2082_multiset_prod","Polynomial.dvd_iterate_derivative_pow","Polynomial.ne_zero_of_trailingDegree_lt","Polynomial.coeffs_one","Polynomial.homogenize_C","Polynomial.homogenize_one","Polynomial.homogenize_finsetProd","Polynomial.aeval_fn_apply","Polynomial.isCoprime_iff_aeval_ne_zero","Polynomial.natDegree_notMem_eraseLead_support","Polynomial.isUnit_leadingCoeff_mul_right_eq_zero_iff","Polynomial.taylor_pow","Polynomial.eval_C_X_comp_eval\u2082_map_C_X","Polynomial.eval_C_X_eval\u2082_map_C_X","Polynomial.hasFDerivAt","Polynomial.hasFDerivWithinAt","Polynomial.fderivWithin","Polynomial.toFinsuppIsoLinear_symm_apply_toFinsupp","Polynomial.reverse_X_mul","Polynomial.gaussNorm_intAdicAbv_le_one","Polynomial.rootMultiplicity_add","Polynomial.aevalTower_algebraMap","Polynomial.hasSMulPi","Polynomial.trailingDegree_ne_zero","Polynomial.monic_X_pow_sub","Polynomial.neg_cancelLeads","Polynomial.toFinsupp_X","Polynomial.iterate_derivative_prod_X_sub_C","Polynomial.logMahlerMeasure_X","Polynomial.support_scaleRoots_eq","Polynomial.ofReal_eval","Polynomial.aeval_pi_apply\u2082","Polynomial.addHom_ext'","Polynomial.natSepDegree_one","Polynomial.lt_rootMultiplicity_of_isRoot_iterate_derivative_of_mem_nonZeroDivisors'","Polynomial.toFinsupp_sum","Polynomial.mul_eq_sum_sum","Polynomial.lsum_apply","Polynomial.generalizedEisenstein","Polynomial.irreducible_of_eisenstein_criterion","Polynomial.nextCoeff_map_of_leadingCoeff_ne_zero","Polynomial.coeff_hermite_succ_zero","Polynomial.natDegree_map_lt","Polynomial.lcoeff_comp_mapAlgHom_eq","Polynomial.resultant_taylor","Polynomial.eval_natCast_map","Polynomial.natDegree_C_mul_eq_of_mul_eq_one","Polynomial.instFintypeGal","Polynomial.hasseDeriv_C","Polynomial.hasseDeriv_apply_one","Polynomial.coeff_hermite_explicit","Polynomial.coeff_hermite_of_even_add","Polynomial.newtonMap_apply_of_isUnit","Polynomial.eq_prod_roots_of_splits_id","Polynomial.comp_C_integral_of_surjective_of_isJacobsonRing","Polynomial.degree_prod","Polynomial.le_rootMultiplicity_mul","Polynomial.taylorAlgHom_apply","Polynomial.evalRingHom_zero","Polynomial.dickson_one_one_eq_chebyshev_T","Polynomial.dickson_one_one_mul","Polynomial.dickson_one_one_comp_comm","Polynomial.isPrimitive_iff_ne_zero","Polynomial.algEquivOfCompEqX_symm","Polynomial.exists_irreducible_of_degree_pos","Polynomial.exists_irreducible_of_natDegree_pos","Polynomial.aeval_algebraMap_eq_zero_iff_of_injective","Polynomial.flt","Polynomial.length_coeffList_eq_withBotSucc_degree","Polynomial.ringHom_ext'_iff","Polynomial.natSepDegree_X_sub_C_pow","Polynomial.continuousWithinAt_aeval","Polynomial.natDegree_hermite","Polynomial.X_mem_nonzeroDivisors","Polynomial.logMahlerMeasure_C_mul","Polynomial.logMahlerMeasure_X_add_C","Polynomial.logMahlerMeasure_C_mul_X_add_C","Polynomial.ringKrullDim_le","Polynomial.disc_C","Polynomial.opRingEquiv_symm_X","Polynomial.int_natDegree","Polynomial.isIntegral_iff_isIntegral_coeff","Polynomial.degree_add_eq_of_leadingCoeff_add_ne_zero","Polynomial.hilbertPoly_zero_left","Polynomial.aeval_algEquiv","Polynomial.ofFn_coeff_eq_val_of_lt","Polynomial.ofFn_comp_toFn_eq_id_of_natDegree_lt","Polynomial.card_eq_of_natDegree_le_of_coeff_le","