RingHom đ | CompData | 4863 mathmath: IsLocalization.algebraMap_apply_eq_map_map_submonoid, WeierstrassCurve.Jacobian.map_addX, Polynomial.mul_div_eq_iff_isRoot, DFinsupp.coprodMap_apply, Complex.norm_conj, MvPowerSeries.coeff_zero_eq_constantCoeff_apply, MvPolynomial.funext_iff, MvPolynomial.eval_indicator_apply_eq_one, IsLocalization.AtPrime.coe_primeSpectrumOrderIso_symm_apply_asIdeal, IsAlgebraic.exists_nonzero_dvd, IsLocalization.localization_localization_isLocalization_of_has_all_units, PresheafOfModules.Monoidal.tensorObj_obj, CommSemiRingCat.forget_obj, MvPowerSeries.hasSubst_def, WeierstrassCurve.Projective.map_dblZ, Polynomial.not_ker_le_map_C_of_surjective_of_quasiFiniteAt, KaehlerDifferential.kerCotangentToTensor_toCotangent, RCLike.conj_re, NumberField.basisMatrix_eq_embeddingsMatrixReindex, Polynomial.isUnit_C_add_X_mul_iff, PrimeSpectrum.closure_range_comap, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', Polynomial.isMonicOfDegree_X_add_one, Algebra.IsUnramifiedAt.exists_primesOver_under_adjoin_eq_singleton_and_residueField_bijective, Polynomial.natDegree_mul_leadingCoeff_inv, minpoly_sub_algebraMap_splits, CliffordAlgebra.contractRight_algebraMap_mul, Complex.log_conj_eq_ite, smoothSheafCommRing.Κ_forgetStalk_inv, Orientation.kahler_map_complex, Ideal.Quotient.exists_algHom_fixedPoint_quotient_under, IsDedekindDomain.differentIdeal_dvd_map_differentIdeal, Polynomial.ker_mapRingHom, NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingOfIsReal, AlgebraicGeometry.SurjectiveOnStalks.eq_stalkwise, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst_assoc, IntermediateField.AdjoinSimple.trace_gen_eq_sum_roots, IsLocalization.map_radical, Language.map_kstar, ValuationRing.mem_integer_iff, RootPairing.RootPositiveForm.algebraMap_rootLength, NumberField.InfinitePlace.isNontrivial, LaurentPolynomial.degree_C_mul_T_ite, MeasureTheory.lpNorm_conj, RingTheory.Sequence.isWeaklyRegular_map_algebraMap_iff, WeierstrassCurve.Projective.map_neg, Polynomial.X_pow_mul_assoc_C, CommRingCat.forgetâRing_preservesLimitsOfSize, NumberField.InfinitePlace.eq_iff_isEquiv, WittVector.ghostMap.bijective_of_invertible, Polynomial.separable_X_add_C, Polynomial.map_dickson, Polynomial.mahlerMeasure_const, Algebra.RingHom.adjoin_algebraMap_apply, LinearMap.BilinForm.dualSubmoduleParing_spec, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, CommRingCat.KaehlerDifferential.map_d, LinearMap.IsSymmetric.conj_eigenvalue_eq_self, MvPolynomial.coe_C, RingHom.ker_evalRingHom, Algebra.idealMap_eq_ofEq_comp_toLocalizedâ, AlgebraicGeometry.StructureSheaf.instIsScalarTowerCarrierStalkCommRingCatStructurePresheafInCommRingCatCarrierAbPresheafOpensCarrierTopModuleStructurePresheaf, MvPowerSeries.coeff_zero_eq_constantCoeff, CliffordAlgebra.contractRight_algebraMap, ExteriorAlgebra.isLocalHom_algebraMap, coe_iterateFrobenius_mul, PerfectionMap.lift_symm_apply, AddMonoidAlgebra.lift_apply', ModularForm.smul_slash, WeierstrassCurve.map_aâ, Polynomial.eq_C_of_derivative_eq_zero, MvPolynomial.map_bindâ, jacobiThetaâ_conj, GaussianInt.toComplex_mul, Orthonormal.inner_left_finsupp, Valuation.IsTrivialOn.valuation_algebraMap_le_one, Polynomial.derivative_X_sq, cfc_le_algebraMap_iff, Polynomial.coe_normUnit_of_ne_zero, PowerSeries.constantCoeff_expand, Subsemiring.coe_subtype, Polynomial.separable_X_pow_sub_C_unit, CommSemiRingCat.hom_inv_apply, Polynomial.splits_iff_exists_multiset, CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_snd, IsIntegrallyClosed.exists_algebraMap_eq_of_isIntegral_pow, ValuationSubring.mem_comap, Algebra.norm_algebraMap_of_basis, derivationToSquareZeroOfLift_apply, Complex.sinh_conj, Polynomial.toLaurent_eq_zero, CategoryTheory.Functor.mapExtLinearMap_toAddMonoidHom, IsDedekindDomain.HeightOneSpectrum.equivPrimesOver_apply, MvPolynomial.map_mapRange_eq_iff, IsLocalRing.ResidueField.algebraMap_residue, exists_isIdempotentElem_eq_of_ker_isNilpotent, RootPairing.linearIndepOn_root_baseOf', taylorWithin_succ, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply, PolyEquivTensor.toFunBilinear_apply_eq_sum, Valuation.FiniteField.algebraMap_le_one, Polynomial.algEquivCMulXAddC_apply, Polynomial.mul_divByMonic_eq_iff_isRoot, IsUltrametricDist.algNormOfAlgEquiv_extends, Valuation.FiniteField.algebraMap_eq_one, CommRingCat.instFullRingCatForgetâRingHomCarrierCarrier, galRestrict_symm_algebraMap_apply, NumberField.InfinitePlace.norm_embedding_of_isReal, Polynomial.monic_X_sub_C, PadicInt.lift_sub_val_mem_span, MvPolynomial.evalâHom_X, RatFunc.num_div, Algebra.algebraMap_self_apply, Subring.coe_subtype, MonomialOrder.monic_X_sub_C, MvPolynomial.hom_C, RingCat.FilteredColimits.instPreservesFilteredColimitsAddCommGrpCatForgetâRingHomCarrierAddMonoidHomCarrier, Valuation.HasExtension.val_map_le_iff, AlgebraicGeometry.StructureSheaf.globalSectionsIso_inv, quasispectrum.algebraMap_mem, CommRingCat.forget_preservesLimitsOfSize, IntermediateField.LinearDisjoint.linearIndependent_right', IsAdicComplete.StrictMono.mk_liftRingHom, PowerSeries.constantCoeff_subst, ExteriorAlgebra.Κ_eq_algebraMap_iff, Matrix.scalar_inj, Submodule.algebraMap_mem, Polynomial.homogenize_map, CommRingCat.forgetReflectIsos, BoolRing.hasForgetToBoolAlg_forgetâ_obj_coe, Subring.coe_comap, CStarAlgebra.mem_Icc_algebraMap_iff_norm_le, RingHom.mul_def, AlgebraicGeometry.RingedSpace.basicOpen_res, Localization.algebraMap_injective_of_span_eq_top, Complex.lim_conj, PowerSeries.coeff_mul_C, LocalSubring.range_toSubring, NumberField.canonicalEmbedding.mem_span_latticeBasis, Polynomial.algebraMap_pi_eq_aeval, NumberField.integralBasis_apply, IsLocalization.Away.algebraMap_isUnit_iff, ModuleCat.restrictScalarsCongr_symm, Polynomial.ker_evalRingHom, StandardEtalePair.inv_aeval_X_g, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv, Polynomial.evalâ_intCastRingHom_X, IsIntegrallyClosedIn.isIntegral_iff, ValuationSubring.integralClosure_algebraMap_injective, Ideal.mem_span_iff_exists_isHomogeneous, IsPurelyInseparable.minpoly_eq', CommRingCat.closure_range_union_range_eq_top_of_isPushout, IntermediateField.algebraMap_mem, Matrix.GeneralLinearGroup.map_det, LaurentPolynomial.mk'_mul_T, Polynomial.expand_eq_sum, IsLocalization.AtPrime.liesOver_map_of_liesOver, Polynomial.root_X_sub_C, PowerSeries.heval_C, Algebra.Norm.Transitivity.polyToMatrix_cornerAddX, RingHomInvPair.comp_apply_eqâ, Matrix.scalar_comm, frobeniusEquiv_apply, NumberField.mixedEmbedding.convexBodyLT'_mem, Complex.kahler, X_pow_sub_C_splits_of_isPrimitiveRoot, Complex.areaForm, Complex.re_eq_add_conj, Differential.implicitDeriv_C, CliffordAlgebraComplex.ofComplex_conj, AlgHom.coe_toRingHom, Pi.algebraMap_apply, WittVector.coeff_truncate, GaussianInt.intCast_im, WeierstrassCurve.VariableChange.map_s, IntermediateField.algHomEquivAlgHomOfSplits_apply_apply, RingHom.IsIntegralElem.map, WeierstrassCurve.Affine.CoordinateRing.smul, Polynomial.resultant_X_add_C_right, Polynomial.pow_rootMultiplicity_dvd, IsLocalization.minimalPrimes_map, MulSemiringAction.toRingHom_apply, AlgebraicGeometry.surjectiveOnStalks_iff, AdjoinRoot.minpoly_root, PowerSeries.coeff_rescale, AlgHom.coe_ringHom_injective, X_pow_sub_C_eq_prod, PositiveLinearMap.apply_le_of_isSelfAdjoint, WeierstrassCurve.Projective.eval_polynomial, IntermediateField.coe_algebraMap_over_bot, IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_apply_mk, Polynomial.rootMultiplicity_eq_rootMultiplicity, RingTheory.Sequence.isWeaklyRegular_cons_iff', NumberField.isCoprime_differentIdeal_of_isCoprime_discr, WittVector.mapFun.zero, WithAbs.algebraMap_left_apply, RootPairing.Base.algebraMap_cartanMatrixIn_apply, MvPolynomial.aeval_algebraMap_eq_zero_iff, NumberField.FinitePlace.mk_apply, RingHom.instRingHomClass, BoundedContinuousFunction.algebraMap_apply, MonoidAlgebra.isLocalHom_algebraMap, coe_frobeniusEquiv_symm_comp_coe_frobenius, spectrumRestricts_iff, GaussianInt.toComplex_def', CoalgHom.coe_addMonoidHom_injective, Algebra.adjoin_algebraMap_image_union_eq_adjoin_adjoin, HahnSeries.C_injective, Ideal.map_ofList, IsLocalization.mk'_spec_mk, IsLocalization.AtPrime.coe_orderIsoOfPrime_apply_coe, differentIdeal_eq_differentIdeal_mul_differentIdeal, RingCon.ker_apply, smoothSheafCommRing.nonunits_stalk, RingHom.star_apply, FractionalIdeal.coeIdealHom_apply, qExpansionRingHom_apply, AlgHom.ker_coe, Polynomial.derivative_C_mul, Algebra.algebraMap_ofSubsemiring_apply, Polynomial.aeval_algebraMap_apply_eq_algebraMap_eval, NumberField.canonicalEmbedding.latticeBasis_apply, Polynomial.support_trinomial, WittVector.constantCoeff_surjective, IsLocalRing.ker_residue, PowerSeries.spanFinrank_le_spanFinrank_map_constantCoeff_add_one_of_X_mem, AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_symm_mk, PerfectClosure.mk_mul_mk, RatFunc.num_div_dvd, FractionalIdeal.coeIdeal_span_singleton, Ideal.exists_mem_span_singleton_map_residueField_eq, AlgebraicGeometry.LocallyRingedSpace.notMem_prime_iff_unit_in_stalk, algebraicIndependent_iff_ker_eq_bot, MonoidAlgebra.mapRangeRingHom_single, IsBaseChange.basis_repr_comp_apply, NumberField.InfinitePlace.le_iff_le, Ideal.smul_top_eq_map, PreTilt.valAux_eq, MvPolynomial.IsSymmetric.map, AlgHom.coe_addMonoidHom_injective, Polynomial.Chebyshev.algebraMap_eval_U, IsLocalization.Away.algebraMap_pow_isUnit, NumberField.norm_norm_le_norm_mul_house_pow, Polynomial.rootMultiplicity_eq_natTrailingDegree, Polynomial.aeval_algebraMap_eq_zero_iff, Ideal.algebraMap_quotient_injective, Algebra.algebraMap_eq_smul_one', PolynomialModule.eval_map, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul', Matrix.det_det, IsLocalization.coeSubmodule_span, SkewMonoidAlgebra.lift_apply', RCLike.star_def, DirectLimit.Module.of_f, Polynomial.div_def, RingHom.rangeRestrict_surjective, Cubic.of_a_eq_zero', WittVector.mapFun.nsmul, Polynomial.C_inj, MvPolynomial.isEmptyRingEquiv_apply, WittVector.ghostComponent_apply, MvPowerSeries.rescaleUnit, DoubleQuot.coe_quotQuotEquivQuotOfLEâ_symm, MvPolynomial.ker_map, Polynomial.prod_X_sub_C_nextCoeff, Algebra.IsPushout.equiv_symm_algebraMap_left, Polynomial.mem_roots_sub_C', WittVector.ghostComponent_verschiebungFun, Ideal.ker_algebraMap_residueField, Polynomial.Monic.leadingCoeff_C_mul, SemiRingCat.inv_hom_apply, RatFunc.laurent_X, Ideal.mem_leadingCoeffNth_zero, Polynomial.leadingCoeff_quadratic, Multiset.prod_X_sub_X_eq_sum_esymm, NumberField.isInfinitePlace_iff, ContinuousLinearMap.toContinuousAddMonoidHom_add, AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, Polynomial.coeffList_C_mul, Polynomial.support_C_mul_X, IsIntegrallyClosed.isIntegral_iff, RCLike.algebraMap_eq_ofReal, NumberField.IsCMField.equivInfinitePlace_symm_apply, SemiRingCat.comp_apply, Polynomial.nnqsmul_eq_C_mul, DividedPowers.IsDPMorphism.ideal_comp, Polynomial.leadingCoeff_C_mul_of_isUnit, CFC.exists_pos_algebraMap_le_iff, RCLike.inner_apply', AlgebraicGeometry.isIso_SpecMap_iff, IsLocalization.to_map_eq_zero_iff, Polynomial.aroots_X_sub_C, Complex.conj_inv, Polynomial.fiberEquivQuotient_tmul, Localization.AtPrime.mapPiEvalRingHom_bijective, NNReal.coe_toRealHom, MvPolynomial.optionEquivLeft_C, NumberField.InfinitePlace.isometry_embedding, Polynomial.degree_quadratic_lt, Matrix.isParabolic_iff_exists, IntermediateField.coe_bot, Ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem, WeierstrassCurve.Projective.comp_equiv_comp, WeierstrassCurve.Affine.CoordinateRing.basis_one, ValuativeExtension.srel_iff_srel, AlgebraicGeometry.Scheme.mem_basicOpen', NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isComplex, MvPolynomial.iterToSum_sumToIter, Polynomial.C_mul_X_eq_monomial, Algebra.Generators.toAlgHom_ofComp_localizationAway, eval_det_add_X_smul, PadicComplex.coe_eq, Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq, TensorProduct.piScalarRight_symm_algebraMap, RCLike.sub_conj, NumberField.mem_maximalRealSubfield_iff, RingHom.rangeS_eq_top, LaurentSeries.LaurentSeriesRingEquiv_def, Polynomial.logMahlerMeasure_C_mul, WittVector.mapFun.add, MvPowerSeries.constantCoeff_subst, StarSubalgebra.range_le, Polynomial.C_1, Matrix.GeneralLinearGroup.mem_center_iff_val_mem_range_scalar, Ideal.map_fst_prod, evalâ_minpolyDiv_of_evalâ_eq_zero, CommRingCat.id_apply, RingHom.Bijective.respectsIso, PowerSeries.algebraMap_apply'', minpoly_algebraMap_add_splits, RingHom.map_neg, Complex.star_def, WeierstrassCurve.Ďâ_sq, Algebra.lmul_algebraMap, EuclideanSpace.inner_single_left, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul, MvPolynomial.optionEquivLeft_X_some, Valuation.HasExtension.instIsLocalHomSubtypeMemValuationSubringValuationSubringRingHomAlgebraMap, Unitization.splitMul_apply, Polynomial.monic_X_pow_add_C, Polynomial.monic_multisetProd_X_sub_C, NumberField.CMExtension.algebraMap_equivMaximalRealSubfield_symm_apply, MvPolynomial.evalâHom_monomial, Matrix.charpoly_map, SkewMonoidAlgebra.single_algebraMap_eq_algebraMap_mul_of, Valuation.IsTrivialOn.eq_one, DoubleCentralizer.nnnorm_def', IsArtinianRing.localization_surjective, frobenius_one, Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero, WeierstrassCurve.Jacobian.map_dblX, PowerSeries.spanFinrank_le_spanFinrank_map_constantCoeff_add_one_of_isPrime, Polynomial.leadingCoeff_det_X_one_add_C, Ideal.comap_cotangentIdeal, WittVector.frobeniusEquiv_symm_apply, Polynomial.quotientSpanXSubCAlgEquiv_symm_apply, Complex.nndist_self_conj, faithfulSMul_iff_algebraMap_injective, NumberField.mixedEmbedding.norm_eq_norm, TopCommRingCat.instReflectsIsomorphismsTopCatForgetâSubtypeRingHomÎąContinuousCoeContinuousMapCarrier, DoubleQuot.coe_quotQuotMkâ, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap_apply, BoolAlg.hasForgetToBoolRing_forgetâ_obj_carrier, Polynomial.coeff_zero_of_isScalarTower, X_pow_sub_C_irreducible_iff_of_odd, Subring.coe_inclusion, WeierstrassCurve.Jacobian.baseChange_polynomialZ, Polynomial.zero_notMem_multiset_map_X_sub_C, Polynomial.card_roots_sub_C', Irreducible.natSepDegree_eq_one_iff_of_monic', IsLocalization.surj, Algebra.Presentation.localizationAway_relation, Polynomial.coeff_map, MeasureTheory.charFun_neg, MvPolynomial.monomial_finsupp_sum_index, KaehlerDifferential.cotangentComplexBaseChange_tmul, Polynomial.eq_C_of_degree_eq_zero, QuadraticAlgebra.algebraMap_inj, NumberField.FinitePlace.norm_def', IsPRadical.pow_mem, quasispectrumRestricts_iff, IsLocalRing.instIsLocalHomRingHomOfNontrivial, IsBaseChange.of_fintype_basis_eq, QuasispectrumRestricts.rightInvOn, Polynomial.nextCoeffUp_C_eq_zero, X_pow_sub_C_irreducible_of_odd, Polynomial.derivative_pow_succ, IsLocalization.algEquivOfAlgEquiv_eq, Circle.ofConjDivSelf_coe, IsLocalRing.finrank_quotient_map, NumberField.mixedEmbedding.mem_idealLattice, smoothSheafCommRing.Κ_evalHom_apply, StandardEtalePresentation.toPresentation_algebra_smul, cyclotomicCharacter.toZModPow, BoxIntegral.unitPartition.mem_smul_span_iff, Ideal.comap_map_eq_self_of_faithfullyFlat, InnerProductSpace.Core.inner_smul_left, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, NumberField.Units.regOfFamily_eq_det, minpoly.eq_of_irreducible, RingCat.Colimits.cocone_naturality_components, Ideal.quotient_map_C_eq_zero, LinearMap.toAddMonoidHom_mulLeft, cfc_apply_one, Module.End.isFinitelySemisimple_sub_algebraMap_iff, PrimeSpectrum.denseRange_comap_iff_ker_le_nilRadical, Polynomial.natDegree_X_pow_sub_C, UpperHalfPlane.specialLinearGroup_apply, RCLike.conj_nat_cast, Polynomial.Monic.natSepDegree_eq_one_iff_of_irreducible', IsLocalization.algEquiv_apply, SemilinearMapClass.toMulActionSemiHomClass, PowerSeries.degree_weierstrassMod_lt, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C, MvPolynomial.evalâ_zero'_apply, Polynomial.evalâ_hom, CategoryTheory.Linear.smulOfRingMorphism_smul_eq', NumberField.FinitePlace.embedding_apply, RingHom.mapMatrix_apply, Complex.conjLIE_apply, Polynomial.roots_C_mul_X_pow, Circle.starRingEnd_addChar, MvPolynomial.degreeOf_C, IsAdjoinRoot.adjoinRootAlgEquiv_symm_apply_eq_mk, Valuation.Integers.isPrincipal_iff_exists_isGreatest, MaximalSpectrum.toPiLocalization_apply_apply, QuadraticAlgebra.norm_algebraMap, MvPowerSeries.mapAlgHom_apply, WeierstrassCurve.Projective.polynomial_relation, IsLocalization.mk'_tmul, RingHom.surjective_of_tmul_eq_tmul_of_finite, WeierstrassCurve.Jacobian.map_negDblY, TruncatedWittVector.iInf_ker_truncate, Algebra.coe_algebraMap_ofSubring, Localization.algEquiv_apply, RingCon.comap_bot, Complex.cosh_conj, RatFunc.laurent_algebraMap, AlgebraicIndependent.repr_ker, AlgebraicGeometry.SpecMap_preimage_basicOpen, Polynomial.iterate_derivative_eq_factorial_smul_sum, HahnSeries.ofPowerSeries_X_pow, CommRingCat.mkUnder_ext_iff, AlgHom.IsArithFrobAt.mk_apply, Ideal.map_mk_comap_factor, Polynomial.iterate_derivative_X_add_pow, MvPolynomial.mem_range_map_iff_coeffs_subset, PowerBasis.quotientEquivQuotientMinpolyMap_apply, DoubleQuot.coe_quotLeftToQuotSupâ, RCLike.re_add_im_ax, PreInnerProductSpace.Core.smul_left, WeierstrassCurve.Projective.map_negAddY, Polynomial.Chebyshev.S_eq_U_comp_half_mul_X, Matrix.map_swap, Complex.oangle, AlgebraicGeometry.Scheme.ideal_ker_le_ker_ÎSpecIso_inv_comp, NumberField.InfiniteAdeleRing.algebraMap_apply, Algebra.injective_of_transcendental, IntermediateField.botEquiv_symm, Ideal.quotientInfToPiQuotient_inj, MvPolynomial.exists_dvd_map_of_isAlgebraic, Cubic.disc_eq_prod_three_roots, NumberField.Units.dirichletUnitTheorem.seq_decreasing, smoothSheafCommRing.eval_germ, Matrix.SpecialLinearGroup.scalar_eq_self_of_mem_center, Polynomial.degree_C_mul_of_isUnit, UpperHalfPlane.Ď_sq, frobenius_natCast, MvPowerSeries.WithPiTopology.isTopologicallyNilpotent_iff_constantCoeff_isNilpotent, WittVector.map_teichmuller, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero', PreTilt.coeff_pow_p, RestrictScalars.ringEquiv_algebraMap, Matrix.blockDiagonal'RingHom_apply, RCLike.is_real_TFAE, Polynomial.degree_mul_leadingCoeff_inv, PerfectClosure.frobenius_mk, ContinuousMap.toNNReal_neg_algebraMap, Submodule.quotientPi_aux.map_smul, RingHom.mem_fieldRange_self, Polynomial.eq_prod_roots_of_splits, Polynomial.map_injective_iff, Polynomial.eq_prod_roots_of_monic_of_splits_id, WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_C, Ideal.torsionMapQuot_apply, AnalyticOnNhd.eval_linearMap', Algebra.adjoin_singleton_algebraMap, inner_gradientWithin_right, Algebra.TensorProduct.algebraMap_apply, IsLocalization.Away.sec_spec, Ideal.Quotient.algEquivOfEqMap_apply, InnerProductSpace.smul_left, MvPowerSeries.map_algebraMap_eq_subst_X, Ideal.Quotient.factor_mk, IsLocalization.mem_span_map, MvPolynomial.optionEquivLeft_apply, minpoly_algHom_toLinearMap, NonUnitalStarSubalgebra.unitizationStarAlgEquiv_apply_coe, Set.algebraMap_mem_centralizer, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eqâ, Ideal.Factors.fact_ramificationIdx_neZero, CommRingCat.forgetâCommSemiRing_preservesLimitsOfSize, Polynomial.prime_C_iff, Ideal.algebraMap_quotient_residueField_mk, AdjoinRoot.mk_surjective, PowerSeries.coeff_ne_zero_C, Field.localization_map_bijective, AlgebraicGeometry.localRingHom_comp_stalkIso_apply, WittVector.map_coeff, exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensional, Matrix.mem_range_scalar_iff_commute_transvectionStruct, IsLocalization.isUnit_comp, RingCat.forgetâAddCommGroup_preservesLimits, FractionalIdeal.coe_extendedHomâ_eq_span, IsIntegralClosure.algebraMap_lift, HomogeneousLocalization.range_awayMapAux_subset, Algebra.IsPushout.cancelBaseChange_symm_tmul, Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C, IsCyclotomicExtension.isCyclotomicExtension_zero_iff, conjneg_conj, CommAlgCat.forgetâ_commRingCat_obj, WeierstrassCurve.Jacobian.eval_polynomialY, Ideal.quotientInfToPiQuotient_surj, RingHom.id_apply, DirectLimit.Module.lift_of, WeierstrassCurve.Affine.CoordinateRing.coe_basis, SemilinearMapClass.distribMulActionSemiHomClass, Polynomial.natSepDegree_X_sub_C_pow, inner_smul_left_eq_star_smul, IsLocalization.algEquivOfAlgEquiv_apply, RCLike.mul_conj, Polynomial.isMonicOfDegree_two_iff', Polynomial.not_isRoot_C, algebraMapCLM_coe, RCLike.norm_conj, MvPolynomial.constantCoeff_rename, AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_comap_ideal, Multiset.prod_X_add_C_coeff, Valuation.Integers.exists_of_le_one, CommRingCat.forget_obj, Ideal.map_spanIntNorm, MvPolynomial.map_bindâ, Polynomial.natDegree_C_add, Algebra.map_leftMulMatrix_localization, Field.isSeparable_algebraMap, Cubic.c_eq_three_roots, QuotientMapQuotient.isNoetherian, PowerSeries.mapAlgHom_apply, Polynomial.Monic.eq_X_pow_char_pow_sub_C_pow_of_natSepDegree_eq_one, PresheafOfModules.Derivation.d_map, IsLocalizedModule.iso_apply_mk, Polynomial.C_mul', Polynomial.eraseLead_add_C_mul_X_pow, KaehlerDifferential.kerToTensor_apply, AlgEquiv.prodQuotientOfIsIdempotentElem_apply, RatFunc.laurent_div, CFC.negPart_algebraMap, MvPolynomial.iterToSum_C_X, FractionalIdeal.coe_mem_one, minpoly.natSepDegree_eq_one_iff_eq_X_pow_sub_C, MvPolynomial.map_evalâ, MvPolynomial.eval_map, AlgebraicGeometry.ValuativeCriterion.Existence.instIsLocalHomCarrierRingHomHomHomCommRingCat, Polynomial.isMonicOfDegree_X_sub_one, WittVector.mapFun.one, CommRingCat.free_map_coe, RingHom.coe_monoidHom_id, IsLocalization.AtPrime.comap_map_eq_map, Algebra.Generators.defaultHom_val, MvPolynomial.map_evalâHom, DoubleQuot.quotQuotEquivQuotOfLEâ_symm_toRingEquiv, AlgebraNorm.extends_norm, LinearMap.sum_repr_mul_repr_mulââ, IsScalarTower.coe_toAlgHom', Ideal.map_under_le_under_map, ConjRootClass.minpoly.map_eq_prod, NumberField.mixedEmbedding.commMap_apply_of_isComplex, Valuation.Integers.valuation_irreducible_lt_one, TruncatedWittVector.truncate_wittVector_truncate, NumberField.Units.pos_at_place, NumberField.InfinitePlace.Completion.norm_coe, RingHom.map_rat_algebraMap, algebraMap_le_of_le_spectrum, ExteriorAlgebra.algebraMap_inj, PowerSeries.rescale_X, Algebra.Generators.compLocalizationAwayAlgHom_toAlgHom_toComp, map_preNormEDS, Polynomial.sumIDeriv_C, char_dvd_card_solutions_of_add_lt, NumberField.InfinitePlace.comap_apply, MvPolynomial.comp_evalâHom, Ideal.height_eq_height_add_of_liesOver_of_hasGoingDown, IsLocalization.coe_primeSpectrumOrderIso_symm_apply_asIdeal, Polynomial.roots_C_mul, Algebra.mem_adjoin_iff, AddMonoidAlgebra.lift_mapRangeRingHom_algebraMap, IsFractionRing.mk'_eq_div, Polynomial.coeff_divByMonic_X_sub_C_rec, Ideal.Quotient.tower_quotient_map_quotient, GaussianInt.toComplex_defâ, SetSemiring.imageHom_def, Ideal.liesOver_iff_dvd_map, Localization.localRingHom_injective_of_primesOver_eq_singleton, Complex.isCauSeq_conj, Ring.DirectLimit.congr_symm_apply_of, PowerSeries.coe_add, WittVector.factorPowSucc_fontaineThetaModPPow_eq, HasDerivAt.hasGradientAt, RingCat.forgetâ_map, Ideal.Quotient.factor_comp_apply, IntermediateField.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply, RootPairing.RootPositiveForm.zero_lt_posForm_iff, MvPolynomial.aeval_eq_eval, PowerSeries.catalanSeries_constantCoeff, FractionalIdeal.extendedHomâ_coeIdeal_eq_map, MvPolynomial.schwartz_zippel_totalDegree, IsLocalization.smul_mk'_self, Polynomial.leadingCoeff_X_pow_add_C, Ring.ordFrac_eq_ord, Ideal.comap_map_eq_self_iff_of_isPrime, Polynomial.eval_C, Matrix.charmatrix_apply_eq, IsGalois.mem_range_algebraMap_iff_fixed, Lagrange.nodal_insert_eq_nodal, Algebra.SubmersivePresentation.map_jacobianOfHasCoeffs, Localization.mk_algebraMap, Polynomial.mapAlgHom_eq_evalâAlgHom'_CAlgHom, MvPolynomial.evalâHom_C_id_eq_joinâ, Algebra.dvd_algebraMap_intNorm_self, map_complEDS', Polynomial.count_map_roots, WeierstrassCurve.map_câ, PrimeSpectrum.vanishingIdeal_range_comap, PolyEquivTensor.toFunAlgHom_apply_tmul, MvPolynomial.eval_mem, LinearMap.toMatrix_baseChange, Algebra.Generators.algebraMap_surjective, LocallyConstant.comapRingHom_apply_apply, Ideal.spanIntNorm_localization, IsLocalization.Away.algebraMap_surjective_of_isIdempotentElem, Polynomial.eval_divByMonic_eq_trailingCoeff_comp, Polynomial.algebraMap_apply, Valuation.Integers.map_le_one, Algebra.isInvariant_iff, RingCat.inv_hom_apply, MvPolynomial.eval_rename_prod_mk, jacobiThetaâ'_conj, RingEquiv.ofHomInv_symm_apply, RingHom.map_matrix_mul, MvPolynomial.optionEquivRight_C, Ideal.isPrime_map_of_isLocalizationAtPrime, Valuation.HasExtension.val_map_eq_iff, Pi.evalRingHom_apply, WeierstrassCurve.Affine.map_addY, Algebra.Extension.lTensor_cotangentComplex_eq_cotangentComplexBaseChange, ExteriorAlgebra.algebraMap_eq_one_iff, MvPolynomial.map_mvPolynomial_eq_evalâ, Polynomial.monomial_mul_C, Unitization.starLift_apply_apply, WeierstrassCurve.integralModel_Î_eq, X_pow_sub_C_irreducible_iff_forall_prime_of_odd, MvPolynomial.eval_evalâ, IsLocalization.mk'_mul_cancel_left, Polynomial.trunc_toLaurent, Algebra.traceMatrix_localizationLocalization, Algebra.algebraMap_intNorm, RingHom.rangeSRestrict_surjective, WittVector.iterate_verschiebung_mul, LaurentSeries.ofPowerSeries_powerSeriesPart, MvPolynomial.evalâ_id, Polynomial.scaleRoots_evalâ_mul, RingHom.toRatAlgHom_apply, Polynomial.as_sum_range_C_mul_X_pow', AlgebraicGeometry.Scheme.exists_germ_injective, LaurentSeries.single_order_mul_powerSeriesPart, coe_algebraMapCLM, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_quotMk, Complex.cos_conj, Matrix.derivative_det_one_add_X_smul, Polynomial.integralNormalization_C, Polynomial.rootMultiplicity_X_sub_C_pow, QuadraticAlgebra.algebraMap_re, Polynomial.resultant_X_sub_C_right, CliffordAlgebra.Κ_mul_Κ_comm, Module.associatedPrimes.preimage_comap_associatedPrimes_eq_associatedPrimes_of_isLocalizedModule, IsLocalRing.residue_eq_zero_iff, MvPowerSeries.isUnit_iff_constantCoeff, RatFunc.liftMonoidWithZeroHom_apply_div', GaussianInt.toComplex_div_re, bijective_iterateFrobenius, HahnSeries.embDomainRingHom_apply, nnnorm_algebraMap_nnreal, Complex.conj_rootsOfUnity, RingHom.ker_rangeRestrict, algebraMap_pos, IsLocalization.AtPrime.coe_orderIsoOfPrime_symm_apply_coe, WithAbs.equiv_algebraMap_apply, LocallyConstant.evalRingHom_apply, WittVector.mapFun.sub, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd_assoc, Polynomial.update_eq_add_sub_coeff, RootPairing.restrictScalars_pairing, Polynomial.monic_finprod_X_sub_C, Polynomial.degree_C_mul_of_mul_ne_zero, Cubic.discr_eq_prod_three_roots, Ideal.jacobson_bot_polynomial_le_sInf_map_maximal, MvPolynomial.constantCoeff_C, MvPowerSeries.smul_eq_C_mul, AlgebraicGeometry.Scheme.Hom.toImage_app_injective, CliffordAlgebra.Κ_sq_scalar, Quaternion.algebraMap_def, Algebra.intTrace_eq_of_isLocalization, Real.Polynomial.isRoot_cos_pi_div_five, Polynomial.coe_C, RingHom.mem_range, MvPowerSeries.trunc_C, NumberField.mixedEmbedding.convexBodyLT_mem, Zsqrtd.hom_ext_iff, NumberField.InfinitePlace.coe_apply, WeierstrassCurve.Affine.C_addPolynomial, Ideal.Quotient.factorâ_apply_mk, MvPolynomial.map_map, AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_ker_glueDataObjΚ, OrderRingHom.coe_coe_ringHom, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_snd_coe, Algebra.trace_algebraMap, Module.Basis.repr_algebraMap, Polynomial.bernoulli_generating_function, NumberField.Units.coe_mul, PEquiv.map_toMatrix, LinearMap.det_baseChange, Polynomial.natDegree_finset_prod_X_sub_C_eq_card, RCLike.conjCLE_apply, Polynomial.support_C_mul_X', RingHom.congr_fun, Ideal.Quotient.instIsPrimeQuotientMapRingHomAlgebraMapMkOfLiesOver, ValuationSubring.subtype_injective, RatFunc.coe_X, NumberField.InfinitePlace.comp_of_comap_eq, IsPurelyInseparable.iterateFrobenius_algebraMap, IsUltrametricDist.invariantExtension_extends, CFC.rpow_algebraMap, Polynomial.evalâ_ofFinsupp, WittVector.frobenius_isPoly, Polynomial.evalâ_monomial, AdjoinRoot.smul_mk, PowerSeries.map_cos, AdjoinRoot.quotEquivQuotMap_symm_apply_mk, Orthonormal.inner_left_fintype, PowerSeries.coeff_coe, IsIntegrallyClosedIn.exists_algebraMap_eq_of_pow_mem_subalgebra, Polynomial.coe_compRingHom_apply, MonoidHom.map_iterate_frobenius, FunctionField.inftyValuation.polynomial, AdjoinRoot.liftAlgHom_of, Polynomial.pow_rootMultiplicity_not_dvd, Polynomial.divByMonic_add_X_sub_C_mul_derivative_divByMonic_eq_derivative, LocalizedModule.divBy_mul_by, IsFractionRing.algHom_commutes, IsLocalRing.basisQuotient_repr, AdjoinRoot.evalEval_apply, QuadraticAlgebra.omega_mul_coe_mul_mk, PowerSeries.constantCoeff_X, Ideal.Quotient.algebraMap_quotient_of_ramificationIdx_neZero, LinearEquiv.det_baseChange, algebraicIndependent_empty_iff, Algebra.FormallyUnramified.iff_map_maximalIdeal_eq, DoubleCentralizer.norm_def', Module.End.ringHomEndFinsupp_apply_apply, BoolAlg.hasForgetToBoolRing_forgetâ_map, Polynomial.constantCoeff_apply, QuadraticAlgebra.algebraMap_dvd_iff, algebra_compatible_smul, IsLocalization.comap_map_of_isPrime_disjoint, AlgHom.commutes', Algebra.compHom_algebraMap_apply, span_eq_top_localization_localization, IsFractionRing.injective, MvPolynomial.evalâ_mul_monomial, MvPolynomial.weightedHomogeneousComponent_zero, instIsLocalHomAtPrimeRingHomAlgebraMap, Complex.isometry_conj, Polynomial.Bivariate.aveal_eq_map_swap, Polynomial.le_trailingDegree_C, WithLp.unitization_algebraMap, Polynomial.eval_natCast_map, Ideal.FG.map, Polynomial.integralNormalization_aeval_eq_zero, RatFunc.coe_mapRingHom_eq_coe_map, MvPolynomial.esymmAlgHomMonomial_single, MvPolynomial.homogeneousComponent_C_mul, AlgEquiv.quotientBot_mk, LaurentPolynomial.evalâ_C_mul_T, LaurentSeries.coe_algebraMap, Polynomial.toLaurent_C_mul_T, PadicInt.algebraMap_apply, Complex.summable_conj, UpperHalfPlane.denom_cocycle_Ď, MvPolynomial.IsHomogeneous.map, Polynomial.aevalTower_algebraMap, MvPolynomial.map_expand, Algebra.Norm.Transitivity.comp_det_mul_pow, NNReal.algebraMap_eq_coe, Complex.log_inv_eq_ite, Algebra.traceMatrix_of_matrix_vecMul, RingEquiv.quotientBot_symm_mk, HomogeneousLocalization.awayMap_mk, Polynomial.Bivariate.swap_apply, DifferentialAlgebra.deriv_algebraMap, MvPolynomial.map_aeval, IsLocalization.AtPrime.inertiaDeg_map_eq_inertiaDeg, Matrix.center_eq_range, RatFunc.coe_coe, Algebra.coe_algebraMap_ofSubsemiring, Ideal.quotEquivOfEq_mk, WeierstrassCurve.Jacobian.map_negY, Algebra.TensorProduct.basis_repr_tmul, RingHom.rangeS_toSubmonoid, AlgebraicGeometry.stalkwise_SpecMap_iff, MvPolynomial.map_frobenius_expand, Valuation.Integers.le_of_dvd, NumberField.FinitePlace.norm_embedding_eq, WittVector.mapFun.pow, Ideal.injective_quotient_le_comap_map, Polynomial.C_eq_zero, Polynomial.dvd_comp_X_add_C_iff, IntermediateField.LinearDisjoint.trace_algebraMap, Polynomial.separable_X_pow_sub_C, Int.coe_castRingHom, QuadraticAlgebra.C_eq_algebraMap, ValuativeExtension.mapValueGroupWithZero_mk, LinearMap.range_toAddSubmonoid, Ideal.comap_of_equiv, Polynomial.dvd_comp_C_mul_X_add_C_iff, PowerSeries.isUnit_iff_constantCoeff, AlgebraicGeometry.Scheme.ker_ideal_of_isPullback_of_isOpenImmersion, Ideal.Quotient.algebraMap_quotient_map_quotient, FirstOrder.Ring.lift_genericPolyMap, WittVector.truncate_surjective, PresheafOfModules.Derivation.postcomp_d_apply, NumberField.ComplexEmbedding.Extension.not_isReal_of_not_isReal, RingCat.forget_map_apply, Complex.mul_conj', RootPairing.exists_ge_zero_eq_rootForm, norm_algebraMap_nnreal, SkewPolynomial.Ď_iterate_apply, Algebra.mem_bot, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_appTop_coord, PresheafOfModules.Derivation.d_one, Polynomial.X_pow_sub_one_splits, injective_frobenius, MvPolynomial.expand_char, Polynomial.coeff_C_ne_zero, Polynomial.isMonicOfDegree_add_add_two, Algebra.right_comm, Polynomial.degree_X_pow_add_C, ExteriorAlgebra.algebraMap_eq_zero_iff, Matrix.det_one_add_smul, minpoly_algebraMap_sub_splits, PreTilt.mk_comp_untilt_eq_coeff_zero, PowerSeries.WithPiTopology.continuous_constantCoeff, MvPolynomial.evalâHom_congr, Polynomial.Monic.comp_X_sub_C, Rat.coe_castHom, ZMod.ringHom_rightInverse, DoubleQuot.quotQuotEquivComm_comp_quotQuotMk, WeierstrassCurve.Jacobian.eval_polynomialX_of_Z_ne_zero, Localization.AtPrime.eq_maximalIdeal_iff_comap_eq, MvPolynomial.map_rename, PrimeSpectrum.toPiLocalization_surjective_of_discreteTopology, Polynomial.hom_evalâ, IsFractionRing.surjective_iff_isField, Algebra.PreSubmersivePresentation.ofHasCoeffs_Ď', MvPolynomial.killCompl_C, Algebra.Presentation.quotientEquiv_symm, FractionalIdeal.mem_coeSubmodule, AddMonoidAlgebra.singleZeroRingHom_apply, LaurentPolynomial.algebraMap_apply, DoubleQuot.quotQuotEquivComm_quotQuotMk, AlgebraicGeometry.StructureSheaf.comap_const, frobenius_mul, Algebra.Generators.H1Cotangent.δAux_C, Polynomial.degree_X_sub_C, Polynomial.iterate_derivative_X_sub_pow, algebraMap_strictMono, Polynomial.support_trinomial', Complex.liftAux_apply, TensorProduct.gradedComm_algebraMap_tmul, CompleteOrthogonalIdempotents.lift_of_isNilpotent_ker_aux, RingEquiv.toNonUnitalRingHom_commutes, Polynomial.C_0, IsLocalization.AtPrime.coe_primeSpectrumOrderIso_apply_coe_asIdeal, LaurentSeries.inducing_coe, WittVector.mk_pow_fontaineTheta, FirstOrder.Ring.realize_termOfFreeCommRing, PowerSeries.IsWeierstrassFactorization.isWeierstrassDivision, Ideal.ker_Pi_Quotient_mk, FirstOrder.Field.lift_genericMonicPoly, NumberField.exists_conjugate_one_le_norm, AlgebraicGeometry.Scheme.IdealSheafData.ideal_map, Polynomial.exists_finset_of_splits, boolRingCatEquivBoolAlg_functor, NumberField.InfinitePlace.conjugate_embedding_injective, RingHom.toAddMonoidHom_eq_coe, map_preNormEDS', Algebra.QuasiFiniteAt.exists_fg_and_exists_notMem_and_awayMap_bijective, NumberField.InfinitePlace.norm_embedding_eq, Submodule.IsPrincipal.contentIdeal_le_span_iff_dvd, PowerSeries.coe_smul, isSeparable_algebraMap, PreTilt.coeff_frobeniusEquiv_symm, FreeAbelianGroup.liftMonoid_coe_addMonoidHom, Algebra.Generators.ofComp_val, MvPowerSeries.comp_aeval, Localization.subalgebra.mem_range_mapToFractionRing_iff_ofField, Algebra.Presentation.map_relationOfHasCoeffs, LaurentSeries.continuous_coe, Matrix.charpoly_of_upperTriangular, algebraMap_apply, IsLocalRing.instIsLocalHomResidueFieldRingHomResidue, LinearMap.convOne_apply, Valuation.HasExtension.val_map_lt_iff, MonoidAlgebra.coe_algebraMap, LaurentSeries.algebraMap_C_mem_adicCompletionIntegers, FreeAlgebra.star_algebraMap, MvPolynomial.evalâ_map, AddMonoidAlgebra.mapRangeRingHom_single, Polynomial.irreducible_mul_leadingCoeff_inv, toRingHom_injective, PresheafOfModules.Derivation.d_mul, iterateFrobenius_one_apply, GaussianInt.toComplex_injective, MulOpposite.algebraMap_apply, IsSepClosed.roots_eq_zero_iff, IsIntegrallyClosedIn.exists_algebraMap_eq_of_isIntegral_pow, Algebra.Generators.naive_val, Ideal.Quotient.factorâ_apply, RingHom.comap_ker, Ideal.map_id, gal_X_pow_sub_C_isSolvable, Lagrange.interpolate_eq_sum, MonoidAlgebra.mapDomain_algebraMap, StarSubalgebra.mem_bot, Module.AEval.C_smul, Algebra.Extension.CotangentSpace.map_tmul, Orientation.kahler_swap, MulChar.ringHomComp_apply, Polynomial.sum_C_index, element_smul_restrictScalars, Matrix.charmatrix_apply_ne, CommSemiRingCat.ofHom_apply, MvPowerSeries.subst_monomial, RatFunc.map_apply, RingHom.coe_coe, IsFractionRing.coe_liftAlgHom, Polynomial.le_rootMultiplicity_map, RingHom.toMonoidHom_eq_coe, RingHom.coe_rangeSRestrict, MvPowerSeries.le_weightedOrder_map, PerfectRing.liftEquiv_comp_apply, Ideal.powQuotSuccInclusion_apply_coe, Algebra.Generators.algebraMap_apply, IsLocalization.map_eq_zero_iff, Subalgebra.algebraMap_mk, RingHom.toIntAlgHom_apply, IsBaseChange.endHom_toMatrix, MvPolynomial.map_esymm, WeierstrassCurve.Affine.map_linePolynomial, IsAdicComplete.of_liftRingHom, Polynomial.natTrailingDegree_C, HopfAlgebra.sum_mul_antipode_eq_algebraMap_counit, PowerBasis.quotientEquivQuotientMinpolyMap_apply_mk, Complex.UnitDisc.coe_conj, Polynomial.X_mul_C, Module.IsTorsionBySet.mk_smul, IsLocalization.mapFrameHom_apply, Derivation.mapCoeffs_C, DirectSum.algebraMap_toAddMonoid_hom, NumberField.InfinitePlace.mkReal_coe, AlgebraicGeometry.StructureSheaf.comap_apply, Polynomial.coeff_C_mul_X, Polynomial.leadingCoeff_cubic, Polynomial.map_monomial, Polynomial.resultant_C_zero_right, Polynomial.natDegree_eq_one, MvPolynomial.expand_C, AlgebraicGeometry.RingedSpace.mem_top_basicOpen, ModuleCat.smul_naturality, CharP.ker_intAlgebraMap_eq_span, LaurentPolynomial.smeval_C_mul, IsLocalization.map_inf, PadicInt.ext_of_toZModPow, MonomialOrder.eq_C_of_degree_eq_zero, minpoly.sub_algebraMap, WeierstrassCurve.Ď_three, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding, AdjoinRoot.mk_eq_mk, MvPolynomial.coeffs_C, UniformSpace.Completion.map_smul_eq_mul_coe, Matrix.IsParabolic.sub_eigenvalue_sq_eq_zero, Polynomial.C_eq_natCast, FractionalIdeal.dual_eq_dual_mul_dual, ContinuousMap.toNNReal_algebraMap, IsLocalization.isMaximal_iff_isMaximal_disjoint, AlgebraicGeometry.IsAffineOpen.ideal_le_iff, Polynomial.derivative_X_sub_C_sq, AlgebraicGeometry.stalkToFiberRingHom_homogeneousLocalizationToStalk, Matrix.charpoly_sub_scalar, Algebra.Generators.compLocalizationAwayAlgHom_X_inl, WeierstrassCurve.Jacobian.comp_equiv_comp, MvPolynomial.optionEquivRight_X_none, PreInnerProductSpace.Core.conj_inner_symm, Polynomial.smul_eq_C_mul, FiniteField.algebraMap_trace_eq_sum_pow, Algebra.coe_bot, Polynomial.opRingEquiv_op_C, RatFunc.mk_def, Submodule.factor_eq_factor, NumberField.ComplexEmbedding.involutive_conjugate, Polynomial.C_eq_intCast, Ideal.IsDedekindDomain.ramificationIdx_eq_normalizedFactors_count, Perfection.coeff_map, Polynomial.degree_C_lt_degree_C_mul_X, Polynomial.aroots_C_mul, WeierstrassCurve.Jacobian.polynomialY_eq, Polynomial.isUnit_iff, RingTheory.Sequence.IsWeaklyRegular.of_flat, WeierstrassCurve.Jacobian.map_dblZ, ContinuousMap.spectrum_eq_preimage_range, PowerSeries.map_constantCoeff_le_self_of_X_mem, Polynomial.roots_X_pow_char_pow_sub_C_pow, Module.Basis.localizationLocalization_apply, NumberField.InfiniteAdeleRing.mixedEmbedding_eq_algebraMap_comp, Algebra.TensorProduct.right_algebraMap_apply, Localization.map_isUnit_of_le, FreeCommRing.lift_of, Multiset.prod_X_sub_C_dvd_iff_le_roots, Algebra.FormallyUnramified.bijective_of_isAlgClosed_of_isLocalRing, Ideal.map_relNorm, Polynomial.leadingCoeff_mul_prod_normalizedFactors, RatFunc.mk_eq_div', IsLocalization.coe_liftAlgHom, IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, WeierstrassCurve.Jacobian.eval_polynomialX, Matrix.IsHermitian.charpoly_cfc_eq, Polynomial.mem_span_C_X_sub_C_X_sub_C_iff_eval_eval_eq_zero, MvPolynomial.C_apply, Ideal.localized'_eq_map, Bialgebra.algebraMap_injective, IsLocalization.mk'_eq_mul_mk'_one, IsLocalization.ringEquivOfRingEquiv_symm_apply, MvPowerSeries.map_subst, HahnSeries.map_C, Polynomial.nextCoeff_C_mul_X_add_C, Polynomial.toLaurent_injective, LaurentSeries.val_le_one_iff_eq_coe, WeierstrassCurve.Projective.eval_polynomialX, PowerSeries.constantCoeff_invUnitsSub, PiTensorProduct.constantBaseRingEquiv_symm, Polynomial.scaleRoots_evalâ_eq_zero, WeierstrassCurve.Projective.baseChange_polynomial, continuous_algebraMap, Algebra.algebraMap_intNorm_fractionRing, QuaternionAlgebra.algebraMap_injective, Polynomial.prod_multiset_root_eq_finset_root, Polynomial.dvd_C_mul, AlgebraicGeometry.StructureSheaf.toPushforwardStalkAlgHom_apply, AlgebraicGeometry.Scheme.Hom.germ_stalkMap_apply, Matrix.toMvPolynomial_map, IsFractionRing.self_iff_surjective, IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_symm_apply_mk, AlgebraicGeometry.Scheme.preimage_basicOpen_top, IsLocalization.AtPrime.exists_algebraMap_quot_eq_of_mem_quot, spectrum.algebraMap_mem_iff, CStarAlgebra.nnnorm_le_iff_of_nonneg, Matrix.SpecialLinearGroup.map_apply_coe, Algebra.Extension.Cotangent.val_smul''', Polynomial.X_pow_sub_C_separable_iff, CFC.spectrum_algebraMap_eq, map_complEDSâ, Algebra.norm_eq_prod_embeddings, AlgCat.forgetâRing_preservesLimitsOfSize, IsPurelyInseparable.minpoly_eq, NumberField.canonicalEmbedding.integralBasis_repr_apply, RingHom.mem_range_self, Module.Invertible.algEquivOfRing_apply, Polynomial.nextCoeff_mul_C, Polynomial.coeff_X_sub_C_mul, WeierstrassCurve.Affine.CoordinateRing.mk_Ď, MvPolynomial.coeff_C, Cubic.of_a_eq_zero, Polynomial.comp_C_mul_X_eq_zero_iff, Representation.IsIrreducible.algebraMap_intertwiningMap_bijective_of_isAlgClosed, Polynomial.modByMonic_eq_zero_iff_quotient_eq_zero, WeierstrassCurve.Jacobian.eval_polynomialY_of_Z_ne_zero, AlgebraicGeometry.IsAffineOpen.basicOpen_fromSpec_app, gal_X_pow_sub_C_isSolvable_aux, MvPolynomial.bindâ_map, Module.Basis.norm_smul, RingHom.Bijective.isStableUnderBaseChange, Polynomial.degree_quadratic, WittVector.frobenius_bijective, Ideal.relNorm_le_comap, SpectrumRestricts.algebraMap_image, SemiRingCat.forgetâMon_preservesLimitsOfSize, PowerSeries.rescale_rescale, ContinuousMap.coeFnRingHom_apply, SubsemiringClass.subtype_injective, Ideal.algebraMap_residueField_surjective, RingHomIsometric.enorm_map, PadicAlgCl.norm_extends, RingHom.coe_rangeRestrictField, Polynomial.monic_X_pow_sub_C, AdicCompletion.mkâ_apply_coe, AlgebraicGeometry.Scheme.germToFunctionField_injective, NumberField.canonicalEmbedding.integerLattice.inter_ball_finite, Algebra.FormallyUnramified.isField_quotient_map_maximalIdeal, Complex.Gamma_conj, UpperHalfPlane.Ď_mul, RingHom.compLeft_apply, Polynomial.leadingCoeff_linear, CommRingCat.instIsRightAdjointCommMonCatForgetâRingHomCarrierMonoidHomCarrier, AdjoinRoot.coe_mapAlgHom, Polynomial.rootMultiplicity_eq_natFind_of_ne_zero, Polynomial.isMonicOfDegree_two_iff, IsLocalization.Away.instMapRingHomPowersOfCoe, NumberField.ComplexEmbedding.IsConj.eq, Polynomial.C_mul_X_pow_eq_monomial, Polynomial.nextCoeff_X_add_C, StandardEtalePair.equivMvPolynomialQuotient_symm_apply, PrimeSpectrum.toPiLocalization_not_surjective_of_infinite, NumberField.Units.regulator_eq_det, DividedPowers.isSubDPIdeal_map, PrimeSpectrum.preimage_comap_zeroLocus, PowerSeries.coe_mul, Ideal.map_mk_comap_factorPow, IsIntegralClosure.isIntegral_iff, PowerSeries.trunc_mul_C, MvPolynomial.eval_ofNat, RingCon.ker_comp, PresheafOfModules.map_smul, xInTermsOfW_eq, Polynomial.eq_X_add_C_of_degree_le_one, Complex.dist_self_conj, RCLike.conj_ofReal, MvPolynomial.eval_eq_eval_mv_eval', RootPairing.exists_value, Module.comap_annihilator, PerfectRing.comp_lift_apply, MvPolynomial.ACounit_C, PowerSeries.IsWeierstrassDivisionAt.degree_lt, Polynomial.expand_C, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply_mk, Polynomial.logMahlerMeasure_X_sub_C, RootPairing.RootPositiveForm.exists_eq, NumberField.AdeleRing.algebraMap_snd_apply, AlgebraicGeometry.Scheme.Opens.