algebra 📖 | CompOp | 731 mathmath: MvPolynomial.pUnitAlgEquiv_symm_monomial, MvPolynomial.join₁_rename, MvPolynomial.aeval_sum, mapRangeAlgEquiv_trans, WittVector.bind₁_frobeniusPoly_wittPolynomial, KaehlerDifferential.mvPolynomialBasis_apply, Algebra.PreSubmersivePresentation.jacobiMatrix_naive, lift_apply', MvPolynomial.algHom_ext_iff, MvPolynomial.map_bind₁, Algebra.Generators.aeval_val_surjective, domCongr_comp_lsingle, wittPolynomial_zmod_self, MvPolynomial.aeval_X_left, MvPolynomial.pUnitAlgEquiv_apply, algHom_ext'_iff, MvPolynomial.exists_finset_rename, AlgebraicIndependent.of_aeval, MvPolynomial.support_finSuccEquiv, Algebra.PreSubmersivePresentation.cotangentComplexAux_apply, WittVector.aeval_verschiebung_poly', MvPolynomial.rTensorAlgEquiv_apply, Algebra.Presentation.naive_toGenerators, MvPolynomial.mem_image_support_coeff_finSuccEquiv, MvPolynomial.comapEquiv_symm_coe, MvPolynomial.eval₂_expand, MvPolynomial.universalFactorizationMap_comp_map, MvPolynomial.aeval_algebraMap_eq_zero_iff, Algebra.PreSubmersivePresentation.ofHasCoeffs_map, MvPolynomial.expand_X, algebraicIndependent_iff_ker_eq_bot, MvPolynomial.derivation_eq_of_forall_mem_vars, Algebra.Generators.cotangentSpaceBasis_apply, MvPolynomial.IsWeightedHomogeneous.pderiv, WittVector.ghostComponent_apply, aeval_wittPolynomial, LieAlgebra.LoopAlgebra.twoCochainOfBilinear_apply_apply, MvPolynomial.aeval_range, KaehlerDifferential.mvPolynomialBasis_repr_D_X, MvPolynomial.optionEquivLeft_C, MvPolynomial.rename_rename, Algebra.Generators.toAlgHom_ofComp_localizationAway, MvPowerSeries.trunc'_expand_trunc', MvPolynomial.optionEquivLeft_X_some, MvPolynomial.aeval_X_left_apply, Polynomial.toPowerSeries_toMvPowerSeries, MvPolynomial.pUnitAlgEquiv_symm_apply, MvPolynomial.expand_eq_zero, MvPolynomial.weightedHomogeneousSubmodule_mul, Ideal.span_pow_eq_map_homogeneousSubmodule, MvPolynomial.natDegree_finSuccEquiv, StandardEtalePresentation.toPresentation_algebra_smul, Ideal.span_eq_map_homogeneousSubmodule, domCongr_toAlgHom, MvPolynomial.algHom_ext'_iff, IntermediateField.mem_adjoin_iff, AlgebraicIndependent.repr_ker, chevalley_mvPolynomial_mvPolynomial, MvPolynomial.aeval_X, MvPolynomial.comapEquiv_coe, Polynomial.pUnitAlgEquiv_symm_toPowerSeries, AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin, Algebra.PreSubmersivePresentation.cotangentComplexAux_zero_iff, MvPolynomial.optionEquivLeft_apply, MvPolynomial.instIsScalarTower, MvPolynomial.totalDegree_coeff_finSuccEquiv_add_le, MvPolynomial.map_comp_rename, MvPolynomial.ACounit_X, MvPolynomial.prime_rename_iff, bind₁_xInTermsOfW_wittPolynomial, MvPolynomial.constantCoeff_rename, Algebra.PreSubmersivePresentation.jacobiMatrix_reindex, CommRingCat.free_map_coe, Algebra.FinitePresentation.mvPolynomial_of_finitePresentation, Algebra.SubmersivePresentation.ofSubsingleton_algebra_algebraMap, MvPolynomial.killCompl_comp_rename, MvPolynomial.supportedEquivMvPolynomial_symm_X, MvPolynomial.pderiv_one, MvPolynomial.mkDerivation_X, MvPolynomial.pderiv_mul, Algebra.Generators.compLocalizationAwayAlgHom_toAlgHom_toComp, MvPolynomial.ACounit_surjective, lift_mapRangeRingHom_algebraMap, MvPolynomial.supported_eq_adjoin_X, MvPolynomial.aeval_eq_eval, mapAlgHom_single, MvPolynomial.aeval_ite_mem_eq_self, MvPolynomial.eval₂Hom_C_id_eq_join₁, PolynomialLaw.exists_lift', PolynomialLaw.toFun_eq_rTensor_φ_toFun', MvPolynomial.comap_id, MvPolynomial.eval_rename_prod_mk, MvPolynomial.optionEquivRight_C, mapDomainBialgHom_id, Polynomial.Bivariate.Polynomial.Bivariate.pderiv_one_equivMvPolynomial, MvPolynomial.aevalTower_comp_C, MvPolynomial.rename_msymm, MvPolynomial.comap_comp_apply, MvPolynomial.eval₂Hom_C_eq_bind₁, Algebra.PreSubmersivePresentation.ofHasCoeffs_relation, MvPolynomial.degreeOf_coeff_finSuccEquiv, mapDomainAlgHom_id, MvPolynomial.rename_id_apply, toRingHom_mapAlgHom, MvPolynomial.nonempty_support_finSuccEquiv, Algebra.Generators.cotangentSpaceBasis_repr_one_tmul, MvPolynomial.pderiv_rename, Algebra.Presentation.comp_relation_inr, MvPolynomial.support_killCompl, AlgebraicIndependent.aeval_comp_repr, MvPolynomial.map_expand, MvPolynomial.map_aeval, MvPolynomial.map_frobenius_expand, MvPolynomial.renameEquiv_trans, MvPolynomial.expand_monomial, MvPolynomial.expand_char, MvPolynomial.map_rename, Algebra.PreSubmersivePresentation.ofHasCoeffs_σ', MvPolynomial.killCompl_C, LaurentPolynomial.algebraMap_apply, MvPolynomial.eval₂_const_pUnitAlgEquiv_symm, MvPolynomial.eval_comp_toMvPolynomial, Algebra.Generators.map_toComp_ker, MvPolynomial.support_finSuccEquiv_nonempty, Algebra.Generators.Hom.toExtensionHom_toAlgHom_apply, MvPolynomial.bind₁_X_left, MvPolynomial.sumAlgEquiv_comp_rename_inr, MvPolynomial.aevalTower_toAlgHom, MvPolynomial.X_mul_pderiv_monomial, MvPolynomial.degree_optionEquivLeft, MvPolynomial.mapAlgHom_id, Algebra.Generators.naive_val, MvPolynomial.coeff_expand_smul, Algebra.Generators.algebraMap_apply, mapDomainRingHom_comp_algebraMap, MvPolynomial.expand_C, MvPolynomial.derivation_eq_zero_of_forall_mem_vars, Algebra.Generators.compLocalizationAwayAlgHom_X_inl, MvPolynomial.optionEquivRight_X_none, MvPolynomial.rename_psum, Algebra.Generators.map_ofComp_ker, mapDomainBialgHom_mapDomainBialgHom, BoundedContinuousFunction.charAlgHom_apply, MvPolynomial.expand_zero, MvPolynomial.degreesLE_nsmul, MvPolynomial.totalDegree_rename_le, domCongr_refl, MvPolynomial.coe_mapEquivMonic_comp', Algebra.Presentation.naive_relation, decomposeAux_coe, Polynomial.toMvPolynomial_eq_rename_comp, Polynomial.aeval_homogenize_X_one, MvPolynomial.adjoin_range_X, MonoidAlgebra.mvPolynomial_aeval_of_surjective_of_closure, mvPolynomial_aeval_of_surjective_of_closure, MvPolynomial.transcendental_polynomial_aeval_X_iff, MvPolynomial.aeval_algebraMap_eq_zero_iff_of_injective, Algebra.Generators.algebraMap_eq, Algebra.SubmersivePresentation.ofSubsingleton_relation, StandardEtalePair.equivMvPolynomialQuotient_symm_apply, MvPolynomial.support_rename_of_injective, Algebra.IsSmoothAt.exists_isStandardEtale_mvPolynomial, MvPolynomial.comap_comp, MvPolynomial.eval_eq_eval_mv_eval', MvPolynomial.ACounit_C, MvPolynomial.transcendental_supported_X_iff, MvPolynomial.optionEquivLeft_X_none, MvPolynomial.algebraicIndependent_polynomial_aeval_X, MvPolynomial.degreeOf_rename_of_injective, MvPolynomial.degreesLE_add, mapRingHom_comp_algebraMap, MvPolynomial.exists_rename_eq_of_vars_subset_range, MvPolynomial.optionEquivRight_symm_apply, tensorEquiv.invFun_tmul, Algebra.Generators.Hom.aeval_val, Polynomial.ofFinsupp_algebraMap, Algebra.Presentation.comp_aeval_relation_inl, WittVector.mulN_coeff, MvPolynomial.pderiv_sumToIter, MvPolynomial.support_expand_subset, commAlgEquiv_single_single, MvPolynomial.coeff_rename_embDomain, TensorProduct.toIntegralClosure_mvPolynomial_bijective, MvPolynomial.finSuccEquiv_coeff_coeff, MvPolynomial.rename_comp_expand, Algebra.PreSubmersivePresentation.aevalDifferential_toMatrix'_eq_mapMatrix_jacobiMatrix, Algebra.PreSubmersivePresentation.jacobiMatrix_apply, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C', MvPolynomial.rename_esymm, Algebra.PreSubmersivePresentation.ofHasCoeffs_algebra_algebraMap_apply, isLocalHom_algebraMap, lift_apply, Algebra.Generators.toAlgHom_ofComp_surjective, MvPolynomial.bind₁_comp_bind₁, MvPolynomial.commAlgEquiv_C, Algebra.Generators.Hom.algebraMap_toAlgHom', Algebra.FinitePresentation.ker_fg_of_mvPolynomial, Algebra.Generators.cotangentSpaceBasis_repr_tmul, MvPolynomial.aevalTower_X, MvPolynomial.commAlgEquiv_X, MvPolynomial.optionEquivRight_X_some, MvPolynomial.aeval_expand, AlgebraicIndependent.lift_reprField, domCongr_single, MvPolynomial.aeval_algebraMap_apply, Algebra.SubmersivePresentation.linearIndependent_aeval_val_pderiv_relation, MvPolynomial.pderiv_X, Algebra.FiniteType.baseChangeAux_surj, Algebra.Generators.H1Cotangent.δAux_toAlgHom, Subalgebra.mvPolynomial_aeval_coe, IsLocalization.Away.mvPolynomialQuotientEquiv_apply, mapDomainBialgHom_apply, coe_algebraMap, Algebra.Presentation.naive_relation_apply, PolynomialLaw.exists_lift, WittVector.mul_polyOfInterest_aux4, MvPolynomial.rename_eval₂, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some, MvPowerSeries.expand_eq_expand, MvPolynomial.mapAlgEquiv_apply, Polynomial.Bivariate.equivMvPolynomial_symm_X_0, MvPolynomial.algebraTensorAlgEquiv_symm_comp_aeval, MvPolynomial.finitePresentation_universalFactorizationMap, MvPolynomial.mapAlgEquiv_refl, Algebra.FiniteType.iff_quotient_mvPolynomial', MvPolynomial.tensorEquivSum_one_tmul_C, Algebra.Generators.sq_ker_comp_le_ker_compLocalizationAwayAlgHom, MvPolynomial.eval₂Hom_rename, MvPolynomial.sumAlgEquiv_comp_rename_inl, AlgebraicIndependent.aeval_of_algebraicIndependent, MvPolynomial.aeval_bind₁, MvPolynomial.algebraMap_apply, MvPolynomial.killCompl_monomial_eq_zero_of_not_subset, MvPolynomial.exists_fin_rename, MvPolynomial.optionEquivLeft_coeff_coeff, MvPolynomial.IsWeightedHomogeneous.sum_weight_X_mul_pderiv, Matrix