Polynomial.sup_ker_aeval_le_ker_aeval_mul","Polynomial.splits_of_exists_multiset","Polynomial.dickson_two_one_eq_chebyshev_U","Polynomial.mul_mem_nthRootsFinset","Polynomial.exists_root_of_degree_eq_one","Polynomial.toFinsupp_eq_zero","Polynomial.splits_of_comp","Polynomial.coeff_toSubring'","Polynomial.toSubring_one","Polynomial.expand_pow","Polynomial.isFixedPt_newtonMap_of_aeval_eq_zero","Polynomial.ofFinsupp_nsmul","Polynomial.rootMultiplicity_le_rootMultiplicity_of_dvd","Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative_of_mem_nonZeroDivisors'","Polynomial.iterate_derivative_neg","Polynomial.eq_zero_of_hasseDeriv_eq_zero","Polynomial.hasDerivWithinAt","Polynomial.degree_C_mul_of_isUnit","Polynomial.natDegree_C_mul_of_isUnit","Polynomial.leadingCoeff_C_mul_of_isUnit","Polynomial.toFinsupp_natCast","Polynomial.derivWithin_aeval","Polynomial.trailingDegree_le_trailingDegree","Polynomial.natDegree_monomial_le","Polynomial.eval\u2082AddMonoidHom_apply","Polynomial.mapAlgEquiv_id","Polynomial.X_pow_sub_one_dvd_prod_cyclotomic","Polynomial.instSMulCommClassElemRootSet","Polynomial.evalEval_dvd","Polynomial.algebraMap_hahnSeries_apply","Polynomial.aeval_eq_prod_aroots_sub_of_monic_of_splits","Polynomial.mapAlgHom_monomial","Polynomial.isRoot_of_aeval_algebraMap_eq_zero","Polynomial.discr_of_degree_eq_three","Polynomial.disc_of_degree_eq_three","Polynomial.natTrailingDegree_one","Polynomial.dvd_comp_X_sub_C_iff","Polynomial.height_eq_height_add_one","Polynomial.ringKrullDim_of_isNoetherianRing","Polynomial.coeff_mul_of_natDegree_le","Polynomial.splits_of_degree_eq_one","Polynomial.isRoot_cyclotomic_iff_charZero","Polynomial.splits_of_natDegree_le_one_of_monic","Polynomial.natDegree_cyclotomic_le","Polynomial.map_div","Polynomial.natSepDegree_C_mul","Polynomial.natSepDegree_C_mul_X_sub_C_pow","Polynomial.roots_ne_zero_of_splits'","Polynomial.coe_smul","Polynomial.separable_X_pow_sub_C'","Polynomial.isUnit_of_isUnit_leadingCoeff_of_isUnit_map","Polynomial.associated_of_dvd_of_degree_eq","Polynomial.resultant_X_pow_left","Polynomial.eq_prod_roots_of_splits","Polynomial.natCast_coeff_zero","Polynomial.map_restriction","Polynomial.toFinsuppIso_apply","Polynomial.evalEval_sum","Polynomial.eq_centerMass_of_eval_derivative_eq_zero","Polynomial.rootSet_derivative_subset_convexHull_rootSet","Polynomial.splits_of_splits_id","Polynomial.ker_constantCoeff","Polynomial.homogenize_map","Polynomial.factorial_mul_shiftedLegendre_eq","Polynomial.neg_one_pow_mul_shiftedLegendre_comp_one_sub_X_eq","Polynomial.shiftedLegendre_eval_symm","Polynomial.nodup_of_separable_prod","Polynomial.exists_finset_of_splits","Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero'","Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero'","Polynomial.abs_tendsto_atTop","Polynomial.abs_isBoundedUnder_iff","Polynomial.trailingDegree_one_le","Polynomial.le_natTrailingDegree_mul","Polynomial.mirror_C","Polynomial.sum_range_pow_eq_bernoulli_sub","Polynomial.bernoulli_succ_eval","Polynomial.natDegree_sub","Polynomial.natDegree_add_le_iff_left","Polynomial.natDegree_sub_le_iff_left","Polynomial.natDegree_sub_le_iff_right","Polynomial.sub_one_pow_totient_le