Κ_image_basicOpen_topIso_inv, IsSelfAdjoint.neg_algebraMap_norm_le_self, PresheafOfModules.Monoidal.tensorObj_map_tmul, Ideal.map_mk_eq_bot_of_le, Polynomial.C_mem_lifts, MatrixEquivTensor.toFunBilinear_apply, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletionIntegers_apply, WittVector.frobenius_frobeniusRotation, NumberField.InfinitePlace.card_filter_mk_eq, HomogeneousLocalization.val_awayMap, PowerSeries.rescale_zero_apply, IsPurelyInseparable.bijective_comp_algebraMap, RCLike.conjLIE_apply, MonoidAlgebra.single_algebraMap_eq_algebraMap_mul_of, LaurentPolynomial.degree_C_mul_T, Subalgebra.algebraMap_def, Polynomial.natDegree_mul_leadingCoeff_self_inv, Localization.awayMap_surjective_iff, Module.End.intCast_def, IsLocalRing.residue_def, RCLike.conj_mul, Polynomial.CAlgHom_apply, PerfectRing.bijective_frobenius, WeierstrassCurve.coe_map_Î', Polynomial.trailingDegree_C_mul_X_pow, Polynomial.Monic.quotient_isIntegralElem, Subring.comap_map_eq, PowerSeries.IsWeierstrassFactorizationAt.natDegree_eq_toNat_order_map_of_ne_top, NormedAlgebra.exists_isMinOn_norm_sub_smul, Polynomial.X_pow_sub_one_eq_prod, Polynomial.prod_multiset_X_sub_C_dvd, Pi.ker_ringHom, WeierstrassCurve.map_bâ, Polynomial.degree_cubic_lt, AdjoinRoot.mul_div_root_cancel, NumberField.Units.coe_coe, Polynomial.eq_X_add_C_of_natDegree_le_one, minpoly.natSepDegree_eq_one_iff_eq_X_sub_C_pow, GradedRing.projZeroRingHom'_apply_coe, AlgebraicGeometry.Scheme.Hom.app_surjective, TrivSqZeroExt.algebraMap_eq_inl', fourier_neg', FunctionField.algebraMap_injective, MvPowerSeries.LinearTopology.isTopologicallyNilpotent_iff_constantCoeff, MvPowerSeries.one_le_order_iff_constCoeff_eq_zero, MvPolynomial.evalâHom_zero_apply, Polynomial.degree_C, FreeCommRing.hom_ext_iff, Cubic.of_b_eq_zero, Algebra.IsCentral.baseField_essentially_unique, PowerSeries.coe_sub, Algebra.map_intNormAux, MvPolynomial.degrees_C, Polynomial.derivative_X_add_C, smoothSheafCommRing.forgetStalk_inv_comp_eval_assoc, MvPowerSeries.constantCoeff_invOfUnit, Algebra.norm_localization, IsLocalization.liftAlgHom_apply, Algebra.mul_sub_algebraMap_commutes, WeierstrassCurve.Jacobian.polynomial_relation, PrimeSpectrum.basicOpen_le_basicOpen_iff_algebraMap_isUnit, PrimeSpectrum.specComap_asIdeal, IsBaseChange.det_endHom, ContinuousLinearMap.toLinearMapRingHom_apply, IsLocalization.injective, AlgEquiv.commutes, AddMonoidAlgebra.mapRangeRingHom_apply, IsDedekindDomain.HeightOneSpectrum.coe_algebraMap_mem, MvPolynomial.eval_prod, RingCon.mk'_surjective, AddValuation.comap_supp, MvPolynomial.C_mul_X_eq_monomial, MatrixEquivTensor.invFun_algebraMap, Algebra.Generators.Hom.aeval_val, RingHom.ext_iff, Polynomial.ofFinsupp_algebraMap, RingQuot.idealQuotientToRingQuot_apply, spectrum.resolvent_eq, LaurentSeries.algebraMap_apply, Ideal.height_le_height_add_of_liesOver, IsPRadical.injective_comp_of_perfect, WeierstrassCurve.Affine.CoordinateRing.C_addPolynomial, NumberField.Units.finrank_mul_regOfFamily_eq_det, Algebra.Presentation.comp_aeval_relation_inl, AdjoinRoot.aeval_eq_of_algebra, AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff', Algebra.commutes', MvPolynomial.C_0, MvPowerSeries.constantCoeff_inv, UpperHalfPlane.norm_Ď, FreeRing.map_of, LaurentPolynomial.smeval_C, LieModule.exists_genWeightSpace_le_ker_of_isNoetherian, Polynomial.support_binomial', isConjRoot_iff_eq_algebraMap, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_apply, CategoryTheory.Linear.smulOfRingMorphism_smul_eq, IsLocalization.mk'_spec', MvPolynomial.bindâ_monomial, minpoly.IsIntegrallyClosed.isIntegral_iff_leadingCoeff_dvd, algebraMap_galRestrict_apply, AddMonoidAlgebra.isLocalHom_singleZeroRingHom, Polynomial.cyclotomic_eq_prod_X_sub_primitiveRoots, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_add_eq, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, CFC.posPart_algebraMap_nnreal, WeierstrassCurve.Projective.map_negDblY, Polynomial.X_add_C_scaleRoots, Matrix.toLin_scalar, Polynomial.resultant_C_right, Polynomial.splits_C, Polynomial.Splits.comp_X_sub_C, WeierstrassCurve.Ψ_ofNat, FractionalIdeal.count_ne_zero, RCLike.conj_conj, MvPolynomial.pderiv_sumToIter, TopCommRingCat.forgetToTopCatTopologicalRing, Algebra.traceMatrix_eq_embeddingsMatrix_mul_trans, Ideal.height_le_height_add_one_of_mem, PowerSeries.le_order_map, PowerSeries.aeval_unique, AdjoinRoot.mk_leftInverse, MvPolynomial.totalDegree_C, PerfectRing.lift_lift_apply, Polynomial.natDegree_C_mul_X, RingEquiv.quotientBot_mk, NumberField.InfinitePlace.Completion.locallyCompactSpace, Rat.subsingleton_ringHom, smoothSheafCommRing.forgetStalk_inv_comp_eval, Ideal.image_subset_nonunits_valuationSubring, KaehlerDifferential.End_equiv_aux, AddMonoidAlgebra.ringHom_ext'_iff, WeierstrassCurve.Projective.polynomialZ_eq, Polynomial.comp_C, WeierstrassCurve.map_aâ, Polynomial.coeff_mul_X_sub_C, SubsemiringClass.coe_subtype, RingHom.one_def, PowerSeries.rescale_mk, FractionalIdeal.mem_one_iff, RingCat.forgetâSemiRing_preservesLimitsOfSize, Complex.normSq_add, Algebra.smul_def', minpoly.frobenius_of_isSeparable, RatFunc.numDenom_div, Ideal.disjoint_map_primeCompl_iff_comap_le, Polynomial.roots_expand_map_frobenius, CStarMatrix.algebraMap_apply, RCLike.re_eq_norm_of_mul_conj, IsIntegralClosure.algebraMap_injective, PowerSeries.constantCoeff_surj, IsLocalization.Away.map_injective_iff, Polynomial.natDegree_X_add_C, IsSimpleModule.algebraMap_end_bijective_of_isAlgClosed, CommSemiRingCat.forgetReflectIsos, Polynomial.map_taylor, NumberField.RingOfIntegers.coe_eq_zero_iff, AlgebraicGeometry.Scheme.ker_of_isAffine, Polynomial.map_under_lt_comap_of_weaklyQuasiFiniteAt, LaurentPolynomial.degree_C, MvPowerSeries.constantCoeff_C, Polynomial.support_C, SemiRingCat.forget_preservesLimitsOfSize, IntermediateField.LinearDisjoint.basisOfBasisLeft_apply, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C', Algebra.essFiniteType_cond_iff, MvPowerSeries.monomial_zero_eq_C, MvPowerSeries.coeff_inv, RCLike.conj_eq_iff_re, MvPolynomial.coeff_C_mul, LaurentPolynomial.evalâ_T, IsPurelyInseparable.injective_comp_algebraMap, Polynomial.roots_expand_image_frobenius, Algebra.PreSubmersivePresentation.ofHasCoeffs_algebra_algebraMap_apply, MvPolynomial.quotient_map_C_eq_zero, MvPolynomial.iterToSum_X, IsLocalization.mk'_mem_iff, Polynomial.natSepDegree_C_mul_X_sub_C_pow, Submodule.span_singleton_algebraMap_of_isUnit, MvPolynomial.C_mul_monomial, PowerSeries.exp_mul_exp_neg_eq_one, AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap, AddMonoidAlgebra.isLocalHom_algebraMap, ClassGroup.mkMMem_surjective, Polynomial.height_map_C, Algebra.Extension.algebraMap_surjective, RatFunc.num_C, AlgebraicGeometry.Scheme.Îevaluation_naturality_apply, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding, WeierstrassCurve.Jacobian.map_add, MonoidAlgebra.coe_mapRangeRingHom, isIntegral_localization', Polynomial.X_sub_C_mul_divByMonic_eq_sub_modByMonic, AdjoinRoot.coe_injective, OnePoint.map_smul, RatFunc.smul_eq_C_mul, PowerBasis.constr_pow_algebraMap, PrimeSpectrum.preimageEquivFiber_apply_asIdeal, Polynomial.roots_C_mul_X_sub_C_of_IsUnit, AnalyticOnNhd.eval_linearMap, isStrictlyPositive_algebraMap, Module.Basis.algebraMap_injective, Algebra.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetCoeRingHomAlgebraMap, RingTheory.Sequence.IsRegular.of_faithfullyFlat, PerfectClosure.mk_add_mk, Polynomial.leadingCoeff_map_eq_of_isUnit_leadingCoeff, LaurentPolynomial.C_apply, galLift_algebraMap_apply, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_symm_quotQuotMk, Polynomial.derivative_X_pow_succ, NumberField.Units.norm, LinearMap.isSymm_def, AlgebraicGeometry.LocallyRingedSpace.coe_toÎSpecSheafedSpace_hom_base_hom_apply_asIdeal, Polynomial.eq_C_of_natDegree_le_zero, MvPolynomial.commAlgEquiv_C, MvPolynomial.coeff_zero_C, Polynomial.monic_X_add_C, Polynomial.logMahlerMeasure_X_add_C, ContinuousLinearMap.toContinuousAddMonoidHom_zero, IsIntegrallyClosed.exists_algebraMap_eq_of_pow_mem_subalgebra, smoothSheafCommRing.forgetStalk_inv_comp_eval_apply, SemilinearMapClass.map_smul_inv, Algebra.FinitePresentation.ker_fg_of_mvPolynomial, IsLocalization.finsetIntegerMultiple_image, Algebra.norm_eq_iff, MonomialOrder.monic_X_add_C, Polynomial.aevalTower_C, MonoidAlgebra.isLocalHom_singleOneRingHom, LaurentSeries.exists_ratFunc_val_lt, PowerSeries.constantCoeff_one, Ideal.under_map_of_isLocalizationAtPrime, WeierstrassCurve.Affine.addPolynomial_slope, Ideal.comp_quotientMap_eq_of_comp_eq, Polynomial.coeff_C_mul, Ideal.Quotient.eq_zero_iff_dvd, RatFunc.num_algebraMap, Ideal.mem_of_liesOver, Ideal.instIsScalarTowerQuotientHPowKerRingHomAlgebraMapOfNat, FractionalIdeal.extendedHomâ_injective, MvPolynomial.bindâ_monomial_one, RingHom.map_one, MonoidHom.iterate_map_frobenius, MvPolynomial.commAlgEquiv_X, Algebra.pushoutDesc_right, PowerSeries.map_sin, smoothSheafCommRing.isUnit_stalk_iff, ExteriorAlgebra.invertibleAlgebraMapEquiv_apply_invOf, Polynomial.rootMultiplicity_eq_nat_find_of_nonzero, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero, IsLocalization.mk'_eq_algebraMap_mk'_of_submonoid_le, MvPolynomial.mapEquiv_apply, MvPolynomial.evalâHom_congr', Polynomial.derivative_X_sub_C_pow, Valuation.HasExtension.maximalIdeal_comap_algebraMap_eq_maximalIdeal, Matrix.charpoly.univ_coeff_evalâHom, Module.Quotient.mk_smul_mk, IsPurelyInseparable.surjective_algebraMap_of_isSeparable, PerfectRing.liftEquiv_id_apply, Polynomial.natDegree_C_mul_eq_of_mul_eq_one, RingHom.Bijective.ofLocalizationSpan, PrimeSpectrum.mem_image_comap_basicOpen, Polynomial.eraseLead_C_mul_X, PowerSeries.derivativeFun_C, IsLocalization.AtPrime.comap_maximalIdeal, DirectSum.toAlgebra_apply, WithAbs.algebraMap_right_apply, IntermediateField.LinearDisjoint.basisOfBasisRight_apply, Polynomial.natDegree_C, TensorProduct.gradedComm_algebraMap, Complex.inv_cpow_eq_ite', liftOfDerivationToSquareZero_mk_apply, isLocalizedModule_iff, AlgebraicIndependent.lift_reprField, ValuativeExtension.vlt_iff_vlt, RCLike.conj_I_ax, Polynomial.ker_constantCoeff, Representation.asModuleEquiv_symm_map_smul, X_pow_sub_C_irreducible_iff_of_prime_pow, Lagrange.basis_eq_prod_sub_inv_mul_nodal_div, PowerSeries.constantCoeff_invOfUnit, MvPolynomial.aeval_algebraMap_apply, IsLocalization.Away.awayToAwayLeft_eq, Polynomial.constantCoeff_coe, MvPolynomial.C_1, MvPolynomial.evalâHom_X', Ideal.Factors.isScalarTower, Algebra.SubmersivePresentation.map_invJacobianOfHasCoeffs, wittPolynomial_one, Polynomial.toLaurent_comp_C, IsField.localization_map_bijective, Polynomial.IsRoot.mul_div_eq, contraction_of_isPowMul, Polynomial.sum_C_mul_X_pow_eq, DifferentiableAt.conj_conj, MvPolynomial.eval_eq', isStronglyTranscendental_mk_radical_conductor, RootPairing.toLinearMap_apply_PolarizationIn, Field.DirectLimit.nontrivial, Polynomial.as_sum_support_C_mul_X_pow, Algebra.Generators.comp_val, DirectSum.algebraMap_apply, nnnorm_algebraMap, Algebra.adjoin_eq_ring_closure, MvPolynomial.evalâ_C, DividedPowers.isDPMorphism_iff, RatFunc.liftMonoidWithZeroHom_apply_div, Submodule.span_algebraMap_image, Polynomial.degree_quadratic_le, Polynomial.eq_quadratic_of_degree_le_two, AlgHom.IsArithFrobAt.localize_algebraMap, WeierstrassCurve.Ď_one, AlgebraicGeometry.RingedSpace.res_zero, RatFunc.num_dvd, Polynomial.divX_eq_zero_iff, minpoly.isIntegrallyClosed_eq_field_fractions, IsLocalization.algebraMap_mem_map_algebraMap_iff, CommRingCat.instIsLocalHomCarrierObjWalkingParallelPairFunctorConstPtEqualizerForkZeroParallelPairRingHomHomΚ, Ideal.Quotient.mk_singleton_self, MulSemiringAction.charpoly_eq_prod_smul, NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_coe, IsLocalization.Away.mvPolynomialQuotientEquiv_apply, AdjoinRoot.mk_eq_zero, FiniteField.frobeniusAlgEquiv_symm_apply, Polynomial.card_support_eq, ContinuousMap.compStarAlgHom_comp, IsLocalization.Away.tensorRight, frobenius_sub, AddMonoidAlgebra.coe_algebraMap, Polynomial.leadingCoeff_pow_X_add_C, Algebra.linearMap_apply, RingHom.isIntegralElem_map, NumberField.mixedEmbedding.indexEquiv_apply_isComplex_fst, MvPolynomial.C_add, NNRat.coe_castHom, HahnSeries.embDomainRingHom_C, Polynomial.coeff_map_eq_comp, WeierstrassCurve.Jacobian.map_addZ, PowerSeries.C_injective, RootPairing.algebraMap_coxeterWeightIn, NumberField.InfinitePlace.isInfinitePlace, IsDedekindDomain.primesOverEquivPrimesOver_apply, algebraMap_monotone, Polynomial.cauchyBound_C, LinearMap.ker_toAddSubmonoid, DifferentiableAt.comp_ringHom, MvPolynomial.isHomogeneous_C_mul_X, RatFunc.laurentAux_div, polyEquivTensor_symm_apply_tmul, Polynomial.roots_C_mul_X_add_C, Polynomial.natDegree_C_mul_le, RootPairing.coroot'_apply_apply_mem_of_mem_span, ContinuousLinearMap.toContinuousAddMonoidHom_comp, Ideal.quotientToQuotientRangePowQuotSucc_mk, Ideal.IsMaximal.comap_piEvalRingHom, AlgebraicGeometry.Scheme.Hom.preimage_basicOpen_top, PadicInt.toZModPow_ofIntSeq_of_pow_dvd_sub, integral_conj, Polynomial.leadingCoeff_X_pow_sub_C, PowerSeries.eq_X_mul_shift_add_const, LaurentPolynomial.mk'_eq, CommRingCat.forget_map, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some, NumberField.FinitePlace.norm_lt_one_iff_mem, Module.support_of_algebra, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descAddMonoidHom_quotMk, WeierstrassCurve.map_aâ, IsIntegrallyClosedIn.algebraMap_eq_of_integral, Algebra.Generators.localizationAway_Ď, AdjoinRoot.quotEquivQuotMap_apply, MvPowerSeries.constantCoeff_smul, TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst, IsLocalization.Away.awayToAwayRight_eq, UnitAddTorus.mFourier_neg, NumberField.mixedEmbedding.unit_smul_eq_iff_mul_eq, LinearIndependent.localization_localization, Ideal.le_pow_ramificationIdx, RatFunc.mk_eq_div, MvPolynomial.mapAlgEquiv_apply, IsAdjoinRoot.lift_root, Polynomial.Bivariate.equivMvPolynomial_symm_X_0, RingHom.toMonoidWithZeroHom_eq_coe, NumberField.InfinitePlace.Completion.bijective_extensionEmbedding_of_isReal, Algebra.adjoin_insert_algebraMap, Valuation.HasExtension.val_map_le_one_iff, smoothSheafCommRing.evalHom_germ, Polynomial.taylor_apply, WittVector.frobeniusPoly_zmod, NumberField.InfinitePlace.ComplexEmbedding.conjugate_sign, Polynomial.natDegree_C_mul_of_mul_ne_zero, PresheafOfModules.Derivation.congr_d, WeierstrassCurve.Affine.C_addPolynomial_slope, MvPolynomial.eval_neg, Complex.normSq_sub, GaussianInt.toComplex_im_div, Polynomial.Splits.eq_prod_roots, algebraMap_isometry, frobenius_zero, RCLike.add_conj, Polynomial.evalEvalRingHom_apply, spectralNorm.spectralNorm_pow_natDegree_eq_prod_roots, RCLike.ofReal_re_ax, RingOfIntegers.norm_algebraMap, RingHom.map_iterate_frobenius, MvPowerSeries.HasSubst.const_coeff, MvPolynomial.tensorEquivSum_one_tmul_C, PowerSeries.exp_mul_exp_eq_exp_add, IsLocalization.height_map_of_disjoint, NumberField.InfinitePlace.smul_coe_apply, AlgebraicGeometry.exists_appTop_Ď_eq_of_isAffine_of_isLimit, Ideal.quotientKerAlgEquivOfRightInverse_symm_apply, RCLike.im_eq_conj_sub, ValuationRing.isFractionRing_iff, PowerSeries.IsWeierstrassDivisorAt.mod'_mk_eq_mod, RingEquiv.symm_toRingHom_apply_toRingHom_apply, WittVector.pow_dvd_ghostComponent_of_dvd_coeff, PerfectRing.liftEquiv_apply, Polynomial.div_wf_lemma, Matrix.charmatrix_fromBlocks, PowerBasis.exists_smodEq, OreLocalization.numeratorRingHom_apply, CliffordAlgebra.EvenHom.contract, RCLike.conj_im_ax, AlgHom.ker_coe_equiv, Polynomial.eq_X_add_C_of_degree_eq_one, IsFractionRing.mk'_num_den', NumberField.RingOfIntegers.ker_algebraMap_eq_bot, WeierstrassCurve.Jacobian.baseChange_polynomialY, PrimeSpectrum.preimage_specComap_zeroLocus, PowerSeries.evalNegHom_X, IsLocalization.Away.commutes, IsLocalization.isPrime_iff_isPrime_disjoint, ValuativeExtension.mapValueGroupWithZero_valuation, MvPolynomial.map_ofNat, Algebra.Generators.sq_ker_comp_le_ker_compLocalizationAwayAlgHom, inner_self_conj, Polynomial.mahlerMeasure_C_mul_X_add_C, MvPolynomial.evalâHom_rename, Algebra.bijective_algebraMap_iff, SemiRingCat.FilteredColimits.forgetâMon_preservesFilteredColimits, Perfection.coeff_mk, Subring.subtype_injective, Localization.localRingHom_id, WittVector.mapFun.mul, Ideal.Quotient.mk_bijective_iff_eq_bot, Subring.mem_map, Ring.DirectLimit.congr_apply_of, Circle.coe_inv_eq_conj, Polynomial.eq_C_of_natDegree_eq_zero, CliffordAlgebra.Κ_mul_Κ_add_swap, IsLocalization.AtPrime.to_map_mem_maximal_iff, Subalgebra.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply, Polynomial.smeval_C, Complex.sub_conj, KaehlerDifferential.ker_map, DividedPowers.DPMorphism.dpow_comp, Algebra.FormallySmooth.mk_lift, WeierstrassCurve.Projective.baseChange_polynomialY, mem_span_C_coeff, Valuation.Integers.le_iff_dvd, IntermediateField.instIsScalarTowerSubtypeMemAdjoinSingletonSetCoeRingHomAlgebraMap, AlgHom.toKerIsLocalization_apply, SetLike.GradeZero.algebraMap_apply, WeierstrassCurve.Affine.CoordinateRing.norm_smul_basis, Orientation.kahler_neg_orientation, IsFractionRing.to_map_eq_zero_iff, Polynomial.X_mul_divX_add, IsFractionRing.div_surjective, Complex.conj_im, cfc_add_const, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, NumberField.mixedEmbedding.fundamentalCone.existsUnique_preimage_of_mem_integerSet, RingHom.isometry, conj_trivial, Matrix.GeneralLinearGroup.fixpointPolynomial_eq_zero_iff, Polynomial.card_support_binomial, PowerSeries.coeff_succ_C, Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_C', HomogeneousLocalization.awayMapâ_apply, IsLocalization.mk'_algebraMap_eq_mk', LinearEquiv.map_smulââ, IsLocalization.toLocalizationMap_apply, TensorProduct.algebraMap_gradedMul, FiniteField.algebraMap_norm_eq_pow, PerfectClosure.of_apply, MvPolynomial.algebraMap_apply, Ideal.mem_quotient_iff_mem, WeierstrassCurve.Affine.CoordinateRing.degree_norm_smul_basis, SubMulAction.algebraMap_mem, IsLocalization.Away.map_surjective_iff, LinearMap.IsSymmetric.toSelfAdjoint_apply, RatFunc.liftOn_div, Polynomial.Splits.comp_X_add_C, RCLike.conj_div, WeierstrassCurve.map_bâ, QuotientRing.isOpenMap_coe, RingCat.FilteredColimits.forget_preservesFilteredColimits, LinearMap.toMvPolynomial_baseChange, IsLocalization.bot_lt_comap_prime, RingHomIsometric.nnnorm_map, Polynomial.C_mul_monomial, AdicCompletion.factorâ_evalâ_one, HasDerivAtFilter.hasGradientAtFilter, RootPairing.algebraMap_pairingIn, HahnSeries.algebraMap_apply, IsFractionRing.ringEquivOfRingEquiv_algebraMap, Bialgebra.comul_algebraMap, ZMod.castHom_apply, LinearMap.toMatrix'_algebraMap, Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_one, TensorProduct.tensorQuotEquivQuotSMul_tmul_mk, QuotientRing.isQuotientMap_coe_coe, Polynomial.separable_X_pow_sub_C', Algebra.IsAlgebraic.algHomEquivAlgHomOfSplits_apply_apply, algebraMap_smul, RCLike.summable_conj, AlgebraicGeometry.Scheme.Hom.ker_apply, Ideal.quotientKerAlgEquivOfRightInverse_apply, IsLocalization.localization_localization_surj, IsLocalization.map_comap, IsLocalization.algEquiv_comp_algebraMap_apply, RingHom.applyFaithfulSMul, RingCon.lift_surjective_iff, IsLocalization.AtPrime.liesOver_comap_of_liesOver, MvPolynomial.C_surjective, AlgebraicGeometry.Scheme.IdealSheafData.ideal_comap_of_isOpenImmersion, Unitization.starMap_inl, IsHausdorff.map_algebraMap_iff, Polynomial.Splits.aeval_eq_prod_aroots, MvPolynomial.isEmptyRingEquiv_symm_apply, MonoidAlgebra.lift_apply', AlgebraicGeometry.AffineSpace.SpecIso_inv_appTop_coord, RingHom.functions_ext_iff, Polynomial.toLaurent_apply, RingQuot.eq_lift_comp_mkRingHom, QuadraticAlgebra.coe_dvd_iff_dvd, PowerSeries.IsWeierstrassFactorization.natDegree_eq_toNat_order_map, PerfectRing.liftEquiv_trans, Representation.IntertwiningMap.algebraMap_apply, Matrix.mem_range_scalar_iff_commute_single, IsPerfectClosure.ker_eq, PreTilt.coeff_frobenius, QuadraticAlgebra.mul_star, PerfectRing.lift_comp_lift_apply, NumberField.place_apply, RootPairing.isValuedIn_iff_mem_range, CliffordAlgebra.comp_Κ_sq_scalar, PerfectRing.liftEquiv_symm_apply, Polynomial.natDegree_mul_C_eq_of_mul_eq_one, Ideal.Quotient.mk_span_range, smoothSheafCommRing.forgetStalk_hom_comp_evalHom_assoc, Derivation.compAlgebraMapL_apply_apply, isLocalization_iff, Polynomial.content_C_mul, Polynomial.Splits.eq_X_sub_C_of_single_root, TruncatedWittVector.commutes_symm', FiniteField.algebraMap_norm_eq_prod_pow, TruncatedWittVector.truncate_truncate, Polynomial.coeff_det_X_add_C_card, WittVector.mapFun.zsmul, MvPowerSeries.constantCoeff_zero, Polynomial.eval_homogenize, Polynomial.quotientSpanXSubCAlgEquiv_mk, AlgebraicGeometry.Scheme.evaluation_eq_zero_iff_notMem_basicOpen, IsLocalization.iff_map_piEvalRingHom, Cubic.of_c_eq_zero', Complex.continuous_conj, Zsqrtd.lift_symm_apply_coe, Localization.mapPiEvalRingHom_bijective, DoubleQuot.ker_quotQuotMk, PadicInt.Coe.ringHom_apply, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_germ_apply, AdjoinRoot.coe_injective', iterateFrobenius_inj, RingOfIntegers.not_dvd_exponent_iff, Submodule.setLike.coe_galgebra_toFun, Lagrange.X_sub_C_dvd_nodal, Algebra.Extension.Hom.toRingHom_algebraMap, IsLocalization.algebraMap_isUnit_iff, LieSubmodule.mapsTo_pow_toEnd_sub_algebraMap, MvPolynomial.bindâ_C_right, UpperHalfPlane.