_cyclotomic_eval","Polynomial.toLaurent_apply","Polynomial.surjective_toFn","Polynomial.nextCoeff_ne_zero","Polynomial.ofFn_degree_lt","Polynomial.div_C","Polynomial.trailingDegree_ne_of_natTrailingDegree_ne","Polynomial.toContinuousMapAlgHom_apply","Polynomial.residueFieldMapCAlgEquiv_algebraMap","Polynomial.hasseDeriv_mul","Polynomial.contentIdeal_zero","Polynomial.coeff_ofNat_mul","Polynomial.homogenize_sub","Polynomial.natDegree_integralNormalization","Polynomial.integralNormalization_mul_C_leadingCoeff","Polynomial.resultant_integralNormalization","Polynomial.modByMonicHom_apply","Polynomial.algHom_eval\u2082_algebraMap","Polynomial.subsingleton_isRoot_of_natDegree_eq_one","Polynomial.aevalTower_toAlgHom","Polynomial.eval\u2082_derivative_of_splits","Polynomial.smul_mem_rootSet_iff","Polynomial.hermite_one","Polynomial.C_div","Polynomial.eval\u2082_C_X_eq_coe","Polynomial.ofMultiset_injective","Polynomial.hilbertPoly_X_pow_succ","Polynomial.repr","Polynomial.roots_X_pow","Polynomial.roots_C_mul_X_pow","Polynomial.roots_monomial","Polynomial.eval\u2082_intCastRingHom_X","Polynomial.mul_modByMonic","Polynomial.support_C_mul_X","Polynomial.natSepDegree_smul_nonzero","Polynomial.degreeLT_eq_span_X_pow","Polynomial.not_isField","Polynomial.add_mod","Polynomial.le_trailingDegree_X","Polynomial.nthRoots_two_eq_zero_iff","Polynomial.hasDerivWithinAt_aeval","Polynomial.natTrailingDegree_X","Polynomial.coeff_mapAlgHom_apply","Polynomial.hasFDerivAt_aeval","Polynomial.hasFDerivWithinAt_aeval","Polynomial.valuation_le_one_of_valuation_X_le_one","Polynomial.opRingEquiv_op_X","Polynomial.opRingEquiv_op_C_mul_X_pow","Polynomial.derivative_intCast_mul","Polynomial.monomial_mul_X_pow","Polynomial.X_pow_mul_monomial","Polynomial.splits_comp_of_splits","Polynomial.natDegree_eq_card_roots","Polynomial.splits_map_iff","Polynomial.eval\u2082_at_ofNat","Polynomial.fderivWithin_aeval","Polynomial.natDegree_map_lt'","Polynomial.residueFieldMapCAlgEquiv_symm_X","Polynomial.head?_coeffList","Polynomial.splits_X_sub_C","Polynomial.ofFinsupp_erase","Polynomial.eval\u2082_list_sum","Polynomial.eval_listSum","Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime","Polynomial.chebyshev_U_eq_dickson_two_one","Polynomial.aevalTower_comp_algebraMap","Polynomial.aevalTower_comp_toAlgHom","Polynomial.comap_C_surjective","Polynomial.natDegree_pos_of_eraseLead_ne_zero","Polynomial.degree_eq_one_of_irreducible_of_splits","Polynomial.isCompact_image_comap_of_monic","Polynomial.aeval_pi_apply","Polynomial.derivativeFinsupp_derivative","Polynomial.natDegree_modByMonic_le","Polynomial.disc","Polynomial.resultant_prod_right","Polynomial.resultant_pow_right","Polynomial.degree_sub_C","Polynomial.C_eq_or_isOpenQuotientMap_eval","Polynomial.isOpenQuotientMap_eval","Polynomial.natDegree_pos_of_not_isUnit_of_dvd_monic","Polynomial.subalgebraNontrivial","Polynomial.coeff_natTrailingDegree_ne_zero","Polynomial.fderiv_aeval","Polynomial.finite_range_coeff","Polynomial.mapAlgHom_coe_ringHom","Polynomial.coeff_divByMonic_X_sub_C_rec","Polynomial.coeff_divByMonic_X_sub_C","Polynomial.contraction_degree_eq_or_insep","Polynomial.coe_taylorEquiv","Polynomial.zero_notMem_multiset_map_X_sub_C","Polynomial.evalEval_X","Polynomial.le_rootMultiplicity_map","Polynomial.eq_rootMultiplicity_map","Polynomial.filter_roots_map_range_eq_map_roots","Polynomial.aeval_eq_smeval","Polynomial.aeval_coe_eq_smeval","Polynomial.splits_of_natDegree_le_one","Polynomial.iterate_derivative_one","Polynomial.mkDerivation_one_eq_derivative","Polynomial.pUnitAlgEquiv_symm_toPowerSeries","Polynomial.hilbertPoly_eq_zero_of_le_rootMultiplicity_one","Polynomial.natDegree_hilbertPoly_of_ne_zero","Polynomial.resultant_self_eq_zero","Polynomial.nextCoeff_mul_C","Polynomial.eq_prod_roots_of_monic_of_splits_id","Polynomial.mul_divByMonic_cancel_left","Polynomial.card_roots_le_map","Polynomial.card_roots_le_map_of_injective","Polynomial.derivativeFinsupp_one","Polynomial.eval_homogenize","Polynomial.leadingCoeff_hermite","Polynomial.hermite_monic","Polynomial.ofFinsupp_natCast","Polynomial.resultant_X_sub_C_right","Polynomial.leadingCoeff_smul_integralNormalization","Polynomial.nextCoeff_map_eq_of_isUnit_leadingCoeff","Polynomial.leadingCoeff_one","Polynomial.height_map_C","Polynomial.logMahlerMeasure_mul_eq_add_logMahelerMeasure","Polynomial.support_map_of_injective","Polynomial.cauchyBound_zero","Polynomial.coe_aeval_eq_evalRingHom","Polynomial.coeff_zero_eq_zero_of_zero_isRoot","Polynomial.hermite_eq_deriv_gaussian'","Polynomial.le_natDegree_of_coe_le_degree","Polynomial.toFinsupp_C_mul_X_pow","Polynomial.algEquivAevalNegX_apply","Polynomial.zero_notMem_multiset_map_X_add_C","Polynomial.coeff_inj","Polynomial.cauchyBound_one","Polynomial.isFixedPt_newtonMap_of_isUnit_iff","Polynomial.natDegree_eq_card_roots'","Polynomial.aroots_one","Polynomial.degree_zero_le","Polynomial.trailingDegree_X_pow","Polynomial.root_mul_right_of_isRoot","Polynomial.head_coeffList","Polynomial.quotientSpanXSubCAlgEquiv_mk","Polynomial.normUnit_content","Polynomial.degree_cubic_lt","Polynomial.divX_C_mul_X_pow","Polynomial.contract_expand","Polynomial.C_mem_lifts","Polynomial.mapAlgHom_eq_eval\u2082AlgHom'_CAlgHom","Polynomial.addHom_ext'_iff","Polynomial.monomial_mem_lifts_and_degree_eq","Polynomial.gaussNorm_monomial","Polynomial.toLaurent_ne_zero","Polynomial.disc_of_degree_eq_one","Polynomial.coeff_zero_eq_leadingCoeff_mul_prod_roots_of_splits","Polynomial.wronskian_neg_right","Polynomial.irreducible_iff_roots_eq_zero_of_degree_le_three","Polynomial.irreducible_of_degree_le_three_of_not_isRoot","Polynomial.nextCoeffUp_C_eq_zero","Polynomial.reverse_C_add","Polynomial.splits_of_degree_le_zero","Polynomial.algEquivAevalXAddC_symm_apply","Polynomial.constantCoeff_coe","Polynomial.toMvPolynomial_injective","Polynomial.le_trailingDegree_C_mul_X_pow","Polynomial.iterate_derivative_mul_X","Polynomial.integralNormalization_C","Polynomial.toFinsuppIsoAlg_apply","Polynomial.coeff_mul_monomial_zero","Polynomial.resultant_zero_zero","Polynomial.dickson_one_one_eval_add_inv","Polynomial.subsingleton_iff_subsingleton","Polynomial.forall_eq_iff_forall_eq","Polynomial.natDegree_X_mul","Polynomial.coe_compRingHom_apply","Polynomial.exists_dvd_map_of_isAlgebraic","Polynomial.constantCoeff_surjective","Polynomial.dickson_one_one_zmod_p","Polynomial.dickson_one_one_charP","Polynomial.instIsLocalHomRingHomAlgebraMap","Polynomial.not_isUnit_of_degree_pos_of_isReduced","Polynomial.monomial_eq_monomial_iff","Polynomial.X_ne_C","Polynomial.eval_derivative_of_splits","Polynomial.splits_of_natDegree_eq_two","Polynomial.eval\u2082RingHom'_apply","Polynomial.eval_derivative_div_eval_of_ne_zero_of_splits","Polynomial.dickson_two","Polynomial.sup_aeval_range_eq_top_of_isCoprime","Polynomial.eq_of_natDegree_lt_card_of_eval_eq'","Polynomial.degree_eq_card_roots","Polynomial.roots_expand_map_frobenius_le","Polynomial.mem_iff_eq_smul_annIdealGenerator","Polynomial.eq_of_degree_le_of_eval_finset_eq","Polynomial.resultant_X_add_C_right","Polynomial.eval\u2082_modByMonic_eq_self_of_root","Polynomial.isMonicOfDegree_two_iff","Polynomial.isMonicOfDegree_two_iff'","Polynomial.aeval_endomorphism","Polynomial.cyclotomic_eval_le_add_one_pow_totient","Polynomial.eval\u2082_list_prod_noncomm","Polynomial.leadingCoeff_sub_of_degree_lt'","Polynomial.natDegree_sum_eq_of_disjoint","Polynomial.eval_monomial_one_add_sub","Polynomial.isRoot_of_isRoot_of_dvd_derivative_mul","Polynomial.valuation_aeval_monomial_eq_valuation_pow","Polynomial.valuation_aeval_eq_valuation_X_pow_natDegree_of_one_lt_valuation_X","Polynomial.resultant_C_zero_right","Polynomial.prod_X_sub_C_nextCoeff","Polynomial.gaussNorm_lt_one_iff_contentIdeal_le","Polynomial.contentIdeal_eq_top_iff_forall_gaussNorm_eq_one","Polynomial.tendsto_nhds_iff","Polynomial.expand_char","Polynomial.rootOfSplits'_eq_rootOfSplits","Polynomial.intCast_comp","Polynomial.degree_restriction","Polynomial.natDegree_restriction","Polynomial.monic_restriction","Polynomial.evalEval_natCast","Polynomial.add_scaleRoots_of_natDegree_eq","Polynomial.not_isUnit_X_pow_sub_one","Polynomial.units_coeff_zero_smul","Polynomial.rootsExpandToRoots_apply","Polynomial.mul_X_pow_comp","Polynomial.mkDerivationEquiv_apply","Polynomial.monic_generator_eq_minpoly","Polynomial.algEquivCMulXAddC_apply","Polynomial.eval_eq_prod_roots_sub_of_monic_of_splits_id","Polynomial.degreeLE_mono","Polynomial.degree_neg_le_of_le","Polynomial.algEquivAevalXAddC_apply","Polynomial.ofFn_zero'","Polynomial.nextCoeffUp_of_constantCoeff_eq_zero","Polynomial.divByMonic_one","Polynomial.evalEval_sub","Polynomial.monic_geom_sum_X","Polynomial.evalEval_add","Polynomial.nthRoots_two_one","Polynomial.homogenize_monomial_of_lt","Polynomial.coeff_homogenize","Polynomial.ofMultiset_apply","Polynomial.not_dvd_of_degree_lt","Polynomial.fwdDiff_iter_eq_zero_of_degree_lt","Polynomial.fwdDiff_iter_degree_add_one_eq_zero","Polynomial.rootsExpandPowToRoots_apply","Polynomial.cyclotomic_eq_prod_X_pow_sub_one_pow_moebius","Polynomial.support_X_empty","Polynomial.support_update_zero","Polynomial.eval_map_apply","Polynomial.algEquivOfCompEqX_symm_apply","Polynomial.derivative'_apply","Polynomial.ctorIdx","Polynomial.card_roots_map_le_degree","Polynomial.splits_X","Polynomial.derivative_C_mul_X","Polynomial.eq_of_degree_le_of_eval_index_eq","Polynomial.leadingCoeff_X_pow_add_one","Polynomial.resultant_C_left","Polynomial.mod_eq_self_iff","Polynomial.div_eq_zero_iff","Polynomial.isCoprime_scaleRoots","Polynomial.signVariations_eraseLead