Ď_num, MvPolynomial.coe_coeffs_map, Subring.coe_map, Complex.conj_cpow, Localization.AtPrime.mapPiEvalRingHom_comp_algebraMap, TrivSqZeroExt.inlHom_apply, Polynomial.roots_X_sub_C, AdicCompletion.mk_ofAlgEquiv_symm, Submodule.traceDual_le_span_map_traceDual, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_apply, NumberField.Embeddings.card, AdicCompletion.mk_smul_mk, Polynomial.isUnit_C, Valuation.Integers.hom_inj, Quaternion.algebraMap_injective, PowerSeries.exp_pow_sum, CliffordAlgebra.contractRight_mul_algebraMap, WeierstrassCurve.C_ΨâSq, IsLocalization.ringEquivOfRingEquiv_eq_map, Polynomial.Chebyshev.algebraMap_eval_C, AdjoinRoot.smul_of, Polynomial.natDegree_quadratic_le, Polynomial.Bivariate.swap_Y, Polynomial.rootSet_C_mul_X_pow, PreTilt.coeff_iterate_frobeniusEquiv_symm, Matrix.toLinearMapâââ_apply, NumberField.Embeddings.instNonemptyRingHomOfIsAlgebraicRatOfIsAlgClosed, cfc_apply_zero, IsLocalizedModule.fromLocalizedModule_mk, MvPolynomial.instIsLocalHomRingHomAlgebraMap, AlgebraicGeometry.Scheme.stalkSpecializes_stalkMap_apply, IsLocalRing.ResidueField.mapEquiv_apply, FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul, PowerSeries.one_le_order_iff_constCoeff_eq_zero, WeierstrassCurve.Jacobian.map_dblXYZ, DoubleQuot.coe_quotQuotEquivQuotSupâ, Ideal.quotientMulEquivQuotientProd_snd, MvPowerSeries.C_inv, Unitization.algebraMap_eq_inl, WittVector.mem_ker_truncate, Polynomial.le_rootMultiplicity_iff, LocalSubring.map_maximalIdeal_eq_top_of_isMax, WittVector.fromPadicInt_comp_toPadicInt_ext, HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero, IsFractionRing.fieldEquivOfAlgEquiv_algebraMap, CommSemiRingCat.forgetâSemiRing_preservesLimits, MonomialOrder.degree_X_sub_C, NumberField.IsCMField.complexEmbedding_complexConj, sum_embeddings_eq_finrank_mul, Subfield.coe_comap, MvPolynomial.aevalTower_C, IsFractionRing.closure_range_algebraMap, Ideal.isPrime_map_quotientMk_of_isPrime, CommRingCat.HomTopology.isClosedEmbedding_hom, Polynomial.support_C_subset, algebraMap_lt_algebraMap, Complex.inv_cpow_eq_ite, FractionalIdeal.canonicalEquiv_spanSingleton, Cubic.of_b_eq_zero', Pi.constRingHom_apply, WeierstrassCurve.Affine.derivative_addPolynomial_slope, MvPolynomial.map_expand_pow_char, isLocalHom_of_comp, Polynomial.support_C_mul_X_pow', Module.End.isSemisimple_sub_algebraMap_iff, xInTermsOfW_aux, RatFunc.ofFractionRing_comp_algebraMap, Polynomial.eq_C_content_mul_primPart, PowerSeries.sub_const_eq_X_mul_shift, CommSemiRingCat.forget_preservesLimits, algebraMap_mk, MvPolynomial.mapRange_eq_map, RestrictedProduct.evalRingHom_apply, FiniteField.frobeniusAlgEquivOfAlgebraic_symm_apply, Polynomial.rootMultiplicity_mul_X_sub_C_pow, WittVector.ghostComponent_frobeniusFun, RatFunc.algebraMap_X, Ideal.Quotient.stabilizerHom_apply, Subalgebra.LinearDisjoint.algebraMap_basisOfBasisRight_apply, NumberField.CMExtension.equivMaximalRealSubfield_apply, IsLocalization.Away.isUnit_of_dvd, apply_eq_dotProduct_toMatrixâ_mulVec, Ideal.map_evalRingHom_pi, PowerSeries.constantCoeff_C, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal, CommRingCat.hom_inv_apply, ENat.toENNRealRingHom_apply, RatFunc.intDegree_C, HomogeneousLocalization.awayMap_fromZeroRingHom, IsIntegralClosure.algebraMap_injective', Polynomial.algebraMap_pi_self_eq_eval, MvPolynomial.totalDegree_eq_zero_iff_eq_C, Polynomial.evalâ_at_natCast, NumberField.Units.mem_torsion, AlgebraicIndependent.algebraMap_injective, Subalgebra.LinearDisjoint.trace_algebraMap, ContinuousLinearMap.map_smulââ, Polynomial.card_support_eq', UpperHalfPlane.coe_smul, Complex.inv_def, RingEquiv.ofHomInv_apply, AlgebraicGeometry.Scheme.zeroLocus_map, Polynomial.scaleRoots_aeval_eq_zero, Polynomial.C_eq_algebraMap, PowerSeries.constantCoeff_inv, Polynomial.map_roots_le, Subalgebra.coe_algebraMap, AlgebraicGeometry.Scheme.AffineZariskiSite.coequifibered_iff_forall_isLocalizationAway, Module.toCentroidHom_apply_toFun, MonoidAlgebra.ringHom_ext_iff, NonUnitalStarSubalgebra.unitization_apply, Matrix.projVandermonde_map, Module.Basis.restrictScalars_repr_apply, WeierstrassCurve.Projective.eval_polynomialX_of_Z_ne_zero, Orthonormal.inner_finsupp_eq_sum_right, IsLocalization.sec_spec', CliffordAlgebra.foldr'_algebraMap, Localization.AtPrime.comap_maximalIdeal, Finset.prod_X_add_C_coeff, Polynomial.Bivariate.equivMvPolynomial_symm_C, IsLocalization.minimalPrimes_comap, AlgebraicGeometry.Scheme.Hom.ideal_ker_le, Polynomial.divX_mul_X_add, AlgebraicGeometry.AffineSpace.comp_homOfVector, Subfield.subtype_apply, Polynomial.Splits.roots_map, RootPairing.isValuedIn_iff, Complex.arg_conj, inner_map_complex, Polynomial.natSepDegree_X_pow_char_pow_sub_C, LaurentPolynomial.algebraMap_X_pow, MvPolynomial.map_hsymm, FractionalIdeal.extendedHomâ_eq_zero_iff, SymmetricAlgebra.algebraMap_eq_zero_iff, HahnSeries.ofPowerSeries_apply_coeff, Submodule.lTensorOne'_tmul, UniformSpace.Completion.continuous_coeRingHom, GaussianInt.toComplex_add, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbeddingOfIsReal, Polynomial.coeffList_C, IsLocalization.mk'_add_eq_iff_add_mul_eq_mul, Polynomial.eval_intCast_map, IsIntegralClosure.algebraMap_equiv, DirectSum.decompose_symm_algebraMap, Matrix.det_one_add_X_smul, RingEquiv.ofRingHom_symm_apply, IsLocalization.OverPrime.mem_normalizedFactors_of_isPrime, RingHom.coe_fst, wittStructureRat_rec, Algebra.compHom_smul_def, AlgebraicGeometry.germ_injective_of_isIntegral, Ideal.Quotient.torsionBy_eq_span_singleton, AddMonoidHom.coe_fn_mkRingHomOfMulSelfOfTwoNeZero, RingHom.pi_bijective_of_isIdempotentElem, Algebra.isUnramifiedAt_iff_map_eq, WeierstrassCurve.Jacobian.map_addY, CFC.abs_algebraMap, MvPolynomial.expand_eq_C, Polynomial.roots_expand_image_frobenius_subset, Submodule.rTensorOne'_tmul, Ideal.relNorm_algebraMap', RingCon.lift_bijective_iff, AlgebraicGeometry.isClosedImmersion_iff_isAffineHom, Polynomial.comp_eq_zero_iff, RatFunc.smul_eq_C_smul, PowerSeries.invUnitsSub_mul_sub, AnalyticAt.harmonicAt_conj, Algebra.Extension.cotangentComplexBaseChange_eq_lTensor_cotangentComplex, exists_root_adjoin_eq_top_of_isCyclic, existsUnique_isIdempotentElem_eq_of_ker_isNilpotent, Algebra.TensorProduct.basisAux_tmul, AlgebraicGeometry.AffineSpace.hom_ext_iff, groupCohomology.norm_ofAlgebraAutOnUnits_eq, CommRingCat.forgetâCommSemiRing_preservesLimits, IsLocalization.isPrime_of_isPrime_disjoint, DividedPowers.IsDPMorphism.map_dpow, MvPowerSeries.monomial_zero_eq_C_apply, ValuativeExtension.vle_iff_vle, RootPairing.algebraMap_rootFormIn, ModP.preVal_mk, QuadraticAlgebra.norm_coe, RingHom.map_closureS, Localization.localAlgHom_apply, RatFunc.valuation_eq_LaurentSeries_valuation, FractionalIdeal.extendedHomâ_eq_one_iff, GaussianInt.toComplex_sub, Polynomial.integralNormalization_evalâ_eq_zero, AlgebraicGeometry.Scheme.Hom.preimage_basicOpen, Perfection.coeff_iterate_frobenius, bijective_algebraMap_of_linearEquiv, Polynomial.degree_X_pow_sub_C, SkewMonoidAlgebra.coe_algebraMap, PowerSeries.monomial_zero_eq_C, isIntegral_algebraMap, NumberField.Units.coe_neg_one, FractionalIdeal.mem_coeIdeal, Matrix.SpecialLinearGroup.scalar_eq_coe_self_center, PrimeSpectrum.toPiLocalization_bijective, Ideal.map_quotient_self, tensorKaehlerQuotKerSqEquiv_symm_tmul_D, Valuation.comap_supp, Unitization.norm_eq_sup, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_lt', Algebra.discr_of_matrix_mulVec, IsLocalization.mk'_mem_map_algebraMap_iff, SemiRingCat.FilteredColimits.forget_preservesFilteredColimits, MvPolynomial.degrees_map_le, Ideal.IsIntegralClosure.comap_lt_comap, Ideal.Quotient.exists_algEquiv_fixedPoint_quotient_under, LinearMap.polyCharpolyAux_eval_eq_toMatrix_charpoly_coeff, AlgEquiv.toUnder_inv_right_apply, Perfection.map_apply_coe, Irreducible.natSepDegree_eq_one_iff_of_monic, Polynomial.natDegree_X_pow_add_C, Matrix.scalar_commute, Submodule.span_algebraMap_image_of_tower, Ideal.mk_mem_cotangentIdeal, RingHom.isLocalHom_comp, RatFunc.map_apply_div, AlgebraicGeometry.Scheme.basicOpen_res_eq, GaussianInt.toComplex_star, Polynomial.divX_C_mul, MvPowerSeries.comp_subst_apply, FreeCommRing.lift_comp_of, Polynomial.iterate_derivative_C, SkewMonoidAlgebra.liftNC_one, WeierstrassCurve.Affine.map_slope, NormedSpace.algebraMap_exp_comm, MvPolynomial.eval_eq, FreeRing.hom_ext_iff, cfc_le_algebraMap, Polynomial.degree_mul_leadingCoeff_self_inv, Polynomial.mahlerMeasure_X_add_C, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, AlgebraicGeometry.Scheme.Hom.stalkFunctor_toImage_injective, NumberField.mixedEmbedding.logMap_eq_logEmbedding, Complex.conjAe_coe, RingHomInvPair.comp_apply_eq, AlgebraicGeometry.Scheme.image_basicOpen, RingHom.map_sub, IsLocalRing.ResidueField.map_map, IsLocalization.algEquivOfAlgEquiv_eq_map, Polynomial.taylor_X_pow, GaussianInt.toComplex_def, CliffordAlgebra.changeForm_Κ_mul_Κ, AlgebraicGeometry.LocallyRingedSpace.Hom.prop, TopCat.Presheaf.SubmonoidPresheaf.map, AlgebraicGeometry.SurjectiveOnStalks.surj_on_stalks, IsLocalRing.exists_surjective_of_not_isLocalRing, IsLocalization.map_integerMultiple, NNRat.tendsto_algebraMap_inv_atTop_nhds_zero_nat, LaurentPolynomial.algebraMap_eq_toLaurent, Polynomial.eq_C_coeff_zero_iff_natDegree_eq_zero, PowerSeries.WithPiTopology.isTopologicallyNilpotent_iff_constantCoeff_isNilpotent, PowerSeries.map_eq_zero, AlgEquivClass.commutes, Differential.mapCoeffs_C, spectrum.preimage_algebraMap, PerfectRing.lift_id_apply, Algebra.FinitePresentation.ker_fG_of_surjective, Polynomial.comp_C_mul_X_coeff, smul_algebraMap, starRingEnd_apply, Ideal.spanRank_map_le, MvPolynomial.isUnit_iff_eq_C_of_isReduced, Complex.conj_mul', gal_C_isSolvable, Ideal.spanFinrank_map_le_of_fg, Polynomial.resultant_X_sub_C_pow_left, NonUnitalSubalgebra.unitizationAlgEquiv_apply_coe, ModuleCat.smulNatTrans_apply_app, Algebra.normalizedTrace_algebraMap_apply_eq_self, algebraMap_le_cfc, Subalgebra.algebraMap_mem', HahnSeries.ofPowerSeries_X, CommRingCat.commMon_forgetâ_obj_coe, Polynomial.toLaurent_X_pow, StarSubalgebra.coe_bot, Complex.sin_conj, GaussianInt.to_real_re, Polynomial.derivative_C_mul_X, CommRingCat.toAlgHom_apply, Polynomial.Bivariate.swap_X, MvPolynomial.eval_add, WeierstrassCurve.Projective.map_polynomialX, AdjoinRoot.lift_mk, Polynomial.eval_iterate_derivative_rootMultiplicity, Algebra.SubmersivePresentation.map_jacobianRelationsOfHasCoeffs, WeierstrassCurve.Affine.CoordinateRing.map_mk, Polynomial.Splits.X_add_C, LocallyConstant.mapRingHom_apply_apply, AlgebraicGeometry.SurjectiveOnStalks.stalkMap_surjective, IsLocalRing.ResidueField.map_residue, RingCat.forget_preservesLimitsOfSize, MvPowerSeries.trunc_map, RingHom.isIntegralElem_leadingCoeff_mul, Polynomial.degree_C_lt, algebraMap_comp_intCast, PowerSeries.coeff_exp, Complex.conj_eq_iff_re, IsSelfAdjoint.algebraMap, Localization.mapToFractionRing_apply, coe_frobeniusEquiv, Polynomial.aeval_conj, StarAlgHom.ofId_apply, Polynomial.nextCoeff_C_eq_zero, CommRingCat.HomTopology.isEmbedding_hom, PerfectRing.liftAux_id_apply, RCLike.re_eq_add_conj, NumberField.integralBasis_repr_apply, Matrix.scalarAlgHom_apply, Polynomial.degree_C_mul_X_pow_le, Polynomial.separable_prod_X_sub_C_iff', RingCon.coe_algebraMap, Polynomial.le_trailingDegree_C_mul_X_pow, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_hom_eq_germ_apply, Polynomial.map_mapRingHom_evalEval, PowerSeries.spanFinrank_eq_spanFinrank_map_constantCoeff_of_X_notMem_of_fg_of_isPrime, AdjoinRoot.root_isInv, MvPolynomial.evalâ_eq', Module.algebraMap_end_eq_smul_id, LocallyConstant.constRingHom_apply, PowerSeries.trunc_one_left, LaurentSeries.coe_X_compare, WeierstrassCurve.Jacobian.baseChange_polynomial, IsAdjoinRoot.adjoinRootAlgEquiv_apply_eq_map, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_eq, RingHom.codomain_trivial_iff_map_one_eq_zero, WittVector.IsPoly.map, Polynomial.coeff_mul_C, MvPolynomial.eval_monomial, PrimeSpectrum.sigmaToPi_asIdeal, MonomialOrder.degree_C, RingCat.ofHom_apply, Ideal.quotientToQuotientRangePowQuotSucc_surjective, smoothSheafCommRing.Κ_forgetStalk_inv_apply, DoubleCentralizer.algebraMap_snd, Polynomial.rootMultiplicity_C, WittVector.ker_map_le_ker_mk_comp_ghostComponent, Polynomial.eq_prod_roots_of_splits_id, RCLike.wInner_const_left, Valuation.Integers.dvdNotUnit_iff_lt, Ideal.le_comap_of_ramificationIdx_ne_zero, RatFunc.laurentAux_algebraMap, RCLike.wInner_cWeight_const_left, MvPolynomial.coe_evalâHom, MvPolynomial.vars_C_mul, Polynomial.coeff_C, PowerSeries.sub_const_eq_shift_mul_X, Algebra.algebraMapSubmonoid_le_comap, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, AdjoinRoot.modByMonicHom_mk, QuadraticAlgebra.coe_norm_eq_mul_star, RingQuot.lift_def, Ideal.localizedâ_eq_restrictScalars_map, Algebra.intNorm_eq_of_isLocalization, Algebra.Generators.toAlgHom_ofComp_rename, DirectSum.decompose_algebraMap, Valuation.Integers.valuation_unit, Polynomial.natDegree_X_sub_C, IsLocalization.localization_localization_map_units, IsLocalization.Away.mul_invSelf, WeierstrassCurve.Affine.CoordinateRing.mk_Ď, wittStructureRat_rec_aux, WittVector.fontaineThetaModPPow_teichmuller, WeierstrassCurve.Projective.eval_polynomialZ, trace_eq_sum_roots, Matrix.matPolyEquiv_charmatrix, Polynomial.natDegree_C_mul, NumberField.canonicalEmbedding.nnnorm_eq, CliffordAlgebra.foldl_algebraMap, Submodule.rTensorOne_tmul, Algebra.Generators.ker_localizationAway, Polynomial.card_support_eq_three, RatFunc.algebraMap_apply_div, algebraMap_memâp_infty, FractionalIdeal.mem_coeIdeal_of_mem, spectrum.mem_resolventSet_iff, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_fst, Algebra.WeaklyQuasiFiniteAt.comap_algEquiv, RatFunc.div_smul, MvPolynomial.constantCoeff_smul, HahnSeries.C_zero, IntermediateField.algebraMap_apply, MvPolynomial.algHom_C, LinearMap.toMatrix_algebraMap, IsAlgClosure.equivOfEquiv_symm_algebraMap, MvPolynomial.leadingCoeff_toLex_C, NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero, Ideal.Quotient.factor_surjective, Polynomial.resultant_X_sub_C_pow_right, RCLike.inner_apply, IsSelfAdjoint.conj_eq, WittVector.iterate_frobenius_coeff, Polynomial.smeval_C_mul, Complex.conj_cpow_eq_ite, PerfectionMap.map_map, Polynomial.X_sub_C_dvd_sub_C_eval, MvPolynomial.eval_pow, QuadraticAlgebra.algebraMap_eq, Algebra.discr_of_matrix_vecMul, RingCon.coe_quotientKerEquivRangeS_mk, WeierstrassCurve.Ψ_three, Subsemiring.comap_toSubmonoid, Polynomial.prime_X_sub_C, Matrix.Module.scalar_smul, IntermediateField.LinearDisjoint.norm_algebraMap, MvPolynomial.evalâHom_zero'_apply, PowerSeries.coe_zero, FractionalIdeal.exists_mem_algebraMap_eq, Polynomial.evalâ_def, DoubleCentralizer.algebraMap_toProd, PowerSeries.IsWeierstrassDivisorAt.isUnit_shift, RatFunc.eval_C, RingTheory.Sequence.isWeaklyRegular_append_iff', Valuation.supp_quot, RCLike.hasSum_conj, Lagrange.iterate_derivative_interpolate, Ideal.ideal_prod_eq, PowerSeries.map_X, RingHom.injective, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, CommRingCat.forgetToRingCat_obj, WeierstrassCurve.Projective.map_addY, Ideal.map_snd_prod, CommRingCat.Colimits.cocone_naturality_components, isSMulRegular_algebraMap_iff, iterateFrobenius_def, DoubleQuot.coe_quotQuotEquivQuotSupâ_symm, UniformSpace.Completion.algebraMap_def, Matrix.toLinearMapâââ'_apply, NumberField.mixedEmbedding.mixedEmbedding_apply_isReal, IntermediateField.adjoin.range_algebraMap_subset, IsAdjoinRoot.lift_map, Ideal.relNorm_algebraMap, AlgebraicGeometry.Scheme.evaluation_naturality_apply, Polynomial.C_sub, LaurentPolynomial.single_eq_C, NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le, OrthogonalIdempotents.surjective_pi, Polynomial.roots_X_pow_char_sub_C_pow, RingHom.mem_rangeS, PrimeSpectrum.discreteTopology_iff_toPiLocalization_surjective, RingHom.rangeS_top_iff_surjective, Complex.normSq_conj, Valuation.HasExtension.val_algebraMap, WeierstrassCurve.VariableChange.map_t, DividedPowers.DPMorphism.toRingHom_apply, Subfield.coe_subtype, MvPolynomial.derivation_C, PowerSeries.constantCoeff_divXPowOrder, Matrix.submonoidCenter_eq_scalar_map, IsLocalization.isLocalization_of_submonoid_le, Polynomial.Bivariate.swap_C_C, Module.Basis.localizationLocalization_repr_algebraMap, Ideal.Quotient.eq_zero_iff_mem, ValuationSubring.algebraMap_apply, AdjoinRoot.liftAlgHom_mk, IsLocalRing.ResidueField.map_id_apply, MvPolynomial.dvd_smul_X_iff_exists, PowerSeries.inv_eq_zero, tensorKaehlerQuotKerSqEquiv_tmul_D, smoothSheafCommRing.eval_surjective, Complex.add_conj, WeierstrassCurve.Projective.map_dblY, Zsqrtd.lift_apply_apply, NumberField.Embeddings.instNonemptyRingHom, LinearMap.hasEigenvalue_zero_tfae, Polynomial.iterate_derivative_eq_sum, Complex.tanh_conj, AlgebraicGeometry.Scheme.residue_surjective, Ideal.finrank_quotient_map, MvPolynomial.schwartz_zippel_sup_sum, Polynomial.quadratic_dvd_of_aeval_eq_zero_im_ne_zero, MvPolynomial.mem_map_C_iff, Polynomial.algEquivAevalXAddC_symm_apply, FractionalIdeal.coeSubmoduleHom_apply, contraction_of_isPowMul_of_boundedWrt, MvPolynomial.prime_C_iff, derivationToSquareZeroEquivLift_symm_apply_apply_coe, Polynomial.isMaximal_comap_C_of_isJacobsonRing, WittVector.ghostComponentModPPow_teichmuller_coeff, Polynomial.nextCoeff_X_sub_C, LaurentSeries.exists_powerSeries_of_memIntegers, Polynomial.natDegree_C_mul_X_pow, MvPolynomial.eval_mul, AdjoinRoot.coe_mkâ, Ideal.Quotient.algEquivOfEqComap_apply, Ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff, TensorAlgebra.algebraMap_eq_one_iff, WittVector.iterate_verschiebung_iterate_frobenius, GaussianInt.to_real_im, LinearMap.norm_extendTođ'_apply_sq, DirectLimit.Ring.of_f, ENNReal.coe_ofNNRealHom, Ideal.quotEquivOfEq_eq_factor, Polynomial.dvd_mul_leadingCoeff_inv, galRestrictHom_symm_algebraMap_apply, RatFunc.algebraMap_C, Polynomial.C_mul_X_pow_eq_self, MvPowerSeries.map_toSubring, MvPolynomial.universalFactorizationMapPresentation_relation, coe_frobenius_comp_coe_frobeniusEquiv_symm, IsLocalization.isLocalization_isLocalization_atPrime_isLocalization, Polynomial.degree_X_sub_C_le, PowerSeries.trunc_C, Polynomial.evalâ_at_intCast, Ideal.quotientKerAlgEquivOfSurjective_apply, Matrix.mem_range_scalar_iff_commute_single', MvPolynomial.evalâ_zero_apply, GaussianInt.toComplex_re_div, AlgebraicIndependent.algebraMap_aevalEquiv, Valuation.comap_apply, IsBaseChange.toDual_comp_apply, RingHom.toFun_eq_coe, IsBaseChange.linearMapLeftRightHom_toMatrix, AdjoinRoot.Minpoly.coe_toAdjoin_mk_X, IsLocalization.mk'_eq_iff_eq, LinearIsometry.map_smulââ, CStarAlgebra.mem_Icc_algebraMap_iff_nnnorm_le, AlgebraicGeometry.StructureSheaf.algebraMap_obj_top_bijective, Algebra.algebraMap_eq_smul_one, IsConjRoot.add_algebraMap, ContinuousLinearMap.toContinuousAddMonoidHom_injective, smoothSheafCommRing.forgetStalk_hom_comp_evalHom, Polynomial.degree_C_mul_X_le, Module.isTorsionFree_iff_algebraMap_injective, NumberField.FinitePlace.norm_def_int, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.coequalizer_Ď_stalk_isLocalHom, IsAdjoinRoot.lift_algebraMap, Module.Invertible.toModuleEnd_bijective, UpperHalfPlane.J_smul, WittVector.verschiebung_mul_frobenius, MvPolynomial.eq_C_of_isEmpty, Polynomial.expand_zero, IsLocalization.injectiveâ, CliffordAlgebraQuaternion.ofQuaternion_mk, Polynomial.eraseLead_C_mul_X_pow, PerfectRing.lift_comp_lift_apply_eq_self, Polynomial.roots_expand_pow_map_iterateFrobenius_le, WittVector.coeff_frobenius_charP, Polynomial.Monic.natSepDegree_eq_one_iff, Polynomial.trailingDegree_C, GaussianInt.toComplex_re, WeierstrassCurve.Projective.polynomialX_eq, Subsemiring.mem_comap, PowerSeries.WithPiTopology.continuous_C, Ring.DirectLimit.ringEquiv_of, CommRingCat.FilteredColimits.forget_preservesFilteredColimits, MulSemiringActionHom.coe_fn_coe, Module.End.natCast_def, MvPolynomial.monomial_zero', X_pow_sub_C_irreducible_of_prime, AlgebraicGeometry.LocallyRingedSpace.Îevaluation_naturality_apply, Polynomial.roots_multiset_prod_X_sub_C, PowerSeries.coe_C, PrimeSpectrum.mem_range_comap_iff, ZMod.ringHom_map_cast, Ideal.Quotient.algebraMap_quotient_pow_ramificationIdx, Polynomial.eval_one_map, AlgebraicGeometry.StructureSheaf.toStalk_stalkSpecializes_apply, Set.up_image, Algebra.IsPushout.cancelBaseChangeAux_symm_tmul, NumberField.discr_eq_basisMatrix_det_sq, IntermediateField.adjoin.algebraMap_mem, RingHom.prod_bijective_of_isIdempotentElem, Polynomial.homogenize_C_mul, IsLocalRing.exists_factor_valuationRing, AdjoinRoot.powerBasisAux'_repr_symm_apply, spectrum.add_singleton_eq, MvPowerSeries.map_eq_zero, isLocalHom_id, Matrix.algebraMap_eq_diagonal, IsLocalHom.of_specComap_surjective, Localization.mk_one_eq_algebraMap, Polynomial.contract_C, NonUnitalSubalgebra.unitization_apply, IsLocalization.AtPrime.equivQuotMaximalIdeal_apply_mk, Polynomial.sylvester_map_map, AlgebraicGeometry.Spec_zeroLocus_eq_zeroLocus, AdicCompletion.Ideal.mk_eq_mk, Matrix.charpoly_fin_two, LinearMap.eval_charpoly, Algebra.mul_sub_algebraMap_pow_commutes, RCLike.conj_tsum, RingHom.coe_one, ZMod.ringHom_surjective, AddChar.starComp_apply, Polynomial.separable_prod_X_sub_C_iff, Polynomial.resultant_C_left, Valuation.Integers.maximalIdeal_eq_setOf_le_v_algebraMap, LinearMap.charpoly_constantCoeff_eq_zero_iff, Algebra.ofId_apply, Polynomial.natDegree_mul_C_of_isUnit, Polynomial.dickson_add_two, surjective_algebraMap_of_linearMap, FreeRing.lift_comp_of, AdjoinRoot.quotEquivQuotMap_apply_mk, WeierstrassCurve.Projective.map_dblU, PowerSeries.coe_neg, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply, Derivation.map_algebraMap, MvPolynomial.eval_indicator_apply_eq_zero, Polynomial.exists_eq_pow_rootMultiplicity_mul_and_not_dvd, Polynomial.Bivariate.swap_map_C, MvPolynomial.sumToIter_iterToSum, Polynomial.Monic.eq_X_add_C, MvPowerSeries.coeff_C_mul, Perfection.ext_iff, MvPolynomial.map_surjective_iff, Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd, LaurentPolynomial.evalâ_C_mul_T_neg_n, constantCoeff_wittPolynomial, WeierstrassCurve.Affine.CoordinateRing.mk_Ψ_sq, Ideal.comap_map_quotientMk, RingHom.surjective_iff_epi_and_finite, CliffordAlgebra.reverse.commutes, AlgebraicGeometry.Scheme.map_basicOpen, IsLocalization.nonZeroDivisors_le_comap, WeierstrassCurve.Projective.polynomialY_eq, MvPolynomial.aeval_eq_constantCoeff_of_vars, Polynomial.eq_C_of_degree_le_zero, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_tmul, WittVector.liftEquiv_apply, SemiRingCat.forgetReflectIsos, WittVector.ghostMap_apply, GaussianInt.toComplex_inj, WeierstrassCurve.Projective.negDblY_eq, Algebra.norm_eq_prod_automorphisms, PresheafOfModules.Derivation'.d_app, Ideal.minimalPrimes_eq_comap, MvPowerSeries.constantCoeff_toSubring, MulChar.starComp_apply, Submodule.torsionBy.mk_ideal_smul, RCLike.wInner_const_right, SetLike.algebraMap_mem_graded, Matrix.sub_scalar_sq_eq_disc, AddMonoidAlgebra.coe_mapRangeRingHom, Polynomial.contentIdeal_C, Ideal.Quotient.mkâ_ker, Polynomial.eval_C_X_evalâ_map_C_X, MvPolynomial.map_injective_iff, PowerSeries.gaussNorm_C, SetLike.GradeZero.coe_algebraMap, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding_of_isReal, Polynomial.supNorm_C, SetSemiring.down_imageHom, OrthogonalIdempotents.lift_of_isNilpotent_ker, Complex.cot_conj, DividedPowers.DPMorphism.ideal_comp, RingHom.Bijective.containsIdentities, RingHom.FaithfullyFlat.codescendsAlong_surjective, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_le_one, MvPolynomial.constantCoeff_monomial, MvPolynomial.smul_eval, TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd, AlgebraicGeometry.StructureSheaf.const_algebraMap, Subsemiring.inclusion_injective, Ideal.Quotient.mk_surjective, RCLike.conj_eq_iff_real, DividedPowers.isDPMorphism_def, DirectSum.toSemiring_apply, matPolyEquiv_map_C, WittVector.ghostComponent_verschiebung, PowerSeries.map_subst, MvPolynomial.C_eq_zero, MvPolynomial.supDegree_toLex_C, WeierstrassCurve.Projective.eval_polynomialY_of_Z_ne_zero, smoothSheafCommRing.Κ_forgetStalk_inv_assoc, Polynomial.card_roots_X_pow_sub_C, NumberField.InfinitePlace.embedding_of_isReal_apply, MvPolynomial.aeval_zero, Ideal.Quotient.eq, Ideal.quotientEquivAlgOfEq_mk, Valuation.HasExtension.instIsLocalHomValuationInteger, IsPRadical.injective_comp_of_pNilradical_eq_bot, RingHom.equivRatAlgHom_apply, RingHom.sclosure_preimage_le, PresheafOfModules.map_comp, IsScalarTower.algebraMap_smul, IsLocalization.mk'_eq_iff_eq_mul, Algebra.Norm.Transitivity.eval_zero_comp_det, MvPowerSeries.algebraMap_apply'', IsLocalization.coe_toLocalizationMap, LinearMap.map_mul_algebraMap, Ideal.comap_surjective_of_faithfullyFlat, MvPowerSeries.rescale_homogeneous_eq_smul, RingHom.surjectiveOnStalks_iff_forall_maximal', IsFractionRing.mk'_mk_eq_div, NumberField.mixedEmbedding.normAtAllPlaces_mixedEmbedding, NumberField.RingOfIntegers.coe_injective, Language.map_map, MvPolynomial.constantCoeff_X, MvPolynomial.frobenius_zmod, PowerSeries.expand_C, Polynomial.derivative_sq, Polynomial.leadingCoeff_C_mul_X_pow, WittVector.frobeniusPolyAux_eq, Polynomial.mem_roots_sub_C, Orthonormal.inner_left_sum, algebraMap_le_iff_le_spectrum, PowerSeries.map_algebraMap_eq_subst_X, RatFunc.liftAlgHom_apply_div, Subring.closure_preimage_le, CyclotomicRing.adjoin_algebra_injective, Polynomial.isMaximal_comap_C_of_isMaximal, Polynomial.not_isUnit_X_add_C, Polynomial.degree_cubic, ModuleCat.Derivation.d_map, Polynomial.natSepDegree_C_mul, UpperHalfPlane.petersson_symm, Algebra.Extension.Hom.mapKer_apply_coe, StarSubalgebra.algebraMap_mem, FreeAlgebra.algebraMap_inj, PrimeSpectrum.range_comap_snd, LaurentPolynomial.C_eq_algebraMap, Algebra.Presentation.tensorModelOfHasCoeffsHom_tmul, Localization.monoidOf_eq_algebraMap, PowerSeries.constantCoeff_largeSchroderSeries, IsLocalization.AtPrime.algebraMap_equivQuotMaximalIdeal_symm_apply, IsLocalization.toInvSubmonoid_mul, WeierstrassCurve.Projective.baseChange_polynomialX, ExteriorAlgebra.isUnit_algebraMap, isPurelyInseparable_iff_minpoly_eq_X_sub_C_pow, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.coequalizer_Ď_app_isLocalHom, CommRingCat.ofHom_apply, GradedTensorProduct.algebraMap_def', WeierstrassCurve.Affine.CoordinateRing.XYIdeal_neg_mul, MvPolynomial.C_mul', Polynomial.cyclotomic.eval_apply, frobenius_neg, PerfectionMap.comp_equiv, MvPolynomial.isEmptyAlgEquiv_apply, IsPRadical.ker_le, MvPolynomial.bindâ_X_right, Ideal.Quotient.factor_ker, IsLocalization.scaleRoots_commonDenom_mem_lifts, IsSepClosed.algebraMap_surjective, PowerSeries.C_eq_algebraMap, Algebra.Generators.cMulXSubOneCotangent_eq, MvPolynomial.map_C, Polynomial.evalâ_at_one, spectrum.singleton_add_eq, UpperHalfPlane.Ď_ofReal, TruncatedWittVector.truncate_surjective, AlgebraicGeometry.Scheme.IdealSheafData.isLocalization_away, AlgebraicGeometry.isOpenImmersion_eq_inf, Polynomial.resultant_X_add_C_left, gal_X_sub_C_isSolvable, boolRingCatEquivBoolAlg_inverse, IsLocalization.Away.instHMulAwayCoeRingHomAlgebraMap, PrimeSpectrum.piLocalizationToMaximal_surjective, MvPolynomial.C_dvd_iff_dvd_coeff, Algebra.IsInvariant.isInvariant, RingHom.iterate_map_frobenius, isIntegrallyClosedIn_iff, MvPolynomial.pderiv_C_mul, Filter.Germ.coe_coeRingHom, TwoSidedIdeal.comap_comap, RingHom.map_iterate_frobeniusEquiv_symm, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eqâ, IsLocalization.Away.instHMulAwayCoeRingHomAlgebraMap_1, IsLocalization.AtPrime.map_eq_maximalIdeal, DoubleQuot.ker_quotLeftToQuotSup, AlgebraicGeometry.IsClosedImmersion.hasAffineProperty, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq, matrixEquivTensor_apply_symm, Polynomial.IsMonicOfDegree.aeval_add, Polynomial.natDegree_multiset_prod_X_sub_C_eq_card, CommSemiRingCat.FilteredColimits.forget_preservesFilteredColimits, NumberField.RingOfIntegers.isIntegral_coe, Matrix.toMvPolynomial_eval_eq_apply, Polynomial.C_dvd_iff_dvd_coeff, IsAdjoinRoot.lift_self_apply, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, RestrictScalars.ringEquiv_map_smul, LaurentPolynomial.single_eq_C_mul_T, Ideal.under_def, AlgHom.toUnder_right, AddMonoidAlgebra.mapDomain_algebraMap, Polynomial.Splits.C_mul_X_pow, Ideal.Factors.liesOver, WittVector.constantCoeff_wittMul, AlgHom.liftNormal_commutes, spectrum.singleton_sub_eq, NumberField.Units.complexEmbedding_apply, IsStronglyTranscendental.iff_of_isFractionRing, NumberField.count_multisetInfinitePlace_eq_mult, AlgebraicGeometry.instIsZariskiLocalAtTargetStalkwiseBijectiveCoeRingHom, RingHom.map_mulVec, IsAdicComplete.mk_liftAlgHom, RingHom.op_symm_apply_apply, CStarAlgebra.mul_star_le_algebraMap_norm_sq, Polynomial.exists_eq_X_add_C_of_natDegree_le_one, Algebra.Generators.self_algebra_smul, MvPowerSeries.map_map, Matrix.charpoly_coeff_eq_prod_coeff_of_le, AdjoinRoot.Polynomial.quotQuotEquivComm_mk, Ideal.quotientInfEquivQuotientProd_snd, IsLocalization.toLocalizationMap_toMonoidHom, IntermediateField.AdjoinPair.algebraMap_genâ, RatFunc.denom_div, algebraMapCLM_apply, WeierstrassCurve.coe_inv_map_Î', Polynomial.opRingEquiv_symm_C_mul_X_pow, Polynomial.eval_map_apply, RingHom.ker_coe_toRingHom, PowerSeries.invOfUnit_eq, DirectSum.coeRingHom_of, IsIntegralClosure.algebraMap_mk', WeierstrassCurve.Affine.CoordinateRing.exists_smul_basis_eq, BoundedLatticeHom.asBoolRing_apply, PrimeSpectrum.preimage_comap_zeroLocus_aux, ValuationRing.of_integers, Polynomial.contentIdeal_map_eq_map_contentIdeal, Algebra.smulTower_leftMulMatrix_algebraMap_ne, PerfectRing.liftAux_id, quasispectrum.algebraMap_mem_iff, IsDiscreteValuationRing.exists_lift_of_le_one, Polynomial.iterate_derivative_prod_X_sub_C, CompleteOrthogonalIdempotents.lift_of_isNilpotent_ker, NumberField.InfinitePlace.Completion.extensionEmbedding_coe, Polynomial.signVariations_eraseLead_mul_X_sub_C, IsLocalization.AtPrime.isMaximal_map, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map_d, Valuation.HasExtension.algebraMap_mem_valuationSubring, eval_det, Polynomial.dvd_content_iff_C_dvd, NoZeroSMulDivisors.iff_algebraMap_injective, cfc_const, LaurentPolynomial.comul_C, NumberField.InfinitePlace.denseRange_algebraMap_pi, Polynomial.coeff_C_succ, algebraMap_injective_of_field_isFractionRing, MvPolynomial.funext_set_iff, RingHom.map_adjugate, IsLocalization.algEquivOfAlgEquiv_symm_apply, Algebra.commute_algebraMap_left, Complex.inner, WittVector.map_verschiebung, Polynomial.separable_C, coe_iterateFrobenius, WittVector.verschiebung_frobenius, NumberField.mixedEmbedding.fundamentalCone.mixedEmbedding_preimageOfMemIntegerSet, Orthonormal.inner_finsupp_eq_sum_left, MvPolynomial.map_monomial, QuasispectrumRestricts.algebraMap_image, Polynomial.instIsLocalHomRingHomC, HopfAlgebra.mul_antipode_rTensor_comul_apply, BoolRing.hasForgetToBoolAlg_forgetâ_map, AddMonoidAlgebra.liftNC_smul, MvPowerSeries.rescale_rescale, Ring.DirectLimit.quotientMk_of, AlgEquiv.toUnder_hom_right_apply, MvPolynomial.aeval_map_algebraMap, Algebra.Generators.Hom.toAlgHom_C, NumberField.RingOfIntegers.mapRingHom_apply, ModuleCat.HasColimit.coconePointSMul_apply, RatFunc.intDegree_polynomial, LaurentPolynomial.evalâ_C, cfc_eval_C, Polynomial.mahlerMeasure_X_sub_C, RCLike.continuous_conj, Ideal.comap_map_mk, minpoly.add_algebraMap, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self_apply, Polynomial.not_ker_le_map_C_of_surjective_of_weaklyQuasiFiniteAt, AlgebraicGeometry.Scheme.stalkMap_hom_inv_apply, iterate_frobenius, Valuation.Integers.eq_algebraMap_or_inv_eq_algebraMap, PowerSeries.map_invUnitsSub, IsLocalization.lift_id, Ideal.isPrime_map_C_of_isPrime, Matrix.GeneralLinearGroup.mem_center_iff_val_eq_scalar, CommRingCat.HomTopology.continuous_apply, Polynomial.div_eq_quo_add_rem_div, norm_algebraMap, UpperHalfPlane.coe_J_smul, ContinuousLinearMap.toContinuousAddMonoidHom_inj, NumberField.Units.coe_pow, IsPurelyInseparable.algebraMap_elemReduct_eq', MulSemiringAction.charpoly_eq, RootPairing.algebraMap_posRootForm_posForm, DoubleQuot.coe_quotQuotEquivQuotOfLEâ, MvPolynomial.esymmAlgHom_zero, CliffordAlgebra.EquivEven.v_sq_scalar, LaurentSeries.LaurentSeries_coe, MvPowerSeries.map_monomial, MvPolynomial.coeToMvPowerSeries.algHom_apply, Ideal.quotientToQuotientRangePowQuotSucc_injective, WeierstrassCurve.Affine.CoordinateRing.C_addPolynomial_slope, IsAdjoinRoot.adjoinRootAlgEquiv_apply_mk, Algebra.idealMap_isLocalizedModule, Polynomial.isMonicOfDegree_one_iff, PrimeSpectrum.closure_image_comap_zeroLocus, root_X_pow_sub_C_pow, RingHom.mem_rangeS_self, Valuation.Integers.wfDvdMonoid_iff_wellFounded_gt_on_v, PerfectionMap.comp_symm_equiv, NumberField.conj_basisMatrix, char_dvd_card_solutions, RingHom.coe_fieldRange, CommSemiRingCat.comp_apply, AlgebraicGeometry.Scheme.basicOpen_appLE, Mathlib.Tactic.ComputeDegree.natDegree_C_le, AlgHom.coe_ideal_map, WeierstrassCurve.Jacobian.polynomialZ_eq, NumberField.Units.abs_det_eq_abs_det, RingHom.rangeRestrictFieldEquiv_apply_symm_apply, ModuleCat.MonModuleEquivalenceAlgebra.algebraMap, MvPolynomial.evalâHom_map_hom, LaurentPolynomial.evalâ_toLaurent, IsPurelyInseparable.algebraMap_iterateFrobenius, AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap_apply, Polynomial.coe_mapRingHom, CommSemiRingCat.id_apply, Polynomial.C_mul_dvd, AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap', Algebra.trace_localization, MvPolynomial.finSuccEquiv_eq, char_dvd_card_solutions_of_sum_lt, Algebra.adjoin_eq_adjoin_union, CommRingCat.forget_map_apply, Module.algebraMap_end_apply, MvPowerSeries.isUnit_constantCoeff, PowerSeries.constantCoeff_divXPowOrder_eq_zero_iff, MvPolynomial.homogeneousComponent_zero, FractionalIdeal.exists_ne_zero_mem_isInteger, AlgebraicGeometry.Scheme.IdealSheafData.ofIdealTop_ideal, Algebra.discr_powerBasis_eq_prod, MvPolynomial.ker_evalâHom_universalFactorizationMap, Matrix.mem_range_scalar_of_commute_single, NumberField.InfinitePlace.isometry_embedding_of_isReal, Matrix.scalar_comm_iff, Polynomial.C_comp, RingHom.pNilradical_le_ker_of_perfectRing, MvPolynomial.coeff_map, NumberField.ComplexEmbedding.IsReal.coe_embedding_apply, OrthogonalIdempotents.map, MvPolynomial.monomial_sum_index, Polynomial.div_C, LinearMap.IsSymm.eq, spectralNorm_extends, InfiniteGalois.mem_range_algebraMap_iff_fixed, Algebra.Smooth.exists_finiteType, ContinuousLinearEquiv.map_smulââ, Ring.DirectLimit.map_id, CliffordAlgebra.contractLeft_Κ, Matrix.mvPolynomialX_mapMatrix_eval, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero, Polynomial.comp_one, IsLocalization.mem_localizationLocalizationSubmodule, Ideal.mem_map_C_iff, RingHomIsometric.norm_map, isLocalHom_of_isIso, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_apply, PadicInt.ker_toZModPow, Polynomial.sumIDeriv_X, WeierstrassCurve.Î_integral_of_isIntegral, RingHom.map_zero, Algebra.trace_algebraMap_of_basis, WittVector.fontaineTheta_teichmuller, CommRingCat.forgetâRing_preservesLimits, Algebra.IsPushout.equiv_tmul, NumberField.inverse_basisMatrix_mulVec_eq_repr, CStarAlgebra.norm_le_iff_le_algebraMap, Polynomial.dvd_C_mul_X_sub_one_pow_add_one, RatFunc.denom_div_dvd, MonomialOrder.degree_eq_zero_iff, Polynomial.rootSet_C, matPolyEquiv_symm_C, RingCat.forgetReflectIsos, Polynomial.evalâ_at_zero, Polynomial.toFinsupp_algebraMap, RingHom.injective_respectsIso, PowerSeries.constantCoeff_zero, Polynomial.Bivariate.equivMvPolynomial_C_X, isPurelyInseparable_iff_minpoly_eq_X_pow_sub_C, Polynomial.lifts_iff_coeff_lifts, Prod.algebraMap_apply, Polynomial.natDegree_mul_C_eq_of_mul_ne_zero, StarSubalgebra.range_subset, Polynomial.coe_compRingHom, NumberField.IsCMField.ringOfIntegersComplexConj_eq_self_iff, DividedPowers.isSubDPIdeal_ker, RatFunc.laurent_C, Polynomial.ofMultiset_apply, RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply, NumberField.InfinitePlace.card_real_embeddings, RingHom.toNatAlgHom_coe, RingHom.kerLift_injective, DifferentiableAt.comp_semilinearâ, MonomialOrder.leadingTerm_C, ContinuousLinearMap.comp_smulââ, NumberField.Units.coe_injective, CFC.log_smul', Ideal.comap_lt_comap_of_integral_mem_sdiff, Cubic.prod_X_sub_C_eq, PowerSeries.fg_iff_of_isPrime, MvPolynomial.quotientEquivQuotientMvPolynomial_leftInverse, Module.compHom.toLinearMap_apply, Polynomial.coeToPowerSeries.algHom_apply, AdicCompletion.evalOneâ_of, AlgebraicGeometry.LocallyRingedSpace.stalkMap_germ_apply, Polynomial.rootMultiplicity_eq_multiplicity, NumberField.Units.coe_one, WittVector.truncate_lift, spectralAlgNorm_extends, CommSemiRingCat.forget_map, Algebra.IsCentral.mem_center_iff, AlgebraicGeometry.stalkwise_Spec_map_iff, Algebra.FormallySmooth.iff_split_surjection, tendsto_algebraMap_inverse_atTop_nhds_zero_nat, Subring.mem_closure_image_of, LaurentSeries.powerSeriesRingEquiv_coe_apply, Ideal.Quotient.mk_out, Polynomial.multiset_prod_X_sub_C_nextCoeff, frobenius_def, Polynomial.C_div, Subring.integralClosure_le_iff, IsLocalization'.toIsLocalizationMap, AlgebraicGeometry.Scheme.IdealSheafData.ker_subschemeΚ_app, NumberField.InfinitePlace.Completion.bijective_extensionEmbeddingOfIsReal, MvPolynomial.aeval_bindâ, NumberField.IsCMField.mem_realUnits_iff, CentroidHom.toEndRingHom_apply, Polynomial.Chebyshev.algebraMap_eval_T, Lagrange.nodal_eq_mul_nodal_erase, IsFractionRing.injective_comp_algebraMap, RingHom.map_iterateFrobenius, RingHom.map_det, CFC.abs_algebraMap_nnreal, WittVector.ghostComponent_zero_verschiebung, Polynomial.divX_C_mul_X_pow, Submodule.mker_spanSingleton, MvPolynomial.prod_X_add_C_coeff, PowerSeries.coeff_zero_eq_constantCoeff_apply, RingQuot.mkRingHom_surjective, SeparationQuotient.mk_algebraMap, DirectSum.toSemiring_of, MvPowerSeries.inv_eq_zero, Polynomial.roots_expand_pow_map_iterateFrobenius, bijective_algebraMap_of_linearMap, LaurentPolynomial.toLaurent_support, RCLike.conj_wInner_symm, Algebra.trace_quotient_mk, IsSMulRegular.of_flat_of_isBaseChange, Complex.coe_algebraMap, CommRingCat.equalizer_Κ_isLocalHom', NumberField.canonicalEmbedding.mem_rat_span_latticeBasis, AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo', WeierstrassCurve.Ď_three, surjective_frobenius, GradedTensorProduct.includeLeftRingHom_apply, IsCoprime.map, Algebra.surjective_algebraMap_iff, Ideal.polynomialQuotientEquivQuotientPolynomial_symm_mk, LaurentSeries.powerSeriesEquivSubring_apply, MvPolynomial.counit_surjective, MvPowerSeries.map_iterateFrobenius_expand, Polynomial.eval_zero_map, NumberField.mixedEmbedding.unitSMul_smul, RingCon.kerLift_injective, Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, Subring.mem_comap, Polynomial.nextCoeff_map_eq, Polynomial.derivative_pow, CommRingCat.FilteredColimits.forgetâRing_preservesFilteredColimits, QuadraticAlgebra.omega_mul_algebraMap_mul_mk, AlgebraicIndependent.sumElim_comp, Polynomial.C_ofNat, Polynomial.reverse_add_C, AlgebraicGeometry.stalkMap_toStalk_apply, Polynomial.roots_map_of_map_ne_zero_of_card_eq_natDegree, WeierstrassCurve.Projective.negDblY_eq', MvPolynomial.quotient_mk_comp_C_injective, SymmetricAlgebra.algebraMap_eq_one_iff, RingHom.injective_nat, Polynomial.isSplittingField_C, LinearMap.polyCharpolyAux_coeff_eval, IsIntegral.map_of_comp_eq, AlgebraicClosure.Monics.map_eq_prod, RingHom.coe_snd, liftOfDerivationToSquareZero_apply, LocalizedModule.mul_by_divBy, AlgHomClass.commutes, Orientation.kahler_rotation_left, minpoly.dvd_map_of_isScalarTower', AlgebraicGeometry.Scheme.stalkMap_germ_apply, Ring.DirectLimit.map_comp, Polynomial.isLocalization, SemiRingCat.ofHom_apply, PowerSeries.coeff_map, GaussianInt.intCast_real_norm, SemiRingCat.hom_inv_apply, Ideal.map_of_equiv, PowerSeries.evalâ_C, ContinuousLinearMap.toContinuousAddMonoidHom_neg, WeierstrassCurve.Affine.map_negAddY, AdicCompletion.mk_smul_top_ofAlgEquiv_symm, RingHom.surjective_of_epi_of_finite, PowerSeries.constantCoeff_smul, NumberField.AdeleRing.algebraMap_injective, MvPolynomial.killCompl_map, IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap, Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_aeval_zero_of_monic_mem_map, IsFractionRing.algEquivOfAlgEquiv_algebraMap, IsAlgClosed.algebraMap_bijective_of_isIntegral, IsLocalization.Away.tensor, IsLocalization.orderIsoOfPrime_symm_apply_coe, Complex.hasSum_conj, IsScalarTower.of_compHom, NormedRing.algEquivComplexOfComplete_apply, Polynomial.dickson_one_one_eq_chebyshev_T, AdjoinRoot.coe_liftAlgHom, IsLocalization.sec_spec, Polynomial.leadingCoeff_mul_C_of_isUnit, PowerSeries.comp_aeval, FunctionField.ringOfIntegers.algebraMap_injective, TrivSqZeroExt.algebraMap_eq_inl, Ideal.isMaximal_comap_of_isIntegral_of_isMaximal, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst, IsAdicComplete.mk_liftRingHom, DoubleCentralizer.algebraMap_fst, MvPowerSeries.coeff_rescale, spectrum.mem_iff, NumberField.mixedEmbedding.indexEquiv_apply_isReal, OrderRingHom.coe_ringHom_apply, NumberField.ComplexEmbedding.Extension.comp_eq, rootOfSplitsXPowSubC_pow, UpperHalfPlane.coe_specialLinearGroup_apply, Polynomial.not_isUnit_X_sub_C, Ideal.map_map, MvPolynomial.dvd_X_iff_exists, IsLocalization.surj_of_gcd_domain, MvPolynomial.finSuccEquiv_X_succ, WittVector.StandardOneDimIsocrystal.frobenius_apply, Polynomial.card_support_eq_two, TensorAlgebra.algebraMap_inj, AdicCompletion.factor_eval_liftRingHom, MvPowerSeries.constantCoeff_one, Algebra.smulTower_leftMulMatrix_algebraMap, CStarAlgebra.star_mul_le_algebraMap_norm_sq, Algebra.TensorProduct.tmul_one_eq_one_tmul, Algebra.TensorProduct.quotIdealMapEquivTensorQuot_symm_tmul, ModuleCat.mkOfSMul_smul, RingHom.IsIntegral.quotient, RCLike.nnnorm_conj, MvPolynomial.evalâHom_eq_zero, GradedTensorProduct.algebraMap_def, Ideal.map_eq_submodule_map, IsLocalization.map_units_map_submonoid, Polynomial.eq_mul_leadingCoeff_of_monic_of_dvd_of_natDegree_le, Module.End.eigenspace_div, MonomialOrder.leadingCoeff_C, PowerSeries.constantCoeff_mk, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_obj, PowerSeries.eq_shift_mul_X_add_const, iterateFrobeniusEquiv_apply, Algebra.Extension.Hom.subToKer_apply_coe, spectrum.add_mem_add_iff, MvPolynomial.ker_mapAlgHom, Ideal.comap_map_eq_self_of_isMaximal, IsLocalRing.quotient_span_eq_top_iff_span_eq_top, Polynomial.chebyshev_T_eq_dickson_one_one, ModuleCat.restrictScalars.smul_def, MvPolynomial.aeval_injective_iff_of_isEmpty, AlgebraicGeometry.StructureSheaf.comapâ_const, Polynomial.resultant_map_map, WittVector.constantCoeff_wittAdd, TopCat.Presheaf.restrictOpenCommRingCat_apply, RCLike.wInner_one_const_right, GaussianInt.toComplex_im, Matrix.diagonalRingHom_apply, FaithfulSMul.algebraMap_injective, CommSemiRingCat.FilteredColimits.forgetâSemiRing_preservesFilteredColimits, GaussianInt.im_toComplex, HomogeneousLocalization.val_awayMap_eq_aux, Polynomial.iterate_derivative_C_mul, FreeRing.lift_of, MvPolynomial.eval_sub, IsLocalization.disjoint_comap_iff, Polynomial.reflect_C_mul_X_pow, Algebra.commute_algebraMap_right, Polynomial.card_support_eq_one, MonoidHom.map_iterateFrobenius, spectralNorm.eq_of_normalClosure', Ideal.Factors.finrank_pow_ramificationIdx, NumberField.InfinitePlace.Completion.bijective_extensionEmbedding_of_isComplex, NumberField.mixedEmbedding.normAtPlace_apply, IsPRadical.comap_pNilradical, Polynomial.aroots_C_mul_X_pow, DividedPowers.Quotient.isDPMorphism, Ideal.quotientMulEquivQuotientProd_fst, Matrix.charpoly_sub_diagonal_degree_lt, CliffordAlgebra.forall_mul_self_eq_iff, Complex.dist_conj_conj, IsAlgClosure.equivOfEquiv_algebraMap, Subring.subtype_apply, Polynomial.leadingCoeff_C_mul_X, Polynomial.map_smul, nnnorm_algebraMap', LieModule.isNilpotent_toEnd_sub_algebraMap, RootPairing.IsValuedIn.exists_value, continuous_algebraMap_iff_smul, RCLike.norm_sq_re_conj_add, Complex.conjCLE_apply, Polynomial.constantCoeff_surjective, scaleRoots_aeval_eq_zero_of_aeval_mk'_eq_zero, Polynomial.eraseLead_C, Polynomial.Splits.X_sub_C, PresheafOfModules.Derivation.d_app, Polynomial.isUnit_primPart_C, PowerSeries.coeff_zero_C, IsLocalRing.isLocalHom_iff_comap_closedPoint, Complex.arg_conj_coe_angle, ContinuousLinearMap.toContinuousAddMonoidHom_restrictScalars, HomogeneousLocalization.val_awayMap_mk, Complex.nndist_conj_self, Valuation.Integers.coe_span_singleton_eq_setOf_le_v_algebraMap, Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_C, IsSMulRegular.of_isLocalization, PrimeSpectrum.comap_basicOpen, IsLocalization.eq_iff_eq, ZMod.ker_intCastRingHom, minpoly.eq_X_sub_C', MonoidAlgebra.lift_mapRangeRingHom_algebraMap, Set.algebraMap_mem_center, isNilpotent_tensor_residueField_iff, LinearEquiv.isSMulRegular_congr', constantCoeff_wittStructureRat_zero, Rat.ringOfIntegersEquiv_apply_coe, Polynomial.algebraMap_hahnSeries_apply, SheafOfModules.unitToPushforwardObjUnit_val_app_apply, WeierstrassCurve.Jacobian.map_polynomialZ, Matrix.eval_charpoly, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeÎUnitOpensCarrierCarrierCommRingCatRingCatSheaf, WeierstrassCurve.Projective.map_addXYZ, IsIntegrallyClosed.algebraMap_eq_of_integral, Algebra.weaklyQuasiFiniteAt_iff, RingHom.injective_stableUnderComposition, Ideal.rank_pow_quot_aux, MeasureTheory.SimpleFunc.const_algebraMap, UpperHalfPlane.cosh_half_dist, Unitization.starMap_apply, Valuation.Integers.valuation_pos_iff_ne_zero, MvPolynomial.bindâ_C_right, RCLike.conj_im, MvPowerSeries.algebraMap_apply', PowerSeries.coeff_C, MvPolynomial.constantCoeff_eq, LinearMap.toMvPolynomial_constantCoeff, IntermediateField.AdjoinSimple.norm_gen_eq_prod_roots, Ideal.Quotient.mkâ_eq_mk, WeierstrassCurve.Projective.map_polynomialZ, FaithfulSMul.algebraMap_eq_one_iff, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt', MvPolynomial.eval_rename, Ideal.rootsOfUnityMapQuot_apply, Polynomial.Monic.comp_X_add_C, Ideal.IntegralClosure.comap_lt_comap, MvPolynomial.mkDerivationâ_C, AlgebraicGeometry.Scheme.AffineZariskiSite.opensRange_relativeGluingData_map, RCLike.conj_I, Polynomial.divX_C, coeff_minpolyDiv, IsLocalization.tmul_mk', NumberField.canonicalEmbedding.norm_le_iff, StandardEtalePresentation.toPresentation_Ď', Submodule.mem_one, Polynomial.cyclotomic_eq_prod_X_pow_sub_one_pow_moebius, witt_structure_prop, Subsemiring.map_toSubmonoid, Ideal.map_comap_of_equiv, RingHom.smul_def, Polynomial.Monic.C_dvd_iff_isUnit, bijective_frobenius, RingHom.rangeRestrictField_bijective, map_nonunit, Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_one, Matrix.SpecialLinearGroup.eq_scalar_center_equiv_rootsOfUnity, RingHom.surjective_stableUnderComposition, Algebra.Presentation.coeffs_subset_range, AdjoinRoot.map_root, Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree_le, Polynomial.nextCoeff_map_of_leadingCoeff_ne_zero, MvPowerSeries.order_ne_zero_iff_constCoeff_eq_zero, Polynomial.natSepDegree_C, IsIntegrallyClosed.eq_map_mul_C_of_dvd, Ideal.smul_restrictScalars, matPolyEquiv_eval_eq_map, Polynomial.monic_mul_leadingCoeff_inv, Polynomial.eq_X_sub_C_of_splits_of_single_root, AlgebraicGeometry.RingedSpace.basicOpen_res_eq, Ideal.mem_primesOver_iff_mem_normalizedFactors, WittVector.constantCoeff_wittNSMul, Polynomial.card_support_C_mul_X_pow_le_one, AlgebraicGeometry.Spec_zeroLocus, PowerSeries.coeff_inv, AlgEquiv.restrictNormal_commutes, ValuationSubring.coe_comap, PerfectClosure.mk_eq_iff, Polynomial.discr_C, NumberField.mixedEmbedding_injective, PowerSeries.rescale_injective, Polynomial.coeToPowerSeries.ringHom_apply, Polynomial.support_C_mul_X_pow, MvPolynomial.prod_C_add_X_eq_sum_esymm, spectrum.algebraMap_eq_of_mem, Polynomial.modByMonic_X_sub_C_eq_C_eval, PresheafOfModules.Monoidal.tensorHom_app, Polynomial.binomial_eq_binomial, RCLike.inv_def, DividedPowers.IsDPMorphism.dpow_comp, PowerSeries.map_expand, NumberField.RingOfIntegers.coe_eq_algebraMap, Valuation.HasExtension.val_map_eq_one_iff, Polynomial.iterate_derivative_X_pow_eq_C_mul, IsAdjoinRootMonic.coeff_algebraMap, RingCat.instFullSemiRingCatForgetâRingHomCarrierCarrier, MvPolynomial.evalâ_map_comp_C, Matrix.GeneralLinearGroup.coe_map_mul_map_inv, MvPowerSeries.rescaleAlgHom_apply, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map, MvPowerSeries.coeff_zero_C, RatFunc.liftOn'_div, Polynomial.derivative_X_pow, MvPolynomial.optionEquivRight_apply, MvPolynomial.finSuccEquiv_apply, Subfield.closure_preimage_le, IsPerfectClosure.equiv_comp_apply, Polynomial.degree_C_mul, UpperHalfPlane.exp_half_dist, Polynomial.Splits.map_roots, HomogeneousLocalization.awayMapAux_mk, MvPowerSeries.coeff_C, Polynomial.gaussNorm_C, TensorProduct.gradedComm_tmul_algebraMap, MvPolynomial.C_eq_coe_nat, SubalgebraClass.coe_algebraMap, WittVector.liftEquiv_symm_apply_coe, Polynomial.Splits.eq_prod_roots_of_monic, Subalgebra.lTensorBot_tmul, IntermediateField.adjoin_eq_range_algebraMap_adjoin, RingTheory.Sequence.IsRegular.of_faithfullyFlat_of_isBaseChange, WittVector.quotientPEquiv_mk, AdjoinRoot.mk_X, Ideal.map_algebraMap_eq_finset_prod_pow, IsLocalization.injective_iff_map_algebraMap_eq, CommRingCat.inv_hom_apply, cfc_const_add, Polynomial.isNilpotent_C_mul_pow_X_of_isNilpotent, WittVector.toPadicInt_comp_fromPadicInt_ext, AlgEquiv.prodQuotientOfIsIdempotentElem_apply_snd, fourier_neg, Polynomial.leadingCoeff_X_sub_C, RatFunc.denom_C, IsLocalization.mk'_one, Polynomial.expand_eq_C, RatFunc.num_div_dvd', WeierstrassCurve.Jacobian.baseChange_polynomialX, WeierstrassCurve.ÎŚ_two, CyclotomicRing.algebraBase_injective, Polynomial.aeval_C, Polynomial.Monic.roots_map_of_card_eq_natDegree, Polynomial.aeval_eq_prod_aroots_sub_of_splits, Complex.conj_re, Ideal.rank_pow_quot, spectrum.add_mem_iff, PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_2, LaurentSeries.powerSeriesEquivSubring_coe_apply, WeierstrassCurve.Jacobian.Equation.map, MvPolynomial.degreeOf_mul_C_le, Polynomial.toLaurent_inj, PerfectClosure.r_iff, AdicCompletion.mk_ofAlgEquiv_symm_eq_evalOneâ, PresheafOfModules.Derivation'.app_apply, CommRingCat.comp_apply, MvPolynomial.algebraTensorAlgEquiv_symm_map, MvPowerSeries.map.isLocalHom, Ideal.map_height_le_one_of_mem_minimalPrimes, Complex.im_eq_sub_conj, AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_symm_mk_mk, Algebra.discr_eq_det_embeddingsMatrixReindex_pow_two, Polynomial.taylor_monomial, DoubleQuot.quotQuotEquivQuotSup_quotQuotMk, WittVector.map_eq_zero_iff, AlgebraicGeometry.StructureSheaf.instIsLocalizedModuleCarrierStalkAbPresheafOpensCarrierTopModuleStructurePresheafPrimeComplAsIdealToStalkâ, Algebra.Extension.Hom.algebraMap_toRingHom, Lagrange.interpolate_apply, IsPurelyInseparable.minpoly_eq_X_pow_sub_C, Polynomial.C_mul, MvPolynomial.isHomogeneous_C_mul_X_pow, Algebra.normalizedTrace_algebraMap_apply, MvPolynomial.tensorEquivSum_C_tmul_one, Polynomial.natDegree_X_sub_C_le, Polynomial.splits_X_sub_C_mul_iff, AlgebraicGeometry.basicOpen_eq_of_affine', AlgHom.toRingHom_unop, MvPolynomial.map_iterateFrobenius_expand, NumberField.Units.dirichletUnitTheorem.logEmbedding_component, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_algebraMap, PowerSeries.coeff_zero_eq_constantCoeff, NumberField.Units.coe_zpow, MvPowerSeries.constantCoeff_map, GaussianInt.toComplex_neg, Algebra.Extension.tensorCotangentInvFun_smul_mk, instIsPrincipalMapRingHom, MvPowerSeries.rescale_eq_subst, RingHom.Int.subsingleton_ringHom, RootPairing.RootPositiveForm.exists_pos_eq, ContinuousLinearMap.toContinuousAddMonoidHom_id, PowerSeries.coe_X, Rat.int_algebraMap_injective, Polynomial.dickson_of_two_le, Ring.DirectLimit.ringEquiv_symm_mk, Matrix.coeff_det_one_add_X_smul_one, AlgebraicGeometry.LocallyRingedSpace.stalkSpecializes_stalkMap_apply, AlgebraicGeometry.Spec.coe_toTop_map_hom_apply_asIdeal, DoubleCentralizer.coe_eq_algebraMap, MvPolynomial.sumAlgEquiv_apply, Differential.logDeriv_algebraMap, Polynomial.degree_add_degree_leadingCoeff_inv, ContinuousLinearMap.toContinuousAddMonoidHom_sub, RootPairing.algebraMap_pairingIn', Module.Finite.toModuleEnd_moduleEnd_surjective, MvPolynomial.degreeOf_C_mul_le, Polynomial.trinomial_def, LinearEquiv.isWeaklyRegular_congr', DirectLimit.Module.hom_ext_iff, smoothSheafCommRing.Κ_forgetStalk_hom_apply, Polynomial.coe_algebraMap_eq_CC, TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd, selfZPow_natCast, AlgebraicGeometry.stalkToFiberRingHom_germ, MvPolynomial.sumToIter_Xr, Polynomial.X_sub_C_scaleRoots, DirectSum.ringHom_ext'_iff, Complex.conj_ofNat, Ideal.quotientKerAlgEquivOfSurjective_symm_apply, mem_coeSubmodule_conductor, Module.toModuleEnd_apply, Polynomial.resultant_C_zero_left, AlgebraicGeometry.StructureSheaf.Localizations.comapFun_mk, conjnegRingHom_apply, Polynomial.C_eq_or_isOpenQuotientMap_eval, RingTheory.Sequence.IsWeaklyRegular.of_flat_of_isBaseChange, WeierstrassCurve.Projective.eval_polynomial_of_Z_ne_zero, RatFunc.C_injective, TopCat.Sheaf.objSupIsoProdEqLocus_inv_eq_iff, MvPolynomial.eval_toMvPolynomial, Ideal.quotientKerAlgEquivOfSurjective_mk, MonoidAlgebra.singleOneRingHom_apply, FractionalIdeal.one_le_extendedHomâ_iff, Polynomial.sum_taylor_eq, Subalgebra.range_subset, Nat.coe_castRingHom, UnitAddTorus.hasSum_prod_mFourierCoeff, MvPolynomial.sum_C, LocalizedModule.algebraMap_mk, Ideal.mem_quotient_iff_mem_sup, Polynomial.algebraMap_hahnSeries_injective, NumberField.mixedEmbedding.latticeBasis_apply, AlgebraicGeometry.exists_eq_pow_mul_of_isAffineOpen, MvPowerSeries.constantCoeff_X, IsLocalRing.isLocalHom_residue, smoothSheafCommRing.Κ_forgetStalk_hom_assoc, cyclotomicCharacter.toZModPow_toFun, LaurentSeries.valuation_coe_ratFunc, MvPolynomial.monomial_eq, Polynomial.isNilpotent_C_iff, CliffordAlgebra.star_algebraMap, Algebra.left_comm, Polynomial.disc_C, CliffordAlgebra.changeForm_algebraMap, LaurentPolynomial.counit_C_mul_T, Valuation.Integers.isPrincipal_iff_exists_eq_setOf_valuation_le, MvPolynomial.aeval_eq_evalâHom, LinearMap.eqLocus_toAddSubmonoid, Algebra.TensorProduct.algebraMap_apply', GaussianInt.re_toComplex, DoubleQuot.coe_quotQuotToQuotSupâ, Ideal.Quotient.norm_mk_lt, MvPolynomial.vars_C, Algebra.Extension.algebraMap_Ď, Subsemiring.mem_map, Complex.ofRealHom_eq_coe, AlgebraicIndependent.aevalEquivField_apply_coe, ZMod.castHom_bijective, MvPolynomial.aeval_C, MvPolynomial.support_map_subset, IsSimpleRing.injective_ringHom_or_subsingleton_codomain, FreeAbelianGroup.liftMonoid_coe, Subalgebra.LinearDisjoint.basisOfBasisLeft_apply, NonUnitalAlgHom.toAlgHom_apply, Polynomial.hasseDeriv_C, AlgEquiv.quotientBot_symm_mk, frobenius_apply_frobeniusEquiv_symm, Unitization.nnnorm_eq_sup, Finsupp.sum_smul_index_semilinearMap', MvPowerSeries.map_frobenius_expand, IsLocalization.submonoid_map_le_is_unit, TruncatedWittVector.zmodEquivTrunc_apply, Perfection.coeff_pthRoot, Polynomial.natDegree_linear_le, algebraMap_mem, RingEquiv.ofRingHom_apply, RingHom.coe_mk, IsLocalRing.basisQuotient_apply, RingHomCompTriple.comp_apply, MvPolynomial.pderiv_map, PowerSeries.exp_pow_eq_rescale_exp, Polynomial.derivation_C, minpoly_algEquiv_toLinearMap, NumberField.InfinitePlace.Completion.extensionEmbedding_of_isReal_coe, CommRingCat.coyonedaUnique_inv_app_hom_apply, WeierstrassCurve.Jacobian.eval_polynomial, PowerBasis.trace_gen_eq_sum_roots, Polynomial.natDegree_det_X_add_C_le, Ideal.injective_algebraMap_quotient_residueField, Polynomial.eval_C_X_comp_evalâ_map_C_X, AdjoinRoot.algHom_subsingleton, spectralNorm.eq_of_tower, IsPRadical.injective_comp, spectrum.scalar_eq, Complex.hasSum_conj', SubringClass.subtype_injective, Polynomial.toLaurent_one, RingHom.star_def, NumberField.norm_embedding_le_house, AlgebraicGeometry.specTargetImageFactorization_app_injective, minpoly.root, Polynomial.mod_X_sub_C_eq_C_eval, MvPowerSeries.coeff_map, HomogeneousLocalization.Away.eventually_smul_mem, NumberField.FinitePlace.norm_eq_one_iff_notMem, AlgebraicGeometry.Scheme.IsGermInjectiveAt.cond, NumberField.canonicalEmbedding_injective, PowerSeries.monomial_eq_C_mul_X_pow, trace_quotient_eq_trace_localization_quotient, RingCat.forgetâSemiRing_preservesLimits, MvPolynomial.rename_C, Ideal.Quotient.mk_eq_mk_iff_sub_mem, WeierstrassCurve.Projective.map_dblXYZ, LinearMap.map_smulââ, FirstOrder.realize_genericPolyMapSurjOnOfInjOn, AlgHom.commutes, MvPowerSeries.map_expand, Algebra.Extension.Hom.sub_aux, MvPolynomial.evalâ_mul_C, StandardEtalePresentation.aeval_val_equivMvPolynomial, LaurentPolynomial.degree_C_ite, Perfection.coeff_frobeniusEquiv_symm, Polynomial.smul_C, Ideal.ker_quotientMap_mk, ULift.down_algebraMap, PowerBasis.exists_gen_dvd_sub, Bialgebra.counit_algebraMap, RCLike.conj_eq_iff_im, Complex.exp_conj, Algebra.discr_localizationLocalization, AdjoinRoot.Polynomial.quotQuotEquivComm_symm_mk_mk, Padic.isUniformInducing_cast_withVal, KaehlerDifferential.derivationTensorProduct_algebraMap, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal', Pi.conj_apply, MvPolynomial.C_neg, Ideal.powQuotSuccInclusion_injective, SemiRingCat.forgetâAddCommMon_preservesLimits, Matrix.GeneralLinearGroup.val_map_apply, LinearMap.charpoly_sub_smul, LaurentPolynomial.evalâ_T_neg_n, IsLocalization.AtPrime.comap_map_of_isMaximal, IsAdjoinRoot.lift_algEquiv, MvPolynomial.coeToMvPowerSeries.ringHom_apply, WeierstrassCurve.Jacobian.map_negAddY, CommSemiRingCat.forgetâSemiRing_preservesLimitsOfSize, Polynomial.Bivariate.swap_C, NumberField.mixedEmbedding.commMap_apply_of_isReal, IsFractionRing.num_mul_den_eq_num_iff_eq, Submodule.span_singleton_eq_one_iff, Algebra.RingHom.adjoin_algebraMap_surjective, PowerSeries.ker_coeff_eq_max_ideal, AlgHom.map_coe_real_complex, IsAlgebraic.exists_nonzero_eq_adjoin_mul, isDedekindRing_iff, MvPolynomial.coeffs_map, Polynomial.natSepDegree_X_sub_C, Polynomial.coe_normUnit, RatFunc.algebraMap_apply, AlgebraicGeometry.IsOpenImmersion.app_ÎIso_hom_apply, WittVector.ghostComponent_frobenius, Perfection.lift_apply_apply_coe, ExteriorAlgebra.algebraMap_leftInverse, RCLike.conj_re_ax, RingHom.smulOneHom_apply, WeierstrassCurve.Affine.CoordinateRing.coe_norm_smul_basis, spectralNorm.spectralMulAlgNorm_eq_of_mem_roots, IsLocalization.comap_map_of_isPrimary_disjoint, Algebra.trace_quotient_eq_of_isDedekindDomain, Polynomial.degree_le_zero_iff, PreTilt.coeff_iterate_frobenius, WeierstrassCurve.Jacobian.map_polynomial, HahnSeries.C_mul_eq_smul, GradedRing.projZeroRingHom'_surjective, Complex.conj_conj, AlgebraicGeometry.StructureSheaf.stalkAlgebra_map, Pi.ringHom_apply, IntermediateField.set_range_subset, IsAdjoinRoot.algebraMap_apply, Matrix.circulant_single, AdjoinRoot.lift_of, spectralValue_X_sub_C, StandardEtalePair.aeval_X_g_mul_mk_X, RootPairing.algebraMap_coroot'In_apply, AdicCompletion.transitionMap_ideal_mk, MvPolynomial.sumAlgEquiv_symm_apply, UpperHalfPlane.sinh_half_dist_add_dist, PrimeSpectrum.comap_asIdeal, RingHom.coe_id, IsLocalization.map_units, MvPowerSeries.constantCoeff_expand, CommRingCat.equalizer_Κ_isLocalHom, AlgebraicGeometry.Scheme.stalkMap_inv_hom_apply, MvPolynomial.evalâ_comp, Polynomial.roots_C_mul_X_sub_C, conjneg_apply, MvPolynomial.weightedHomogeneousComponent_C_mul, WeierstrassCurve.map_câ, AlgEquiv.algebraMap_eq_apply, TensorProduct.gradedMul_algebraMap, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_symm_tmul, SeparationQuotient.mkRingHom_apply, ClassGroup.exists_mk0_eq_mk0, RingHom.IsStableUnderBaseChange.isLocalization_map, injective_algebraMap_of_linearMap, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, RingHom.coe_comp, RingHom.ker_coe_equiv, RingCat.comp_apply, LinearIsometry.im_apply_eq_im, RingHom.isIntegralElem_localization_at_leadingCoeff, WeierstrassCurve.Jacobian.eval_polynomial_of_Z_ne_zero, MvPolynomial.dvd_C_iff_exists, PowerSeries.map_C, AdjoinRoot.coe_mapAlgEquiv, RingHom.range_eq_top, WeierstrassCurve.Affine.CoordinateRing.mk_Ďâ_sq, NumberField.mixedEmbedding.latticeBasis_repr_apply, LaurentPolynomial.antipode_C, Algebra.Generators.ker_ofAlgHom, Polynomial.rootMultiplicity_le_iff, NumberField.canonicalEmbedding.apply_at, Polynomial.eraseLead_mul_eq_mul_eraseLead_of_nextCoeff_zero, RingCon.kerLift_mk, AddMonoidAlgebra.liftNC_one, FreeCommRing.restriction_of, RatFunc.mk_one, AlgebraicGeometry.AffineSpace.reindex_appTop_coord, DirectSum.liftRingHom_symm_apply_coe, MvPolynomial.C_mem_pow_idealOfVars_iff, Complex.mul_conj, AlgHom.toRingHom_op, RatFunc.algebraMap_injective, Ideal.quotientInfToPiQuotient_mk', SubsemiringClass.subtype_apply, CommSemiRingCat.forget_preservesLimitsOfSize, isIntegrallyClosed_iff, Matrix.charmatrix_map, Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange, RingTheory.Sequence.IsWeaklyRegular.isRegular_of_isLocalizedModule_of_mem, RingHom.surjective_respectsIso, Polynomial.modByMonic_X, IsDedekindDomain.primesOverEquivPrimesOver_symm_apply, RingHom.coe_monoidHom_injective, Complex.nndist_conj_comm, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_apply, IsPurelyInseparable.minpoly_eq_X_sub_C_pow, AlgEquiv.prodQuotientOfIsIdempotentElem_apply_fst, MonoidAlgebra.liftNC_smul, AlgebraicGeometry.RingedSpace.isUnit_res_basicOpen, Ideal.Quotient.mk_eq_mk, DividedPowers.DPMorphism.coe_toRingHom, Algebra.mem_ideal_map_adjoin, LaurentSeries.coe_range_dense, X_pow_sub_C_irreducible_of_prime_pow, Algebra.algebraMap_intNorm_of_isGalois, NumberField.AdeleRing.algebraMap_fst_apply, Algebra.isEpi_iff_surjective_algebraMap_of_finite, Polynomial.integralNormalization_mul_C_leadingCoeff, WittVector.map_frobeniusPoly, RingCat.forgetâAddCommGroup_preservesLimitsOfSize, MvPolynomial.sum_eval_eq_zero, Ideal.exists_coeff_ne_zero_mem_comap_of_root_mem, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero', WittVector.constantCoeff_wittZSMul, WeierstrassCurve.Jacobian.polynomialX_eq, IsLocalization.injective_iff_isRegular, MvPolynomial.aeval_C_comp_left, MvPolynomial.C_mul_X_pow_eq_monomial, NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isReal, Rat.int_algebraMap_surjective, PerfectionMap.surjective, Polynomial.iterate_derivative_X_sub_pow_self, Algebra.traceMatrix_of_matrix_mulVec, Complex.conj_natCast, FreeCommRing.map_of, IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_pow, Polynomial.X_dvd_sub_C, AlgebraicGeometry.exists_appTop_Ď_eq_of_isLimit, IsLocalization.mapâ_coe, Polynomial.eval_mul_X_sub_C, AlgebraicGeometry.Proj.stalkIso'_germ, minpolyDiv_spec, Polynomial.leadingCoeff_map_of_leadingCoeff_ne_zero, SubringClass.subtype_apply, cyclotomicCharacter.spec, RingCon.lift_mk', Complex.nndist_conj_conj, Polynomial.reverse_C, RingHom.restrict_apply, RingHom.comp_apply, Polynomial.Splits.C_mul, Polynomial.Monic.eq_X_pow_char_pow_sub_C_of_natSepDegree_eq_one_of_irreducible, Polynomial.reflect_C, Polynomial.evalâ_C, TruncatedWittVector.coeff_truncate, CliffordAlgebra.contractLeft_mul_algebraMap, MvPolynomial.eval_C, MvPolynomial.IsWeightedHomogeneous.C_mul, Polynomial.comp_zero, RingHom.map_geom_sumâ, PresheafOfModules.map_id, Algebra.pushoutDesc_left, WeierstrassCurve.Projective.map_addU, AlgebraicGeometry.Scheme.mem_basicOpen_top, PowerSeries.IsWeierstrassFactorization.degree_eq_coe_lift_order_map, Polynomial.reflect_C_mul, SemiRingCat.forget_preservesLimits, CommRingCat.coyonedaUnique_hom_app_hom_apply, WittVector.mapFun.intCast, MvPowerSeries.substAlgHom_monomial, Orientation.areaForm_map_complex, RCLike.conj_to_real, Algebra.Presentation.HasCoeffs.coeffs_subset_range, Matrix.charpoly_inv, galLiftEquiv_algebraMap_apply, Ideal.instIsTwoSidedMapRingHomOfRingHomSurjective, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_symm_D_algebraMap, Complex.cpow_conj, Algebra.TensorProduct.quotIdealMapEquivTensorQuot_mk, WeierstrassCurve.map_bâ, AlgebraicGeometry.Scheme.Opens.Κ_image_basicOpen', Algebra.SubmersivePresentation.ofSubsingleton_algebra_smul, PowerSeries.rescale_neg_one_X, Polynomial.natDegree_sub_C, HahnSeries.C_one, RingHom.prod_apply, PowerSeries.constantCoeff_exp, MaximalSpectrum.toPiLocalization_injective, GaussianInt.toComplex_zero, map_wittPolynomial, StandardEtalePresentation.toPresentation_algebra_algebraMap_apply, Ideal.IsDedekindDomain.ramificationIdx_eq_factors_count, Ideal.minimalPrimes_comap_subset, RatFunc.denom_algebraMap, Polynomial.hasseDeriv_natDegree_eq_C, AlgebraicGeometry.LocallyRingedSpace.preimage_basicOpen, WeierstrassCurve.Jacobian.map_dblY, isLocalHom_of_le_jacobson_bot, QuadraticAlgebra.algebraMap_dvd_iff_dvd, RingHom.map_field_closure, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, Polynomial.as_sum_range_C_mul_X_pow, Submodule.IsPrincipal.contentIdeal_generator_dvd, RCLike.wInner_one_const_left, WeierstrassCurve.Projective.map_addX, MonoidAlgebra.ringHom_ext'_iff, AlgebraicGeometry.AffineSpace.homOverEquiv_apply, PrimeSpectrum.BasicConstructibleSetData.map_f, Ideal.quotientInfToPiQuotient_mk, MvPowerSeries.algebraMap_apply, MvPolynomial.isLocalization_C_mk', FractionalIdeal.exists_eq_spanSingleton_mul, derivationToSquareZeroEquivLift_apply_coe_apply, IsLocalization.isMaximal_of_isMaximal_disjoint, Module.ker_algebraMap_end, Ideal.spanNorm_le_comap, MvPolynomial.algebraTensorAlgEquiv_tmul, matPolyEquiv_symm_map_eval, MonoidAlgebra.single_eq_algebraMap_mul_of, AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_mk, WeierstrassCurve.Projective.map_addZ, MvPolynomial.vars_map, Polynomial.evalâ_at_apply, LinearMap.restrictScalarsField_apply_apply, Padic.coe_withValRingEquiv_symm, AlgebraicGeometry.Scheme.basicOpen_res, algebraMap_nonneg, Polynomial.derivative_C_mul_X_pow, RCLike.norm_sq_re_add_conj, Polynomial.signVariations_X_sub_C_mul_eraseLead_le, Polynomial.support_binomial, Polynomial.derivative_C, QuadraticAlgebra.mk_eq_add_smul_omega, Polynomial.roots_X_pow_char_sub_C, TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst, Polynomial.degree_mul_C_of_isUnit, AdjoinRoot.minpoly_powerBasis_gen, GradedRing.projZeroRingHom_apply, MvPolynomial.degreeOf_C_mul, AlgHom.ker_kerSquareLift, Polynomial.Chebyshev.algebraMap_eval_S, Matrix.GeneralLinearGroup.map_apply, MvPolynomial.C_injective, Algebra.norm_eq_prod_roots, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_apply, Polynomial.map_under_lt_comap_of_quasiFiniteAt, Valuation.HasExtension.mk_smul_mk, Polynomial.dickson_two_one_eq_chebyshev_U, IsLocalization.algEquiv_symm_apply, CFC.sqrt_algebraMap, MvPolynomial.C_mul, Ring.DirectLimit.exists_of, CFC.posPart_algebraMap, trace_eq_sum_embeddings, exists_integer_of_is_root_of_monic, Ideal.span_singleton_absNorm, CliffordAlgebra.contractLeft_algebraMap_mul, PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_1, RingHom.coe_mul, IntermediateField.botEquiv_def, SemilinearEquivClass.map_smulââ, liftOfDerivationToSquareZero_mk_apply', LaurentPolynomial.support_C_mul_T_of_ne_zero, AlgebraicGeometry.IsClosedImmersion.isAffine_surjective_of_isAffine, Ideal.quotientInfEquivQuotientProd_fst, HomogeneousLocalization.den_smul_val, FreeAlgebra.algebraMap_eq_one_iff, Polynomial.C_mul_comp, PowerSeries.IsWeierstrassFactorizationAt.degree_eq_coe_lift_order_map_of_ne_top, Complex.conj_eq_iff_real, WittVector.verschiebung_frobenius_comm, MvPolynomial.evalâHom_eq_constantCoeff_of_vars, AlgebraicGeometry.germ_eq_zero_of_pow_mul_eq_zero, Ideal.map_comap_natCastRingHom_int, RootPairing.RootPositiveForm.algebraMap_apply_eq_form_iff, Polynomial.roots_expand_image_iterateFrobenius, NumberField.InfinitePlace.embedding_injective, AdjoinRoot.lift_root, IsLocalization.mk'_spec'_mk, WittVector.quotEquivOfEq_ghostComponentModPPow, NumberField.InfinitePlace.Completion.surjective_extensionEmbeddingOfIsReal, RatFunc.eq_C_iff, AdicCompletion.evalâ_of, RatFunc.num_mul_eq_mul_denom_iff, InnerProductSpaceable.innerProp, Polynomial.aeval_monomial, Equiv.algebraMap_def, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_comp, Algebra.Norm.Transitivity.eval_zero_det_det, Algebra.IsUnramifiedAt.exists_notMem_forall_ne_mem_and_adjoin_eq_top, MvPolynomial.isLocalization, LaurentPolynomial.counit_C, IsTranscendenceBasis.sumElim_comp, AdjoinRoot.quotEquivQuotMap_symm_apply, Polynomial.bernoulli_one, HahnSeries.order_C, CompleteOrthogonalIdempotents.bijective_pi', SkewMonoidAlgebra.single_eq_algebraMap_mul_of, WeierstrassCurve.map_Î', PowerSeries.isWeierstrassDivisionAt_iff, Valuation.Integers.valuation_irreducible_pos, RootPairing.restrictScalars_toLinearMap_apply_apply, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding_of_isReal, StandardEtalePresentation.toPresentation_val, ExteriorAlgebra.liftAlternating_algebraMap, AlgebraicGeometry.LocallyRingedSpace.Îevaluation_eq_zero_iff_notMem_basicOpen, Ideal.isDomain_map_C_quotient, Polynomial.IsWeaklyEisensteinAt.map, RingEquiv.toRingHom_apply_symm_toRingHom_apply, matPolyEquiv_eval, FiniteField.frobenius_pow, RCLike.conj_inv, WittVector.exists_frobenius_solution_fractionRing_aux, Ideal.height_le_height_add_encard_of_subset, DirectLimit.Module.lift_apply, Ring.DirectLimit.Polynomial.exists_of, smoothSheafCommRing.