","Polynomial.support_X","Polynomial.natDegree_cubic_le","Polynomial.degree_pos_of_aeval_root","Polynomial.coeff_sub_eq_left_of_lt","Polynomial.leadingCoeff_opRingEquiv","Polynomial.trailingCoeff_mul","Polynomial.coe_eq_one_iff","Polynomial.card_roots_le_one_of_irreducible","Polynomial.coe_neg","Polynomial.dvd_mul_leadingCoeff_inv","Polynomial.splits_of_splits_gcd_left","Polynomial.leadingCoeff_sum_of_degree_eq","Polynomial.support_C_subset","Polynomial.eval_surjective","Polynomial.map_contract","Polynomial.algHom_ext'_iff","Polynomial.comp_neg_X_comp_neg_X","Polynomial.contentIdeal_eq_top_of_contentIdeal_mul_eq_top","Polynomial.cyclotomic_prime_mul_X_sub_one","Polynomial.aevalTower_id","Polynomial.contDiff_aeval","Polynomial.eraseLead_X","Polynomial.toFn_zero","Polynomial.unique_int_coeff_of_cycl","Polynomial.bernoulli_eval_neg","Polynomial.smeval_mul_X_pow","Polynomial.aeval_derivative_of_splits","Polynomial.exists_max_root","Polynomial.update_eq_add_sub_coeff","Polynomial.supDegree_eq_degree","Polynomial.degree_leadingCoeff_inv","Polynomial.trailingDegree_lt_wf","Polynomial.coeff_mul_intCast","Polynomial.abs_tendsto_atTop_iff","Polynomial.exists_root_of_splits","Polynomial.restriction_zero","Polynomial.C_smul_derivation_apply","Polynomial.natDegree_lt_coeff_mul","Polynomial.splits_of_splits_gcd_right","Polynomial.valuation_eq_valuation_X_pow_natDegree_of_one_lt_valuation_X","Polynomial.iterate_derivative_eq_zero_of_degree_lt","Polynomial.dvd_C_mul","Polynomial.root_or_root_of_root_mul","Polynomial.algEquivOfCompEqX_eq_iff","Polynomial.algEquivAevalXAddC_eq_iff","Polynomial.prod_roots_eq_coeff_zero_of_monic_of_splits","Polynomial.resultant_one_left","Polynomial.coeff_hermite_of_odd_add","Polynomial.hilbertPoly_add_left","Polynomial.adjoin_rootSet_eq_range","Polynomial.natDegree_sub_eq_left_of_natDegree_lt","Polynomial.eval\u2082_list_prod","Polynomial.smeval_X_pow","Polynomial.rootMultiplicity_expand","Polynomial.orderOf_root_cyclotomic_dvd","Polynomial.comp_one","Polynomial.resultant_C_zero_left","Polynomial.sumIDeriv_apply_of_lt","Polynomial.monomial_zero_one","Polynomial.exists_irreducible_of_natDegree_ne_zero","Polynomial.differentiableWithinAt","Polynomial.natTrailingDegree_le_natTrailingDegree","Polynomial.support_C_mul_X'","Polynomial.derivation_ext_iff","Polynomial.modByMonic_eq_zero_iff_quotient_eq_zero","Polynomial.splits_iff","Polynomial.resultant_eq_zero_of_lt_lt","Polynomial.gaussNorm_nonneg","Polynomial.degree_prod_of_monic","Polynomial.mkDerivationEquiv_symm_apply","Polynomial.restriction_one","Polynomial.separable_prod","Polynomial.evalEval_pow","Polynomial.le_gaussNorm","Polynomial.sumIDeriv_C","Polynomial.integralNormalization_eval\u2082_eq_zero","Polynomial.toFinsuppIsoLinear_apply","Polynomial.of_irreducible_expand_pow","Polynomial.cyclotomic_dvd_geom_sum_of_dvd","Polynomial.leadingCoeff_add_of_degree_eq","Polynomial.leadingCoeff_sub_of_degree_eq","Polynomial.disc_of_degree_eq_two","Polynomial.forall_iff_forall_finsupp","Polynomial.linearIndependent_powers_iff_aeval","Polynomial.taylor_X_pow","Polynomial.natSepDegree_X_pow","Polynomial.eraseLead_a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