Κ_forgetStalk_hom, RingHom.toIntAlgHom_coe, Polynomial.natDegree_mul_C_le, IsLocalizedModule.fromLocalizedModule'_mk, Complex.normSq_eq_conj_mul_self, Algebra.FormallyUnramified.map_maximalIdeal, ModularForm.slash_def, AlgebraicGeometry.Scheme.IdealSheafData.subschemeΚ_app_surjective, LinearMap.mulRight_toAddMonoidHom, AlgebraicGeometry.Scheme.preimage_zeroLocus, WittVector.iterate_verschiebung_mul_left, LinearMap.map_smul', NumberField.InfinitePlace.mkComplex_coe, Polynomial.Chebyshev.C_eq_two_mul_T_comp_half_mul_X, Subalgebra.algebraMap_mem, HopfAlgebra.mul_antipode_lTensor_comul_apply, LinearAlgebra.FreeProduct.lift_algebraMap, SymmetricAlgebra.algebraMap_leftInverse, Complex.conj_eq_iff_im, DividedPowers.Quotient.dpow_apply, RingHom.isUnit_map, Algebra.adjoin_algebraMap, AlgEquiv.liftNormal_commutes, MvPolynomial.IsSymmetric.C, SubringClass.coe_subtype, ModP.v_p_lt_val, Algebra.Generators.compLocalizationAwayAlgHom_relation_eq_zero, QuadraticAlgebra.coe_mem_nonZeroDivisors_iff, Localization.localRingHom_bijective_of_saturated_inf_eq_top, Polynomial.monomial_zero_left, LocalSubring.le_def, MvPolynomial.evalâ_eq, Ideal.Quotient.mk_eq_one_iff_sub_mem, Algebra.smul_def, PowerSeries.constantCoeff_toSubring, Polynomial.natDegree_mul_C, MeasureTheory.BoundedContinuousFunction.inner_toLp, MvPolynomial.ringHom_ext'_iff, Complex.dist_conj_comm, HahnSeries.map_smul, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_mk, DividedPowers.isSubDPIdeal_map_of_isSubDPIdeal, RatFunc.liftAlgHom_apply_div', AlgebraicGeometry.SpecToEquivOfLocalRing_symm_apply, Submodule.lTensorOne_tmul, WeierstrassCurve.Ď_four, Polynomial.roots_expand_pow_image_iterateFrobenius_subset, RingCon.coe_mk', IsLocalization.ringEquivOfRingEquiv_eq, PowerSeries.C_inv, RingHom.surjectiveOnStalks_iff_of_isLocalHom, Polynomial.rootMultiplicity_X_sub_C_self, NumberField.IsCMField.RingOfIntegers.complexConj_eq_self_iff, Polynomial.splits_X_sub_C, RingHom.surjective, MvPolynomial.eval_sum, Complex.GammaIntegral_conj, spectralNorm_extends_of_finiteDimensional, Algebra.discr_powerBasis_eq_prod'', Polynomial.algEquivCMulXAddC_symm_apply, RingHom.mem_fieldRange, TensorAlgebra.algebraMap_leftInverse, AlgebraicGeometry.Scheme.map_basicOpen_map, LocallyConstant.coe_algebraMap, Polynomial.Chebyshev.T_eq_half_mul_C_comp_two_mul_X, Polynomial.opRingEquiv_symm_C, FractionalIdeal.mem_canonicalEquiv_apply, MvPolynomial.smul_eq_C_mul, FunctionField.inftyValuation.C, MvPolynomial.evalâ_monomial, SkewPolynomial.monomial_mul_monomial, MvPolynomial.counitNat_C, RCLike.enorm_conj, Ideal.quotientMap_injective, IntermediateField.adjoin_subset_adjoin_iff, IsAlgClosed.roots_eq_zero_iff, ContinuousMap.C_apply, PowerSeries.algebraMap_apply, Algebra.map_intTraceAux, Polynomial.natDegree_cubic, Polynomial.degree_leadingCoeff_inv, IsLocalization.mk'_mul_cancel_right, CommSemiRingCat.inv_hom_apply, LaurentPolynomial.comul_C_mul_T, IsLocalization.exists_integer_multiple', Polynomial.IsMonicOfDegree.aeval_sub, AdicCompletion.factor_evalâ_eq_eval, IsLocalization.Away.surj, Algebra.Presentation.HasCoeffs.relation_mem_range_map, CliffordAlgebra.foldr_algebraMap, isStronglyTranscendental_mk_of_mem_minimalPrimes, CliffordAlgebraComplex.toComplex_involute, LaurentPolynomial.smeval_C_mul_T_n, RCLike.conjAe_coe, MaximalSpectrum.toPiLocalization_not_surjective_of_infinite, Valuation.Integers.isUnit_iff_valuation_eq_one, ModuleCat.restrictScalars.smul_def', NormedSpace.algebraMap_exp_comm_of_mem_ball, Polynomial.toFinsupp_C_mul_X_pow, Polynomial.logMahlerMeasure_const, MvPolynomial.universalFactorizationMapPresentation_algebra_smul, Polynomial.natDegree_C_mul_of_isUnit, Polynomial.hermite_zero, Algebra.algebra_ext_iff, ZMod.castHom_injective, MvPolynomial.derivation_C_mul, Polynomial.dickson_two, iterateFrobenius_eq_pow, Polynomial.succ_signVariations_X_sub_C_mul_monomial, Module.toAddMonoidEnd_apply_apply, Polynomial.derivative_X_add_C_sq, Ideal.Factors.finiteDimensional_quotient_pow, Cubic.eq_sum_three_roots, MvPolynomial.aeval_sumElim_pderiv_inl, WittVector.frobeniusEquiv_apply, RingHom.RespectsIso.isLocalization_away_iff, RatFunc.mk_one', IsLocalization.isLocalization_algebraMapSubmonoid_map_algHom, AlgHom.map_algebraMap, Polynomial.comp_eq_sum_left, Polynomial.rootMultiplicity_X_sub_C, cfc_predicate_algebraMap, MvPolynomial.iterToSum_C_C, MvPolynomial.totalDegree_sub_C_le, WeierstrassCurve.Jacobian.map_dblU, AlgCat.forgetâRing_preservesLimits, WeierstrassCurve.Projective.Equation.map, HahnSeries.ofPowerSeries_apply, AdjoinRoot.aeval_eq, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux, RingEquiv.toRingHom_injective, ValuativeExtension.mapPosSubmonoid_apply_coe, MvPowerSeries.comp_subst, Polynomial.coeff_zero_eq_aeval_zero', PowerSeries.evalâ_trunc_eq_sum_range, Ideal.Quotient.liftâ_apply, IsLocalizedModule.map_units, IsLocalization.adjoin_inv, WeierstrassCurve.Affine.Equation.map, WeierstrassCurve.Projective.map_add, RingCat.forget_preservesLimits, CliffordAlgebra.ofEven_Κ, Polynomial.dvd_comp_X_sub_C_iff, AdjoinRoot.liftHom_of, LaurentPolynomial.leftInverse_trunc_toLaurent, Ideal.le_pow_of_le_ramificationIdx, CliffordAlgebra.ofBaseChange_tmul_one, WittVector.truncate_mk', Algebra.normalizedTrace_algebraMap_of_lifts, HopfAlgebra.sum_antipode_mul_eq_algebraMap_counit, LinearMap.IsSymmetric.conj_inner_sym, SemiRingCat.forget_obj, Subsemiring.subtype_apply, conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj, PowerSeries.map_exp, QuaternionAlgebra.algebraMap_eq, Valuation.extendToLocalization_apply_map_apply, Localization.le_comap_primeCompl_iff, AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.opensRange_map, algebraMap_mono, Polynomial.pow_mul_divByMonic_rootMultiplicity_eq, Localization.awayMap_injective_iff, PowerSeries.coe_one, Polynomial.algEquivAevalXAddC_apply, WeierstrassCurve.inv_map_Î', Polynomial.leadingCoeff_C, MvPolynomial.aeval_sumElim, MvPolynomial.universalFactorizationMapPresentation_Ď', jacobiSum_ringHomComp, isAlgebraic_algebraMap, Polynomial.leadingCoeff_map, LinearMap.toMvPolynomial_eval_eq_apply, IsLocalRing.ResidueField.residue_smul, AlgebraicGeometry.StructureSheaf.comap_basicOpen, Matrix.SpecialLinearGroup.coe_matrix_coe, Algebra.IsPushout.equiv_symm_algebraMap_right, Polynomial.evalâ_eq_sum_range, PowerSeries.IsWeierstrassDivisorAt.mk_mod'_eq_self, Derivation.compAlgebraMap_apply, PerfectRing.liftEquiv_id, NumberField.mixedEmbedding.indexEquiv_apply_isComplex_snd, QuadraticAlgebra.algebraMap_norm_eq_mul_star, AlgebraicGeometry.Scheme.mem_basicOpen'', WeierstrassCurve.Jacobian.map_addU, LaurentPolynomial.smul_eq_C_mul, Polynomial.cauchyBound_X_add_C, Polynomial.degree_cubic_le, IsLocalization.AtPrime.isUnit_to_map_iff, RingHom.smul_toAlgebra, WeierstrassCurve.Ψ_four, IsLocalization.isLocalization_atPrime_localization_atPrime, RingHom.map_mul, RingOfIntegers.algebraMap_norm_algebraMap, RCLike.ofReal_im_ax, bijective_rangeRestrict_comp_of_valuationRing, IsLocalization.Away.associated_sec_fst, IsPurelyInseparable.iterateFrobeniusââ_algebraMap, IsLocalization.mul_toInvSubmonoid, IsLocalization.algebraMap_mk', RegularExpression.matches'_map, NumberField.InfinitePlace.eq_iff_eq, HurwitzZeta.jacobiThetaâ''_conj, Subalgebra.setRange_algebraMap, AlgebraicGeometry.specTargetImageRingHom_surjective, SemiRingCat.id_apply, map_normEDS, AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe, Polynomial.toLaurent_C_mul_eq, SymmetricAlgebra.algebraMap_inj, AdicCompletion.evalâ_mk, PowerSeries.inv_eq_inv_aux, Submodule.mapHom_apply, Algebra.discr_powerBasis_eq_prod', QuaternionAlgebra.coe_algebraMap, PadicAlgCl.coe_eq, Polynomial.X_sub_C_mul_removeFactor, Algebra.algebraMap_intTrace, Polynomial.logMahlerMeasure_C_mul_X_add_C, RingHom.fieldRange_eq_top_iff, Ideal.IsDedekindDomain.ramificationIdx_eq_multiplicity, IsLocalization.mk'_eq_iff_eq', RingHom.coe_monoidHom_mk, IsSimpleRing.iff_injective_ringHom, AlgebraicGeometry.basicOpen_eq_of_affine, Ideal.KerLift.map_smul, IsLocalization.AtPrime.equivQuotientMapMaximalIdeal_apply_mk, RingHom.congr_arg, IsLocalization.eq_mk'_of_mul_eq, MvPolynomial.schwartz_zippel_sum_degreeOf, MvPolynomial.isHomogeneous_C, Ideal.IsPrimary.comap, Algebra.IsIntegral.quotient, Subalgebra.algebraMap_apply, Cubic.eq_prod_three_roots, SpectrumRestricts.nnreal_iff_spectralRadius_le, Algebra.adjoin_res_eq_adjoin_res, PadicInt.ker_toZMod, DoubleQuot.quotQuotEquivComm_mk_mk, Algebra.FinitePresentation.out, AlgHom.toRingHom_toAddMonoidHom, dist_algebraMap, Multiset.prod_X_add_C_eq_sum_esymm, WittVector.IsPolyâ.map, MvPowerSeries.invOfUnit_eq, Polynomial.coeff_C_zero, AlgHom.IsArithFrobAt.restrict_mk, FaithfulSMul.ker_algebraMap_eq_bot, isLocalHom_of_iso, RCLike.wInner_cWeight_const_right, AdicCompletion.evalâ_mkâ, AlgebraicGeometry.LocallyRingedSpace.isUnit_res_toÎSpecMapBasicOpen, NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv, RCLike.inv_eq_conj, Ideal.Factors.isPrime, LaurentPolynomial.evalâ_T_n, Polynomial.exists_prod_multiset_X_sub_C_mul, Polynomial.degree_linear_le, Matrix.blockDiagonalRingHom_apply, SubMulAction.mem_one', PrimeSpectrum.piLocalizationToMaximal_bijective, Algebra.Presentation.quotientEquiv_mk, DirectSum.toSemiring_coe_addMonoidHom, IsSMulRegular.of_flat, RingHom.ker_equiv_comp, RingHom.toNatAlgHom_apply, Matrix.charmatrix_apply, IsLocalization.Away.mapâ_apply, Algebra.PowerBasis.norm_gen_eq_prod_roots, IsPurelyInseparable.iterateFrobeniusââ_algebraMap_base, Polynomial.derivative_X_add_C_pow, Polynomial.homogenize_C, RingHom.map_add, Matrix.map_pow, le_algebraMap_of_spectrum_le, Polynomial.content_C, trace_eq_sum_automorphisms, UpperHalfPlane.Ď_conj, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, RingHom.surjective_localizationPreserves, IntermediateField.LinearDisjoint.linearIndependent_mul', IsTranscendenceBasis.algebraMap_comp, PrimeSpectrum.toPiLocalization_injective, quasispectrum.preimage_algebraMap, DoubleQuot.quotQuotEquivQuotOfLE_symm_comp_mk, MonoidAlgebra.lift_def, IntermediateField.LinearDisjoint.basisOfBasisLeft_repr_apply, FractionalIdeal.equivNum_apply, RingHom.coe_addMonoidHom_mk, Polynomial.splits_iff_exists_multiset', PowerSeries.coeff_heval_zero, Polynomial.toFinsupp_C_mul_X, PowerSeries.order_ne_zero_iff_constCoeff_eq_zero, minpoly.natSepDegree_eq_one_iff_eq_expand_X_sub_C, CommRingCat.commMon_forgetâ_map, IsLocalization.invertible_mk'_one_invOf, Algebra.algebraMapSubmonoid_powers, Polynomial.dvd_iff_isRoot, Perfection.coeff_iterate_frobeniusEquiv_symm, HahnSeries.ofPowerSeries_injective, MvPolynomial.aeval_zero', NumberField.RingOfIntegers.map_mk, IsAlgebraic.algebraMap, Zsqrtd.toReal_apply, Ideal.Quotient.quotient_ring_saturate, MvPolynomial.counit_C, DoubleQuot.quotQuotEquivQuotSup_symm_quotQuotMk, Subalgebra.LinearDisjoint.norm_algebraMap, Complex.conj_ofReal, Ideal.comap_fiberIsoOfBijectiveResidueField_symm, Polynomial.qsmul_eq_C_mul, IsPurelyInseparable.bijective_algebraMap_of_isSeparable, PerfectClosure.iterate_frobenius_mk, IsFractionRing.algEquiv_commutes, AlgebraicGeometry.isomorphisms_eq_stalkwise, IsStronglyTranscendental.iff_of_isLocalization, WeierstrassCurve.Projective.baseChange_polynomialZ, SpectrumRestricts.rightInvOn, Multiset.prod_X_add_C_coeff', norm_algebraMap', Polynomial.degree_linear_lt_degree_C_mul_X_sq, Polynomial.cauchyBound_X_sub_C, Polynomial.splits_of_exists_multiset, WeierstrassCurve.Jacobian.comp_smul, IsLocalization.mul_mk'_eq_mk'_of_mul, Algebra.norm_algebraMap, Polynomial.map_C, Submodule.map_toAddSubgroup, IsPurelyInseparable.algebraMap_elemReduct_eq, NumberField.mixedEmbedding.fundamentalCone.mem_idealSet, WittVector.ker_constantCoeff, Ideal.mk_ker, MvPolynomial.counitNat_X, CommRingCat.isLocalHom_comp, WeierstrassCurve.Affine.map_addPolynomial, PowerSeries.coeff_C_mul, OrthogonalIdempotents.lift_of_isNilpotent_ker_aux, MonomialOrder.degree_X_add_C, Polynomial.evalâ_at_ofNat, AddChar.map_neg_eq_conj, AdjoinRoot.map_of, MvPolynomial.evalâHom_bindâ, Polynomial.C_neg, IsLocalization.integerNormalization_spec, WeierstrassCurve.map_aâ, SkewMonoidAlgebra.ringHom_ext'_iff, EuclideanSpace.inner_single_right, Matrix.scalar_apply, ValuationSubring.coe_primeSpectrumOrderEquiv_symm_apply_asIdeal, NumberField.prod_archAbsVal_eq, Polynomial.ringHom_evalâ_intCastRingHom, Polynomial.isNilpotent_pow_X_mul_C_of_isNilpotent, Polynomial.prod_X_sub_C_coeff_card_pred, GradedTensorProduct.tmul_algebraMap_mul_coe_tmul, Localization.localRingHom_bijective_of_not_conductor_le, Ideal.height_le_height_add_spanFinrank_of_le, MvPolynomial.optionEquivLeft_symm_C_X, IsIntegral.algebraMap, Subsemiring.subtype_injective, Polynomial.not_irreducible_C, Polynomial.degree_quadratic_lt_degree_C_mul_X_cb, IsLocalization.eq_mk'_iff_mul_eq, Algebra.algebraMap_intTrace_fractionRing, Valuation.HasExtension.val_map_lt_one_iff, Polynomial.coeff_C_mul_X_pow, LaurentPolynomial.trunc_C_mul_T, Unitization.lift_apply_apply, MvPolynomial.bindâ_bindâ, AlgebraicGeometry.instIsQuasicoherentOpensCarrierCarrierCommRingCatSpecTilde, RatFunc.num_div_denom, Submodule.torsionBySet.mk_smul, ValuationSubring.subtype_apply, PowerSeries.derivative_C, RingHom.mem_eqLocusField, LaurentPolynomial.support_C_mul_T, Zsqrtd.lift_injective, WeierstrassCurve.Ď_two, MvPolynomial.evalâHom_bindâ, RCLike.normSq_add, RootPairing.Base.cartanMatrixIn_mul_diagonal_eq, Polynomial.degree_C_mul_X, MvPolynomial.evalâ_comp_left, Ideal.under_map_eq_map_under, FractionalIdeal.den_mul_self_eq_num', Polynomial.comp_X_add_C_eq_zero_iff, MonomialOrder.monic_one, Polynomial.resultant_X_sub_C_left, isLocalization_iff_isLocalizationMap, NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply, KaehlerDifferential.map_D, instIsLocalHomZModRingHomOfIsLocalRingOfNontrivial, Algebra.adjoin_toSubsemiring, QuadraticAlgebra.algebraMap_mem_nonZeroDivisors_iff, WeierstrassCurve.Projective.dblX_eq, Polynomial.toLaurent_X, Orientation.oangle_map_complex, Algebra.Presentation.baseChange_relation, AlgebraicGeometry.Scheme.IdealSheafData.ker_glueDataObjΚ_appTop, minpoly_add_algebraMap_splits, Polynomial.scaleRoots_C, ZMod.subsingleton_ringHom, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_apply, Cubic.d_eq_three_roots, SemiRingCat.forgetâAddCommMon_preservesLimitsOfSize, DoubleQuot.coe_quotQuotEquivCommâ, AdjoinRoot.mk_self, PerfectRing.lift_comp_apply, minpoly.iterateFrobenius_of_isSeparable, WeierstrassCurve.map_aâ, MonoidWithZeroHomClass.ext_rat_iff, Complex.inv_eq_conj, MvPolynomial.C_mem_coeffsIn, ContMDiffMap.coeFnRingHom_apply, Polynomial.map_monic_eq_zero_iff, IsLocalization.mem_coeSubmodule, WeierstrassCurve.Affine.map_negY, DirectSum.liftRingHom_apply, RingHom.map_dfinsuppSumAddHom, TensorPower.toTensorAlgebra_galgebra_toFun, MvPolynomial.joinâ_map, Polynomial.degree_mul_C, LinearMap.not_hasEigenvalue_zero_tfae, TensorAlgebra.algebraMap_eq_zero_iff, MvPolynomial.aeval_monomial, Polynomial.div_C_mul, PowerSeries.X_dvd_iff, Subalgebra.range_le, Polynomial.resultant_C_mul_left, AddMonoidAlgebra.lift_def, Perfection.lift_symm_apply, Complex.conj_neg_I, WittVector.constantCoeff_apply, StandardEtalePresentation.toPresentation_relation, PowerSeries.invUnitsSub_mul_X, CauSeq.Completion.ofRatRingHom_apply, NumberField.mixedEmbedding.mixedEmbedding_apply_isComplex, Polynomial.evalâ_eq_sum, isDedekindDomain_iff, Ideal.map_prodComm_prod, Algebra.PreSubmersivePresentation.localizationAway_jacobiMatrix, NumberField.InfiniteAdeleRing.denseRange_algebraMap, spectrum.algebraMap_mem, MvPolynomial.coeff_eval_eq_eval_coeff, HasDerivAt.conj_conj, NumberField.canonicalEmbedding_eq_basisMatrix_mulVec, MvPolynomial.C_pow, QuadraticAlgebra.coe_algebraMap, LinearMap.map_smul_inv, CharP.quotient_iff_le_ker_natCast, AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo, CFC.log_algebraMap, MvPolynomial.coeffs_C_subset, Algebra.PreSubmersivePresentation.ofHasCoeffs_val, Polynomial.evalâ_eq_sum_range', Polynomial.opRingEquiv_op_C_mul_X_pow, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen', Ideal.polynomialQuotientEquivQuotientPolynomial_map_mk, AlgebraicGeometry.Scheme.basicOpen_restrict, AlgHom.toRingHom_toMonoidHom, NumberField.mixedEmbedding.fundamentalCone.mem_integerSet, TruncatedWittVector.commutes', Polynomial.evalâ_smul, MvPolynomial.C_sub, GradedTensorProduct.tmul_coe_mul_algebraMap_tmul, AlgebraicGeometry.IsAffineOpen.app_basicOpen_eq_away_map, HasGradientAt.hasDerivAt, UpperHalfPlane.denom_cocycle', Polynomial.roots_X_add_C, Subfield.mem_map, iterateFrobenius_add_apply, PrimeSpectrum.mem_image_comap_zeroLocus_sdiff, CommRingCat.forget_preservesLimits, IsDedekindDomain.exists_representative_mod_finset, Polynomial.map_surjective_iff, Matrix.mem_range_scalar_of_commute_transvectionStruct, MvPowerSeries.evalâ_C, Algebra.smulTower_leftMulMatrix_algebraMap_eq, HasDerivAt.comp_ringHom, AlgebraicGeometry.Scheme.preimage_basicOpen, AddMonoidHom.coe_addMonoidHom_mkRingHomOfMulSelfOfTwoNeZero, IntermediateField.adjoin_toSubfield, UpperHalfPlane.tanh_half_dist, MvPolynomial.quotientEquivQuotientMvPolynomial_rightInverse, Polynomial.coe_toLaurentAlg, KaehlerDifferential.tensorKaehlerEquiv_tmul_D, PerfectClosure.eq_iff, MvPolynomial.pderiv_C, PowerSeries.coeff_C_mul_X_pow, Ideal.comap_coe, RCLike.conj_eq_re_sub_im, DoubleQuot.quotQuotEquivQuotSup_quot_quot_algebraMap, IsLocalization.AtPrime.equivQuotMaximalIdeal_symm_apply_mk, Ideal.quotient_mk_maps_eq, AlgebraicGeometry.SpecToEquivOfLocalRing_eq_iff, RingHom.map_geom_sum, Submodule.map_toAddSubmonoid', constantCoeff_xInTermsOfW, RingHom.coe_toSemilinearMap, MvPolynomial.C_dvd_iff_zmod, AlgebraicGeometry.Scheme.exists_le_and_germ_injective, Polynomial.mul_star_dvd_of_aeval_eq_zero_im_ne_zero, isPRadical_iff, CFC.spectrum_algebraMap_subset, RingCat.hom_inv_apply, selfZPow_of_nonneg, NumberField.Units.finrank_mul_regulator_eq_det, RingHom.coe_pow, IsLocalization.ringEquivOfRingEquiv_apply, IsLocalization.ideal_eq_iInf_comap_map_away, DoubleQuot.quotQuotEquivQuotOfLE_symm_mk, RatFunc.aeval_X_left_eq_algebraMap, Polynomial.base_mul_mem_lifts, Algebra.coe_linearMap, MonoidAlgebra.mapDomainRingHom_apply, RingHom.op_apply_apply, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, ValuationRing.coe_equivInteger_apply, Ideal.exists_notMem_dvd_algebraMap_of_primesOver_eq_singleton, isIntegral_quotientMap_iff, Submodule.map_mem_span_algebraMap_image, Algebra.algebraMap_ofSubring_apply, MvPowerSeries.trunc_C_mul, Ideal.coeff_zero_mem_comap_of_root_mem, IsLocalization.mem_map_algebraMap_iff, Algebra.algebraMap_pUnit, WittVector.constantCoeff_wittNeg, map_wittStructureInt, HahnSeries.C_apply, Algebra.IsIntegral.isLocalHom, exists_reduced_fraction', cfc_algebraMap, MvPowerSeries.map_X, Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_C, IntermediateField.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetAdjoinCoeRingHomAlgebraMap, AlgebraicGeometry.AffineSpace.comp_homOfVector_assoc, ringHom_monotone, AlgHom.restrictNormal_commutes, RingHom.rangeRestrictFieldEquiv_apply_coe, Submodule.span.ringHom_apply, CommRingCat.forgetToRingCat_map_hom, IsLocalization.orderIsoOfPrime_apply_coe, Matrix.IsHermitian.charpoly_eq, PresheafOfModules.germ_ringCat_smul, Polynomial.taylor_X, RCLike.conj_ofNat, Polynomial.multiset_prod_X_sub_C_coeff_card_pred, Polynomial.Splits.roots_map_of_ne_zero, Module.Basis.norm_extends, SemiRingCat.forgetâ_monCat_map, Polynomial.separable_X_sub_C, Algebra.EssFiniteType.cond, AlgebraicGeometry.Scheme.Hom.toImage_app, Polynomial.finiteMultiplicity_X_sub_C, IsLocalization.primeHeight_comap, NumberField.mixedEmbedding.disjoint_span_commMap_ker, NumberField.FinitePlace.norm_le_one, Complex.conj_tsum, MvPolynomial.aevalTower_algebraMap, WeierstrassCurve.Affine.CoordinateRing.XYIdeal'_eq, Ring.le_comap_jacobson, NumberField.Units.sum_mult_mul_log, RingHom.Bijective.stableUnderComposition, MvPolynomial.optionEquivLeft_elim_eval, Subfield.coe_map, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eq, MvPowerSeries.map_C, Subalgebra.LinearDisjoint.leftMulMatrix_basisOfBasisRight_algebraMap, Polynomial.leadingCoeff_X_add_C, Polynomial.degree_sum_fin_lt, Language.map_id, UpperHalfPlane.Ď_mul_comm, PowerSeries.algebraMap_apply', HahnSeries.ofPowerSeries_C, NumberField.ComplexEmbedding.conjugate_coe_eq, NumberField.Embeddings.range_eval_eq_rootSet_minpoly, exists_C_coeff_notMem, Ideal.algebraMap_residueField_eq_zero, MvPolynomial.evalâHom_C, Module.Basis.repr_smul', PowerSeries.coe_pow, Polynomial.ringHom_ext'_iff, RootPairing.RootPositiveForm.algebraMap_posForm, MvPolynomial.counitNat_surjective, Polynomial.irreducible_X_sub_C, NumberField.ComplexEmbedding.lift_algebraMap_apply, PreTilt.mk_untilt_eq_coeff_zero, NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace_apply, LinearEquiv.isRegular_congr', PrimeSpectrum.range_comap_fst, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_apply, Polynomial.Monic.as_sum, RingHom.coe_addMonoidHom_id, AlgEquiv.commutes', AlgHom.kerSquareLift_mk, MvPolynomial.sumToIter_C, AlgebraicGeometry.Scheme.image_zeroLocus, Polynomial.preimage_eval_singleton, WeierstrassCurve.Projective.dblX_eq', RingHom.FaithfullyFlat.injective, trace_eq_sum_embeddings_gen, MvPolynomial.eval_expand, WeierstrassCurve.map_j, CliffordAlgebra.contractRight_Κ, AlgebraicGeometry.Scheme.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, LaurentSeries.mem_integers_of_powerSeries, CompleteOrthogonalIdempotents.map, Ideal.bijective_algebraMap_quotient_residueField, AlgebraicGeometry.LocallyRingedSpace.evaluation_eq_zero_iff_notMem_basicOpen, IsConjRoot.sub_algebraMap, algebraMap_galRestrict'_apply, Ideal.absNorm_algebraMap, RingOfIntegers.coe_algebraMap_norm, WittVector.mk_fontaineTheta, Cubic.C_mul_prod_X_sub_C_eq, Polynomial.map_mapRingHom_eval_map_eval, AlgebraicGeometry.Proj.res_apply, Polynomial.toLaurent_C, Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le, PowerSeries.binomialSeries_constantCoeff, tendsto_algebraMap_cobounded, MvPolynomial.supportedEquivMvPolynomial_symm_C, AlgebraicGeometry.StructureSheaf.comapâ_eq_localRingHom, tendsto_algebraMap_inv_atTop_nhds_zero_nat, PowerSeries.coeff_one_pow, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletion, coe_iterateFrobeniusEquiv, Ideal.map_pointwise_smul, RatFunc.algebraMap_monomial, IsPRadical.ker_le', AdjoinRoot.coe_algHomOfDvd, Subsemiring.coe_map, IsNilpotent.isUnit_quotient_mk_iff, Matrix.toMvPolynomial_constantCoeff, RatFunc.denom_dvd, PresheafOfModules.Sheafify.map_smul, RingHom.surjective_isStableUnderBaseChange, Matrix.GeneralLinearGroup.coe_map_inv_mul_map, MvPowerSeries.trunc'_map, WittVector.ghostComponent_zero_verschiebungFun, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, RingCon.coe_liftâ, Polynomial.toLaurentAlg_apply, dist_algebraMap', CategoryTheory.Linear.toCatCenter_apply_app, Complex.tan_conj, PowerSeries.smul_eq_C_mul, RingHom.field_closure_preimage_le, Polynomial.irreducible_C_mul_X_add_C, Ideal.Quotient.norm_mk_le, Ideal.quotientToQuotientRangePowQuotSuccAux_mk, PresheafOfModules.germ_smul, MonoidAlgebra.liftNC_one, Polynomial.succ_signVariations_le_X_sub_C_mul, Projectivization.map_mk, MvPolynomial.C_inj, RCLike.conj_smul, WeierstrassCurve.Jacobian.map_polynomialY, MvPowerSeries.rescale_zero_apply, Subalgebra.LinearDisjoint.basisOfBasisLeft_repr_apply, RingHom.surjectiveOnStalks_iff_forall_ideal, LinearMap.map_smulâââ, Polynomial.Splits.C, LinearMap.isSymmetric_iff_inner_map_self_real, LocalizedModule.algebraMap_mk', WeierstrassCurve.Affine.CoordinateRing.map_smul, MvPolynomial.eval_X, ExteriorAlgebra.invertibleAlgebraMapEquiv_symm_apply_invOf_toQuot, Ideal.mem_span_pow_iff_exists_isHomogeneous, AlgebraicGeometry.AffineSpace.map_appTop_coord, Subfield.subtype_injective, Polynomial.reverse_C_add, MonoidHom.map_frobenius, PowerSeries.IsWeierstrassDivisorAt.seq_one, Valuation.HasExtension.coe_algebraMap_valuationSubring_eq, Polynomial.natDegree_linear, ValuationSubring.algebraMap_injective, IsLocalization.bijective, IsSimpleRing.iff_injective_ringHom_or_subsingleton_codomain, autAdjoinRootXPowSubC_root, AlgebraicGeometry.LocallyRingedSpace.isLocalHom_stalkMap_congr, Polynomial.toLaurent_C_mul_X_pow, PowerSeries.map_id, RingHom.codomain_trivial_iff_range_trivial, FreeAbelianGroup.liftMonoid_symm_coe, RestrictScalars.addEquiv_symm_map_algebraMap_smul, WeierstrassCurve.map_Î, Ideal.ResidueField.liftâ_algebraMap, WeierstrassCurve.Projective.comp_smul, frobenius_add, IntermediateField.mem_bot, Ideal.isPrime_map_C_iff_isPrime, Ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem, PrimeSpectrum.BasicConstructibleSetData.map_g, MatrixEquivTensor.toFunAlgHom_apply, NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion, RingHom.mem_eqLocusS, Matrix.charpoly_diagonal, Cubic.b_eq_three_roots, LaurentPolynomial.evalâ_C_mul_T_n, Perfection.coeff_pow_p, CliffordAlgebra.GradedAlgebra.Κ_sq_scalar, Polynomial.degree_add_C, Polynomial.toAddCircle_C_eq_smul_fourier_zero, Matrix.entryLinearMap_toAddMonoidHom, Polynomial.evalEval_C, Perfection.coeff_iterate_frobenius', IsFractionRing.num_mul_den_eq_num_iff_eq', IsLocalization.AtPrime.isPrime_map_of_liesOver, MvPowerSeries.comp_substAlgHom, Matrix.scalar_commute_iff, PowerSeries.rescale_neg_one_invOneSubPow, HahnSeries.algebraMap_apply', WeierstrassCurve.VariableChange.map_r, Algebra.norm_eq_prod_embeddings_gen, Polynomial.coe_evalâRingHom, WeierstrassCurve.Projective.dblY_of_Y_eq', NumberField.Units.dirichletUnitTheorem.exists_unit, Polynomial.natDegree_pow_X_add_C, LaurentPolynomial.toLaurent_reverse, MeasureTheory.SimpleFunc.coe_algebraMap, IsScalarTower.algebraMap_apply, MvPolynomial.IsHomogeneous.C_mul, PowerSeries.trunc_map, Complex.UnitDisc.coe_star, Polynomial.natDegree_eq_zero, SkewMonoidAlgebra.lift_def, CoalgHom.coe_toAddMonoidHom, Ideal.Factors.piQuotientEquiv_mk, MvPolynomial.constantCoeff_map, Ideal.quotient_map_mkâ, Algebra.QuasiFiniteAt.comap_algEquiv, Polynomial.Monic.natSepDegree_eq_one_iff_of_irreducible, smoothSheafCommRing.forgetStalk_hom_comp_evalHom_apply, RingHom.kerLift_mk, IsSelfAdjoint.le_algebraMap_norm_self, RingHom.map_frobenius, Ideal.map_coe, IsLocalization.Away.integralClosure, Polynomial.IsUnitTrinomial.irreducible_aux1, Polynomial.roots_C_mul_X_add_C_of_IsUnit, LaurentSeries.X_order_mul_powerSeriesPart, AnalyticOnNhd.eval_continuousLinearMap', AlgebraicGeometry.Scheme.Hom.instIsLocalHomCarrierStalkCommRingCatPresheafCoeContinuousMapCarrierCarrierHomTopCatBaseRingHomHomStalkMap, RingHom.coe_prodMap, Polynomial.mirror_C, TopCat.Presheaf.submonoidPresheafOfStalk_obj, Polynomial.nextCoeff_map_eq_of_isUnit_leadingCoeff, IsAdjoinRoot.lift_algebraMap_apply, MvPolynomial.optionEquivLeft_symm_C_C, PerfectionMap.lift_apply, RingTheory.Sequence.IsWeaklyRegular.isRegular_of_isLocalization_of_mem, Matrix.Represents.algebraMap, Cubic.of_c_eq_zero, PrimeSpectrum.maximalSpectrumToPiLocalization_surjective_of_discreteTopology, RingCat.id_apply, QuotientRing.isOpenQuotientMap_mk, matPolyEquiv_eq_X_pow_sub_C, Algebra.Generators.Hom.algebraMap_toAlgHom, Polynomial.coeff_divByMonic_X_sub_C, NumberField.InfinitePlace.card_complex_embeddings, AdjoinRoot.liftHom_mk, Matrix.derivative_det_one_add_X_smul_aux, RingHom.surjectiveOnStalks_iff_forall_maximal, Polynomial.degree_C_mul_X_pow, Polynomial.C_pow, Polynomial.C_add, RCLike.hasSum_conj', MonomialOrder.C_mul_leadingCoeff_monomial_degree, DoubleQuot.quotQuotEquivQuotSupâ_symm_toRingEquiv, Polynomial.zero_notMem_multiset_map_X_add_C, WittVector.coeff_frobenius, TensorAlgebra.Κ_eq_algebraMap_iff, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_apply, WeierstrassCurve.Affine.map_addX, LinearMap.map_algebraMap_mul, NumberField.RingOfIntegers.algebraMap.injective, InnerProductSpace.conj_inner_symm, Polynomial.mod_def, PadicInt.cast_toZModPow, isLocalHom_toRingHom, IsLocalization.algebraMap_pi_surjective_of_isLocalization, TwoSidedIdeal.ker_ringCon_mk', Polynomial.aeval_algebraMap_apply, Polynomial.polynomial_map_coe, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_apply, IsLocalRing.local_hom_TFAE, Valuation.Integers.one_of_isUnit, AlgebraicGeometry.map_injective_of_isIntegral, Polynomial.leadingCoeff_divByMonic_X_sub_C, AnalyticOnNhd.eval_mvPolynomial, Polynomial.pairwise_coprime_X_sub_C, MvPowerSeries.monomial_smul_eq, LaurentSeries.coeff_coe_powerSeries, RingEquiv.coe_toRingHom, Matrix.sub_scalar_sq_eq_discr, AlgebraicGeometry.exists_eq_pow_mul_of_isCompact_of_isQuasiSeparated, AlgebraicGeometry.AffineSpace.homOfVector_appTop_coord, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, WeierstrassCurve.Projective.map_polynomialY, MvPolynomial.tensorEquivSum_C_tmul_C, Polynomial.derivative_X_sub_C, Subalgebra.rTensorBot_tmul, AlgebraicGeometry.Proj.stalkIso'_symm_mk, map_complEDS, IsLocalization.AtPrime.ramificationIdx_map_eq_ramificationIdx, Module.End.ringHomEndFinsupp_surjective, RingHom.map_dotProduct, WeierstrassCurve.Projective.map_polynomial, PiTensorProduct.algebraMap_apply, CommAlgCat.forgetâ_commRingCat_map, RingCat.forget_obj, NumberField.mixedEmbedding.norm_unit, algebraMap_galRestrictHom_apply, Algebra.prod_embeddings_eq_finrank_pow, LocallyConstant.coeFnRingHom_apply, RingTheory.Sequence.IsWeaklyRegular.of_isLocalization, Pi.algebraMap_def, RingCon.map_apply, Polynomial.aroots_C, RingHom.coe_addMonoidHom_injective, Ring.DirectLimit.map_apply_of, minpoly.ker_eval, minpoly.eq_X_sub_C, Ideal.Quotient.mk_smul_mk_quotient_map_quotient, AlgebraicGeometry.Scheme.IdealSheafData.ideal_map_of_isAffineHom, WittVector.frobenius_verschiebung, LinearMap.trace_baseChange, Polynomial.roots_C, Matrix.charmatrix_diagonal, AlgebraicGeometry.LocallyRingedSpace.isLocalHomValStalkMap, PowerSeries.coeff_one_mul, Algebra.idealMap_apply_coe, WeierstrassCurve.Projective.eval_polynomialY, AddValuation.supp_quot, LaurentPolynomial.comul_C_mul_T_self, FractionalIdeal.den_mem_inv, Lagrange.nodal_erase_eq_nodal_div, Localization.AtPrime.map_eq_maximalIdeal, Polynomial.monic_prod_X_sub_C, Complex.log_conj, RingTheory.Sequence.IsWeaklyRegular.of_isLocalizedModule, Polynomial.natDegree_cubic_le, FreeAlgebra.algebraMap_leftInverse, RingHom.toIntAlgHom_injective, RingCat.FilteredColimits.forgetâSemiRing_preservesFilteredColimits, LaurentPolynomial.invert_C, WittVector.mapFun.natCast, Module.Basis.mem_span_iff_repr_mem, PowerSeries.monomial_zero_eq_C_apply, FiniteField.algebraMap_norm_eq_pow_sum, IsBaseChange.toDualBaseChange_tmul, Ideal.isMaximal_comap_of_isIntegral_of_isMaximal', Perfection.coeff_pow_p', IsLocalRing.ResidueField.lift_residue_apply, Polynomial.map_aeval_eq_aeval_map, PowerSeries.map_toSubring, IsDedekindDomain.quotientEquivPiFactors_mk, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_eq_one_iff, MvPolynomial.instIsLocalHomRingHomC, IntermediateField.coe_algebraMap_apply, QuasispectrumRestricts.left_inv, MvPolynomial.evalâ_eq_eval_map, ZMod.castHom_surjective, AdjoinRoot.coe_mapRingEquiv, AlgebraicGeometry.RingedSpace.mem_basicOpen, WeierstrassCurve.Ď_four, NumberField.IsCMField.complexConj_torsion, AlgebraicGeometry.Scheme.Hom.app_injective, AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_mk_of, spectrum.vadd_eq, Polynomial.Bivariate.equivMvPolynomial_C_C, FreeAlgebra.algebraMap_eq_zero_iff, dotProduct_toMatrixâ_mulVec, WeierstrassCurve.Ψ_odd, MvPolynomial.isWeightedHomogeneous_C, Polynomial.natDegree_quadratic, algebraMap_cobounded_le_cobounded, MvPolynomial.map_X, RatFunc.laurentAux_ofFractionRing_mk, Polynomial.natDegree_C_mul_X_pow_le, HasGradientAtFilter.hasDerivAtFilter, ContinuousLinearMap.map_smulâââ, Polynomial.instIsLocalHomRingHomAlgebraMap, MvPowerSeries.WithPiTopology.continuous_constantCoeff, Ring.DirectLimit.of_f, NumberField.InfinitePlace.apply, PowerSeries.IsRestricted.C, MeasureTheory.eLpNorm_conj, Module.Basis.toMatrix_map_vecMul, inner_gradient_right, Module.IsTorsionBy.mk_smul, MvPolynomial.eval_assoc, Algebra.commutes, RingTheory.Sequence.isRegular_cons_iff', ax_grothendieck_zeroLocus, Transcendental.linearIndependent_sub_inv, wittPolynomial_eq_sum_C_mul_X_pow, PowerSeries.isUnit_constantCoeff, Polynomial.card_roots_sub_C, IsLocalization.liesOver_of_isPrime_of_disjoint, WittVector.ghostComponent_teichmuller, Algebra.mem_algebraMapSubmonoid_of_mem, constantCoeff_wittStructureInt_zero, Complex.conj_I, ValuationSubring.coe_unitGroupToResidueFieldUnits_apply, inner_conj_symm, NormedAlgebra.Complex.exists_norm_sub_smul_one_eq_zero, inv_eq_of_aeval_divX_ne_zero, Polynomial.lifts_iff_coeffs_subset_range, IsSMulRegular.of_isLocalizedModule, Ideal.comap_id, Polynomial.resultant_C_mul_right, MonoidWithZeroHomClass.ext_nnrat_iff, MvPowerSeries.aeval_unique, AlgebraicGeometry.StructureSheaf.algebraMap_germ_apply, Polynomial.map_scaleRoots, ValuationSubring.coe_subtype, Polynomial.coe_evalEvalRingHom, Padic.isDenseInducing_cast_withVal, IsLocalization.map_id_mk', AddChar.inv_apply_eq_conj, WeierstrassCurve.Projective.map_negY, Valuation.HasExtension.algebraMap_residue_eq_residue_algebraMap, FractionRing.mk_eq_div, Polynomial.degree_linear, SemiRingCat.forgetâMon_preservesLimits, Ideal.mapHom_apply, HasDerivAt.comp_semilinear, IsLocalization.surjâ, Polynomial.taylor_C, MvPolynomial.hom_bindâ, WeierstrassCurve.map_bâ, WeierstrassCurve.Jacobian.map_polynomialX, WeierstrassCurve.Jacobian.map_neg, CFC.log_smul, DoubleQuot.coe_liftSupQuotQuotMkâ, Polynomial.derivative_apply, RingCon.lift_injective_iff, Polynomial.C_injective, HomogeneousLocalization.algebraMap_apply, LinearMap.toAddMonoidHom_mulRight, AnalyticOnNhd.eval_continuousLinearMap, Submodule.map_toAddSubmonoid, GaussianInt.toComplex_one, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal_basicOpen, HomogeneousIdeal.toIdeal_irrelevant, IsStronglyTranscendental.of_isLocalization, WeierstrassCurve.Jacobian.eval_polynomialZ, AlgebraicGeometry.Scheme.localRingHom_comp_stalkIso_apply, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeÎFreeOpensCarrierCarrierCommRingCat, RingOfIntegers.dvd_norm, Valuation.Integers.bijective_algebraMap_of_subsingleton_units_mrange, Subalgebra.coe_valA', LaurentPolynomial.exists_T_pow, Polynomial.nextCoeff_C_mul, spectrum.sub_singleton_eq, iterateFrobenius_zero_apply, Valuation.coeff_zero_minpoly, SemiRingCat.forget_map, IsLocalization.coe_primeSpectrumOrderIso_apply_coe_asIdeal, RatFunc.map_apply_div_ne_zero, RCLike.normSq_sub, Polynomial.self_sub_C_mul_X_pow, Polynomial.monomial_comp, algebraicIndependent_empty_type_iff, CommSemiRingCat.instFullSemiRingCatForgetâRingHomCarrierCarrier, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, Polynomial.natDegree_add_C, Orthonormal.inner_sum, Ideal.comap_lt_comap_of_root_mem_sdiff, WeierstrassCurve.VariableChange.map_u, PreTilt.coeff_def, Polynomial.coe_evalRingHom, Polynomial.eval_C_mul, PadicInt.val_toZMod_eq_zmodRepr, starRingEnd_self_apply, RingHomSurjective.is_surjective, UpperHalfPlane.Ď_denom, Polynomial.roots_map, Matrix.algebraMap_matrix_apply, MvPolynomial.support_C, Algebra.Presentation.HasCoeffs.coeffs_relation_mem_range, MvPowerSeries.monomial_eq', Polynomial.roots_expand_map_frobenius_le, IsLocalization.height_comap, PerfectionMap.equiv_apply, IntermediateField.AdjoinPair.algebraMap_genâ, DoubleQuot.quotQuotEquivQuotOfLE_comp_quotQuotMk, Polynomial.isCoprime_X_sub_C_of_isUnit_sub, PowerSeries.map.isLocalHom, IsLocalization.eq_iff_exists, AdicCompletion.evalâ_liftRingHom, AlgHom.coe_toAddMonoidHom, MvPolynomial.evalâ_comp_right, PresheafOfModules.map_comp_assoc, IsLocalHom.of_comap_surjective, NumberField.house.basis_repr_norm_le_const_mul_house, Complex.dist_conj_self, SpectrumRestricts.nnreal_iff_nnnorm, Unitization.inlRingHom_apply, NumberField.IsCMField.Units.complexConj_eq_self_iff, HasDerivAt.star_conj, is_integral_localization_at_leadingCoeff, MvPolynomial.map_eval, GradedRing.coe_projZeroRingHom'_apply, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, Module.Basis.restrictScalars_toMatrix, InnerProductSpaceable.inner_.conj_symm, WittVector.truncate_liftFun, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_lt_one_iff, Submodule.torsionBy.mk_smul, Algebra.Extension.Hom.toAlgHom_apply, MvPowerSeries.coeff_mul_C, Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow, LaurentPolynomial.invert_comp_C, Matrix.center_eq_scalar_image, IsLocalRing.residue_surjective, algebraMap_le_algebraMap, LaurentPolynomial.antipode_C_mul_T, PadicInt.toZMod_spec, Algebra.PreSubmersivePresentation.jacobian_eq_jacobiMatrix_det, Polynomial.signVariations_C_mul, WeierstrassCurve.Jacobian.map_addXYZ, Algebra.botEquiv_symm_apply, RingHom.coe_rangeS, GaussianInt.normSq_div_sub_div_lt_one, RingQuot.mkRingHom_rel, AlgebraicGeometry.Scheme.zeroLocus_map_of_eq, RingHom.equivRatAlgHom_symm_apply, RingCon.comap_eq, SemimoduleCat.forgetâ_map, RingHom.map_frobeniusEquiv_symm, RCLike.conj_neg_I, IsLocalization.Away.algebraMap_isUnit, Polynomial.IsRoot.map, Localization.AtPrime.mapPiEvalRingHom_algebraMap_apply, Ideal.pointwise_smul_def, WittVector.ghostComponentModPPow_map_mk, LaurentSeries.valuation_X_pow, LaurentPolynomial.degree_C_le, InnerProductSpace.Core.inner_conj_symm, char_dvd_card_solutions_of_fintype_sum_lt, isConjRoot_iff_eq_algebraMap', RingHom.closure_preimage_le, Ideal.ramificationIdx_map_self_eq_one, MulAlgebraNorm.extends_norm, NumberField.house_eq_sup', GaussianInt.intCast_complex_norm, RingHom.injective_int, RingHom.coe_range, IntermediateField.AdjoinSimple.algebraMap_gen, Valuation.Integers.dvd_iff_le, Ideal.comap_jacobson, GaussianInt.intCast_re, MvPolynomial.bindâ_monomial, Lagrange.interpolate_singleton, Polynomial.C_content_dvd, IsLocalization.mk'_spec, cyclotomicCharacter.toFun_spec, LinearMap.polyCharpoly_coeff_eval, NumberField.FinitePlace.norm_def, PrimeSpectrum.discreteTopology_iff_toPiLocalization_bijective, AdjoinRoot.ringHom_ext_iff, NumberField.mixedEmbedding.convexBodySum_mem, Polynomial.coeff_X_add_C_pow, WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_Y, RootPairing.algebraMap_root'In_apply, Ideal.kerLiftAlg_mk, Polynomial.degree_linear_lt, PreTilt.coeff_iterate_frobenius', PerfectRing.lift_aux, CommRingCat.instIsRightAdjointForgetRingHomCarrier, MvPolynomial.continuous_eval, PowerSeries.trunc_C_mul, PadicInt.lift_self, RingHom.FaithfullyFlat.codescendsAlong_bijective, MvPolynomial.C_eq_smul_one, QuadraticAlgebra.coe_dvd_iff, RingQuot.eq_liftAlgHom_comp_mkAlgHom, FractionalIdeal.extendedHomâ_le_one_iff, MvPolynomial.evalâ_apply, Ideal.pi_quotient_surjective, RestrictScalars.smul_def, RingHom.coe_rangeRestrict, inner_smul_left, DoubleQuot.quotQuotEquivQuotOfLE_quotQuotMk, Polynomial.coeff_det_X_add_C_zero, iterateFrobenius_mul_apply, Polynomial.derivative_C_mul_X_sq, Lagrange.nodal_eq, Polynomial.derivativeFinsupp_C, SkewMonoidAlgebra.liftNC_smul, frobeniusEquiv_symm_apply_frobenius, Polynomial.card_support_trinomial, Valuation.HasExtension.algebraMap_injective, ULift.algebraMap_eq, AddMonoidAlgebra.mapDomainRingHom_apply, LinearMap.prodMapRingHom_apply, Polynomial.taylor_one, X_pow_sub_C_irreducible_iff_of_prime, IsPurelyInseparable.algebraMap_iterateFrobeniusââ, Matrix.SpecialLinearGroup.mem_center_iff, RingHom.surjective_localRingHom_iff, CompleteOrthogonalIdempotents.bijective_pi, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_mul_XYIdeal, inv_eq_of_root_of_coeff_zero_ne_zero, IsScalarTower.toAlgHom_apply, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, AdjoinRoot.mk_C, Polynomial.roots_X_pow_char_pow_sub_C, RingHom.map_vecMul, RatFunc.ofFractionRing_algebraMap, RatFunc.eval_algebraMap, LinearMap.mulLeft_toAddMonoidHom, MvPolynomial.map_id, CFC.eq_algebraMap_of_spectrum_subset_singleton, Ideal.le_comap_pow_ramificationIdx, QuadraticAlgebra.algebraMap_im, RCLike.normSq_conj, GaussianInt.toComplex_div_im, DoubleQuot.quotQuotEquivComm_symm, algebraMap_comp_natCast, NNRat.subsingleton_ringHom, le_algebraMap_iff_spectrum_le, MvPowerSeries.expand_C, Polynomial.toMvPolynomial_C, WittVector.mapFun.neg, RingHom.mem_eqLocus, Ideal.Factors.piQuotientEquiv_map, ClassGroup.exists_mem_finsetApprox, Algebra.TensorProduct.includeLeftRingHom_apply, WeierstrassCurve.Projective.map_dblX, AlgebraicGeometry.IsAffineOpen.appLE_eq_away_map, spectrum.notMem_iff, algebraMap_star_comm, Polynomial.exists_mul_add_mul_eq_C_resultant, Matrix.charpoly_of_card_eq_two, Polynomial.eval_multiset_prod_X_sub_C_derivative, Polynomial.toFinsupp_C, AdjoinRoot.coe_ofAlgHom, AlgebraicGeometry.Scheme.Modules.map_smul, AlgebraicGeometry.RingedSpace.mem_basicOpen', Unitization.algebraMap_eq_inl_comp, RingHom.map_closure, TensorProduct.quotTensorEquivQuotSMul_mk_tmul, RestrictScalars.addEquiv_map_smul, derivationQuotKerSq_mk, Subfield.mem_comap, IsFractionRing.self_iff_bijective, MvPowerSeries.trunc'_C, AdjoinRoot.of.injective_of_degree_ne_zero, Polynomial.X_sub_C_pow_dvd_iff, LaurentPolynomial.degree_C_mul_T_le, IsAlgClosed.ringHom_bijective_of_isIntegral, GaussianInt.toComplex_eq_zero, LinearIsometryEquiv.map_smulââ, AlgebraicGeometry.Scheme.mem_basicOpen, RingHom.FaithfullyFlat.codescendsAlong_injective, RingCat.forget_map, Matrix.charmatrix_zero, Algebra.Generators.C_mul_X_sub_one_mem_ker, Subsemiring.coe_comap, isCyclic_tfae, Polynomial.roots_prod_X_sub_C, Polynomial.integralNormalization_evalâ_leadingCoeff_mul, Algebra.traceMatrix_eq_embeddingsMatrixReindex_mul_trans, NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat, MonoidAlgebra.mapRangeRingHom_apply, SemiRingCat.forgetâ_addCommMonCat_map, Polynomial.C_smul_derivation_apply, MvPowerSeries.trunc'_C_mul, MvPolynomial.commAlgEquiv_C_X, MvPolynomial.expand_zero_apply, ZMod.unitsMap_def, Polynomial.X_pow_mul_C, AdjoinRoot.evalEval_mk, AlgebraicGeometry.IsOpenImmersion.map_ÎIso_inv_apply, Polynomial.degree_sub_C, DoubleCentralizer.toProdMulOppositeHom_apply, ModularForm.slash_apply, Module.Basis.ofIsLocalizedModule_repr_apply, Multiset.prod_X_sub_C_coeff, Valuation.HasExtension.algebraMap_mem_maximalIdeal_iff, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.ofRestrict_invApp_apply, ContinuousLinearMap.algebraMap_apply, RingHom.ker_rangeSRestrict, WeierstrassCurve.Projective.negDblY_of_Y_eq', DoubleQuot.quotQuotEquivComm_algebraMap, IsFractionRing.liftAlgHom_apply, QuadraticAlgebra.algebraMap_injective, Polynomial.degree_X_add_C, IsPRadical.pow_mem', MvPowerSeries.WithPiTopology.continuous_C, Polynomial.isMonicOfDegree_sub_add_two, TensorProduct.liftAux.smulââ, FaithfulSMul.algebraMap_eq_zero_iff, WittVector.frobenius_zmodp, Ideal.Quotient.mk_algebraMap, RingHom.surjective_ofLocalizationSpan, Perfection.coeff_frobenius, Polynomial.degree_C_le, Algebra.FinitePresentation.iff_quotient_mvPolynomial', CliffordAlgebra.even.lift.aux_algebraMap, prod_galRestrict_eq_norm, sum_conjneg, algebraMap_le_cfc_iff, AlgebraicGeometry.homogeneousLocalizationToStalk_stalkToFiberRingHom, AlgebraicGeometry.IsAffineOpen.ideal_ext_iff, Algebra.PreSubmersivePresentation.localizationAway_jacobian, RingCon.lift_coe, Ideal.comap_comap, MvPolynomial.eval_polynomial_eval_finSuccEquiv, MvPolynomial.sumToIter_Xl, Polynomial.isIntegral_isLocalization_polynomial_quotient, frobenius_inj, AlgebraicGeometry.Scheme.Hom.stalkMap_surjective, IsLocalization.map_nonZeroDivisors_le, FreeCommRing.map_subtype_val_restriction, WittVector.constantCoeff_wittSub, Ideal.Quotient.algebraMap_mk_of_liesOver, ModuleCat.forgetâ_map, RingHom.asBoolAlg_toFun, MvPolynomial.counit_X, Polynomial.Monic.eq_X_sub_C_pow_of_natSepDegree_eq_one_of_splits, MvPowerSeries.le_order_map, UpperHalfPlane.petersson_slash, Localization.algEquiv_symm_apply, CliffordAlgebra.contractLeft_algebraMap, IsLocalization.coeSubmodule_span_singleton, RingQuot.ringQuotToIdealQuotient_apply, PerfectRing.lift_self_apply, Algebra.ZariskisMainProperty.exists_fg_and_exists_notMem_and_awayMap_bijective, RingHom.map_pow, Algebra.Presentation.tensorModelOfHasCoeffsInv_aeval_val, NNRat.coe_coeHom, KaehlerDifferential.kerTotal_mkQ_single_algebraMap, AlgebraicGeometry.IsAffineOpen.mem_ideal_iff, Zsqrtd.toReal_injective
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