.charpoly.optionEquivLeft_symm_univ_isHomogeneous, MvPolynomial.pderiv_def, MvPolynomial.mem_supported, MvPolynomial.renameEquiv_apply, MvPolynomial.rename_esymmAlgHom, finiteType_of_fg, MvPolynomial.aeval_eq_zero, MvPolynomial.eval₂_cast_comp, Algebra.PreSubmersivePresentation.naive_toPresentation, addMonoidAlgebraAlgEquivDirectSum_symm_apply, MvPolynomial.bind₁_C_right, MvPolynomial.rename_zero, MvPolynomial.instIsLocalHomRingHomAlgebraMap, WittVector.bind₁_wittMulN_wittPolynomial, PolynomialLaw.exists_range_φ_eq_of_fg, Algebra.FinitePresentation.mvPolynomial, MvPolynomial.aevalTower_C, MvPolynomial.expand_one_apply, MvPolynomial.map_expand_pow_char, MonomialOrder.degree_smul_le, AnalyticOnNhd.aeval_mvPolynomial, Algebra.Generators.Hom.toAlgHom_X, MvPolynomial.bind₁_rename, wittStructureRat_prop, MvPolynomial.degrees_rename, Algebra.Presentation.comp_relation, Polynomial.Bivariate.equivMvPolynomial_symm_C, Algebra.Generators.instIsScalarTowerRing, MvPowerSeries.aeval_coe, WittVector.IsPoly.poly, finiteType_iff_group_fg, MvPolynomial.finite_universalFactorizationMap, MvPolynomial.rTensorAlgHom_toLinearMap, wittStructureRat_rec, MvPolynomial.expand_eq_C, MvPowerSeries.trunc'_expand, MvPolynomial.universalFactorizationMapPresentation_map, MvPolynomial.coeff_rename_mapDomain, MvPolynomial.algebraTensorAlgEquiv_symm_X, MvPolynomial.expand_injective, MvPolynomial.support_coeff_finSuccEquiv, Algebra.Presentation.aeval_val_relation, MvPolynomial.expand_one, MvPolynomial.esymmAlgHom_fin_surjective, MvPolynomial.expand_inj, MvPolynomial.coeffsIn_mul, instIsPushout, MvPowerSeries.rename_coe, MvPolynomial.mk_eq_eval₂, Algebra.Generators.H1Cotangent.δAux_ofComp, MvPolynomial.killCompl_monomial_mapDomain, MvPolynomial.le_coeffsIn_pow, MvPolynomial.supported_strictMono, instIsPushout', exists_integral_inj_algHom_of_quotient, exists_finite_inj_algHom_of_fg, MvPolynomial.aeval_def, lift_single, Algebra.Generators.toAlgHom_ofComp_rename, mapDomainAlgHom_apply, Algebra.FinitePresentation.iff, wittStructureRat_rec_aux, Polynomial.Bivariate.equivMvPolynomial_symm_X_1, MvPolynomial.supported_mono, MonomialOrder.sPolynomial_decomposition, MvPolynomial.totalDegree_expand, MvPolynomial.algHom_C, lift_symm_apply, wittStructureInt_prop, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, MvPolynomial.mkₐ_eq_aeval, MvPolynomial.derivation_C, MvPolynomial.mem_support_coeff_optionEquivLeft, Polynomial.eval_X_toTupleMvPolynomial_zero_eq, MvPolynomial.dvd_smul_X_iff_exists, MvPolynomial.mem_supported_vars, MvPolynomial.mkDerivation_monomial, Algebra.Generators.Hom.toExtensionHom_toRingHom, Algebra.Generators.comp_localizationAway_ker, MvPolynomial.rename_monomial, MvPolynomial.aeval_toMvPolynomial, MvPolynomial.restrictScalars_restrictSupportIdeal, MvPolynomial.universalFactorizationMapPresentation_relation, MvPolynomial.aevalTower_comp_algebraMap, Algebra.PreSubmersivePresentation.aevalDifferential_single, AlgebraicIndependent.algebraMap_aevalEquiv, MvPolynomial.aeval_id_rename, mapAlgHom_apply, Algebra.adjoin_range_eq_range_aeval, coe_liftNCAlgHom, Algebra.Generators.aeval_val_σ, MvPolynomial.mem_zeroLocus_iff, MvPolynomial.totalDegree_coeff_optionEquivLeft_add_le, MvPolynomial.aeval_eq_constantCoeff_of_vars, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_tmul, lift_of, SymmetricAlgebra.equivMvPolynomial_symm_X, MvPolynomial.expand_bind₁, MvPolynomial.smul_eval, MvPowerSeries.substAlgHom_coe, MvPolynomial.universalFactorizationMapPresentation_algebra_algebraMap, MvPolynomial.coeff_rTensorAlgHom_tmul, MvPolynomial.aeval_zero, MvPolynomial.killCompl_rename_app, MvPolynomial.comp_aeval, MvPolynomial.frobenius_zmod, KaehlerDifferential.mvPolynomialBasis_repr_apply, MvPolynomial.optionEquivLeft_coeff_some_coeff_none, IntermediateField.mem_adjoin_range_iff, DividedPowerAlgebra.mkAlgHom_surjective, WittVector.coeff_frobeniusFun, MvPolynomial.renameEquiv_refl, MvPolynomial.totalDegree_renameEquiv, MvPolynomial.expand_mul, LaurentPolynomial.C_eq_algebraMap, Algebra.Presentation.tensorModelOfHasCoeffsHom_tmul, MvPolynomial.isLocalHom_expand, Polynomial.Bivariate.pderiv_zero_equivMvPolynomial, MvPolynomial.C_mul', MvPolynomial.isEmptyAlgEquiv_apply, DividedPowerAlgebra.submodule_span_prod_dp_eq_top, Polynomial.Bivariate.equivMvPolynomial_X, MvPolynomial.pderiv_C_mul, Module.Basis.symmetricAlgebra_repr_apply, MonomialOrder.degree_smul_of_isRegular, AlgebraicClosure.toSplittingField_coeff, MvPolynomial.natDegree_optionEquivLeft, mapDomain_algebraMap, Algebra.Generators.self_algebra_smul, exists_finset_adjoin_eq_top, MvPolynomial.restrictSupport_nsmul, Algebra.Generators.toKaehler_tmul_D, MvPolynomial.mem_support_finSuccEquiv, algebraicIndependent_iff_injective_aeval, MvPolynomial.aeval_map_algebraMap, Algebra.Generators.Hom.toAlgHom_C, MvPolynomial.rename_comp_toMvPolynomial, MvPolynomial.finSuccEquiv_comp_C_eq_C, MvPolynomial.coeToMvPowerSeries.algHom_apply, AlgebraicIndependent.liftAlgHom_comp_reprField, DividedPowerAlgebra.algHom_ext_iff, MvPolynomial.rename_rightInverse, MvPolynomial.finSuccEquiv_eq, SymmetricAlgebra.equivMvPolynomial_ι_apply, lift_unique', LinearMap.polyCharpoly_eq_of_basis, MvPolynomial.ker_eval₂Hom_universalFactorizationMap, MvPolynomial.bind₁_comp_rename, LinearMap.polyCharpolyAux_map_aeval, MvPolynomial.image_support_finSuccEquiv, MvPolynomial.pderiv_monomial_single, MvPolynomial.eval₂_rename, AlgebraicIndependent.aeval_repr, MvPolynomial.support_expand, tensorEquiv_tmul, Polynomial.toFinsupp_algebraMap, LaurentPolynomial.invert_symm, Polynomial.Bivariate.equivMvPolynomial_C_X, MvPolynomial.IsSymmetric.rename, MvPolynomial.IsHomogeneous.aeval, symm_commAlgEquiv, MvPolynomial.aeval_bind₂, MvPolynomial.rename_bind₁, MvPolynomial.pderiv_X_of_ne, MvPolynomial.renameSymmetricSubalgebra_symm_apply_coe, Algebra.Generators.Hom.toAlgHom_comp_apply, MvPolynomial.degree_finSuccEquiv, Polynomial.Bivariate.Polynomial.Bivariate.pderiv_zero_equivMvPolynomial, MvPolynomial.nonempty_support_optionEquivLeft, MvPolynomial.pderiv_monomial, bind₁_rename_expand_wittPolynomial, Algebra.adjoin_eq_range, MvPolynomial.mapAlgEquiv_symm, Algebra.Generators.toComp_toAlgHom_monomial, MvPolynomial.rename_injective, MvPolynomial.monomial_mem_homogeneousSubmodule_pow_degree, Algebra.SubmersivePresentation.aeval_jacobianOfHasCoeffs, mapDomainAlgHom_comp, tensorEquiv_symm_single, lift_of', MvPolynomial.coe_smul, MvPolynomial.killCompl_map, Algebra.FiniteType.iff_quotient_mvPolynomial, MvPolynomial.aeval_eq_bind₁, MvPolynomial.support_optionEquivLeft, MvPolynomial.dvd_X_iff_exists, MvPolynomial.finSuccEquiv_X_succ, MvPolynomial.aeval_ofNat, mem_adjoin_support, Algebra.Presentation.aeval_val_relationOfHasCoeffs, MvPolynomial.expand_comp_bind₁, MvPolynomial.mapAlgEquiv_trans, Algebra.SubmersivePresentation.aeval_invJacobianOfHasCoeffs, MvPolynomial.ker_mapAlgHom, MvPolynomial.aeval_injective_iff_of_isEmpty, Polynomial.toFinsuppIsoAlg_symm_apply_toFinsupp, Algebra.Generators.ofComp_kerCompPreimage, MvPolynomial.X_mem_supported, MvPolynomial.esymmAlgHom_fin_injective, MvPolynomial.aeval_comp_bind₁, domCongr_support, MvPolynomial.eval₂_const_pUnitAlgEquiv, Algebra.Generators.repr_CotangentSpaceMap, DividedPowerAlgebra.dp_sum_smul, MvPolynomial.pderiv_pow, MvPolynomial.aeval_esymm_eq_multiset_esymm, MvPolynomial.supported_le_supported_iff, MvPolynomial.eval_rename, StandardEtalePresentation.toPresentation_σ', witt_structure_prop, MvPolynomial.coe_eval₂AlgHom, LinearMap.toMvPolynomial_comp, MvPolynomial.IsHomogeneous.rename_isHomogeneous_iff, MvPolynomial.vars_bind₁, WittVector.bind₁_verschiebungPoly_wittPolynomial, Algebra.Presentation.instFinitePresentationModelOfHasCoeffsOfFinite, lift_mapRingHom_algebraMap, MvPolynomial.optionEquivRight_apply, MvPolynomial.finSuccEquiv_apply, MvPolynomial.tensorEquivSum_X_tmul_X, curryAlgEquiv_symm_single, domCongr_symm, MvPolynomial.comp_aeval_apply, Algebra.Presentation.relation_comp_localizationAway_inl, WittVector.coeff_select, MvPolynomial.aeval_unique, DividedPowerAlgebra.dp_def, MvPolynomial.coeff_rTensorAlgHom_monomial_tmul, MvPolynomial.bind₁_bind₁, MvPolynomial.algebraTensorAlgEquiv_symm_map, MvPolynomial.rename_polynomial_aeval_X, MvPolynomial.coeff_expand_of_not_dvd, Algebra.Generators.Hom.equivAlgHom_symm_apply_val, MvPolynomial.tensorEquivSum_C_tmul_one, MvPolynomial.map_iterateFrobenius_expand, Polynomial.toMvPolynomial_X, MvPolynomial.sumAlgEquiv_apply, algHom_ext_iff, Algebra.Generators.ker_comp_eq_sup, Algebra.Generators.ofComp_toAlgHom_monomial_sumElim, MvPolynomial.exists_finset_rename₂, LaurentPolynomial.invert_apply, MvPolynomial.algebraMap_eq, MvPolynomial.algebraicIndependent_X, MvPolynomial.eval_toMvPolynomial, Algebra.Presentation.algebraTensorAlgEquiv_symm_relation, Algebra.Generators.aeval_val_eq_zero, MvPolynomial.coeffsIn_pow, MvPolynomial.esymmAlgHom_apply, BoundedContinuousFunction.star_mem_range_charAlgHom, MvPolynomial.aeval_eq_eval₂Hom, MvPolynomial.rename_prod_mk_eval₂, AlgebraicIndependent.aevalEquivField_apply_coe, MvPolynomial.IsSymmetric.smul, MvPolynomial.aeval_C, IsTranscendenceBasis.mvPolynomial, MvPolynomial.toMvPowerSeries_pUnitAlgEquiv, MvPolynomial.transcendental_polynomial_aeval_X, MvPolynomial.pderiv_map, MvPolynomial.aeval_comp_expand, Algebra.Generators.naive_σ, AlgebraicIndependent.aevalEquiv_apply_coe, MvPolynomial.rename_C, StandardEtalePresentation.aeval_val_equivMvPolynomial, MvPolynomial.aevalTower_comp_toAlgHom, MvPolynomial.restrictSupport_add, MvPolynomial.IsHomogeneous.rename_isHomogeneous, WittVector.polyOfInterest_vars_eq, MvPolynomial.pderiv_inr_universalFactorizationMap_X, MvPolynomial.sumAlgEquiv_symm_apply, MvPolynomial.eval₂_pUnitAlgEquiv_symm, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_symm_tmul, Algebra.Generators.ker_eq_ker_aeval_val, MvPolynomial.instIsPushout_1, mapDomainBialgHom_comp, Algebra.Generators.ker_ofAlgHom, scalarTensorEquiv_symm_single, MvPolynomial.supported_empty, Algebra.Generators.toExtension_algebra₁, KaehlerDifferential.mvPolynomialBasis_repr_D, MvPolynomial.pderiv_eq_zero_of_notMem_vars, MvPolynomial.aeval_C_comp_left, MvPolynomial.transcendental_X, MvPolynomial.degrees_rename_of_injective, PolynomialLaw.range_φ, Polynomial.toFinsuppIsoAlg_apply, finiteType_iff_fg, MvPolynomial.mapAlgHom_apply, Algebra.Generators.cotangentRestrict_mk, MvPolynomial.optionEquivLeft_monomial, MvPolynomial.rename_eq_zero_iff_of_injective, Algebra.SubmersivePresentation.ofSubsingleton_algebra_smul, KaehlerDifferential.mvPolynomialBasis_repr_comp_D, WittVector.bind₁_onePoly_wittPolynomial, StandardEtalePresentation.toPresentation_algebra_algebraMap_apply, MvPolynomial.optionEquivLeft_symm_apply, MvPolynomial.algebraTensorAlgEquiv_tmul, MvPolynomial.mem_support_coeff_finSuccEquiv, Algebra.Generators.aeval_val_σ', Algebra.Generators.Hom.toAlgHom_id, Algebra.Generators.Hom.comp_val, MvPolynomial.instIsPushout, MvPolynomial.comap_apply, MvPolynomial.vars_rename, WittVector.bind₁_zero_wittPolynomial, IsTranscendenceBasis.mvPolynomial', StandardEtalePresentation.toPresentation_val, MvPolynomial.rename_comp_bind₁, MvPolynomial.aeval_id_eq_join₁, MvPolynomial.rename_X, MvPolynomial.pUnitAlgEquiv_monomial, Algebra.Generators.compLocalizationAwayAlgHom_relation_eq_zero, Algebra.mvPolynomial, MvPolynomial.comap_id_apply, MvPolynomial.aeval_one_tmul, domCongr_apply, MvPolynomial.smul_eq_C_mul, MvPolynomial.finSuccEquiv_rename_finSuccEquiv, MvPolynomial.rename_expand, MvPolynomial.homogeneousSubmodule_one_pow, MvPolynomial.universalFactorizationMapPresentation_algebra_smul, MonomialOrder.degree_smul, Algebra.FiniteType.instMvPolynomialOfFinite, MvPolynomial.IsHomogeneous.sum_X_mul_pderiv, MvPolynomial.derivation_C_mul, MvPolynomial.aeval_sumElim_pderiv_inl, AnalyticAt.aeval_mvPolynomial, MvPolynomial.tensorEquivSum_one_tmul_X, support_gen_of_gen, MvPolynomial.supported_univ, MvPolynomial.isSymmetric_rename, MvPolynomial.universalFactorizationMap_freeMonic, Algebra.Generators.Hom.toAlgHom_monomial, MvPolynomial.universalFactorizationMapPresentation_val, MvPolynomial.rename_comp_rename, MvPolynomial.coe_expand, MvPolynomial.aeval_sumElim, MvPolynomial.universalFactorizationMapPresentation_σ', MvPolynomial.aeval_comp_rename, KaehlerDifferential.mvPolynomialBasis_repr_symm_single, MvPolynomial.mem_symmetricSubalgebra, decomposeAux_single, MvPolynomial.support_rename_killCompl_subset, MvPolynomial.eval₂_rename_prod_mk, AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe, MvPolynomial.coeff_linearCombination_X_pow_of_fintype, MvPolynomial.mapAlgHom_coe_ringHom, bind₁_wittPolynomial_xInTermsOfW, Algebra.FinitePresentation.out, MvPolynomial.rename_leftInverse, Algebra.FiniteType.iff_quotient_mvPolynomial'', MvPolynomial.esymmAlgHom_fin_bijective, MvPolynomial.esymmAlgEquiv_apply, MvPolynomial.eval₂AlgHom_X, MvPolynomial.mem_vanishingIdeal_iff, MvPolynomial.mem_vanishingIdeal_singleton_iff, MvPolynomial.expand_zmod, MvPolynomial.aeval_zero', MvPolynomial.weightedTotalDegree_rename_of_injective, MvPolynomial.range_mapAlgHom, decomposeAux_eq_decompose, MvPolynomial.rename_toMvPolynomial, MvPolynomial.aeval_rename, WittVector.bind₁_frobeniusPolyRat_wittPolynomial, MvPolynomial.optionEquivLeft_symm_C_X, WittVector.aeval_verschiebungPoly, MvPolynomial.eval₂Hom_bind₁, MvPolynomial.finSuccEquiv_X_zero, MvPolynomial.degreeOf_eq_natDegree, symm_mapAlgEquiv, MvPolynomial.bind₁_X_right, MvPolynomial.coeff_rename_eq_zero, lift_unique, MvPolynomial.eval₂Hom_C_left, MvPolynomial.transcendental_supported_polynomial_aeval_X_iff, MvPolynomial.aeval_monomial, lift_def, StandardEtalePresentation.toPresentation_relation, DividedPowerAlgebra.dp_smul, Polynomial.toMvPolynomial_injective, singleZeroAlgHom_apply, Algebra.PreSubmersivePresentation.ofHasCoeffs_val, Algebra.Generators.self_algebra_algebraMap, MvPolynomial.pderiv_X_self, Polynomial.coe_toLaurentAlg, WittVector.mul_polyOfInterest_aux3, MvPolynomial.pderiv_C, MvPolynomial.universalFactorizationMapPresentation_jacobiMatrix, Algebra.PreSubmersivePresentation.ofHasCoeffs_algebra_smul, scalarTensorEquiv_tmul, MvRatFunc.rank_eq_max_lift, MvPolynomial.aeval_prod, MvPolynomial.homogeneousSubmodule_mul, Matrix.toMvPolynomial_mul, Polynomial.Bivariate.pderiv_one_equivMvPolynomial, MvPolynomial.exists_restrict_to_vars, wittStructureInt_rename, MvPolynomial.algebraTensorAlgEquiv_symm_monomial, LieAlgebra.LoopAlgebra.twoCocycleOfBilinear_coe, MvPolynomial.aevalTower_algebraMap, MvPolynomial.optionEquivLeft_elim_eval, MvPolynomial.optionEquivLeft_symm_X, SymmetricAlgebra.IsSymmetricAlgebra.mvPolynomial, MvPolynomial.renameEquiv_symm, MvPolynomial.eval_expand, MvPolynomial.aeval_comp_toMvPolynomial, MvPolynomial.supportedEquivMvPolynomial_symm_C, MvPolynomial.derivation_eqOn_supported, Polynomial.toLaurentAlg_apply, MvPolynomial.killCompl_monomial_eq_monomial_comapDomain_of_subset, MvPolynomial.eval₂AlgHom_apply, MvPolynomial.tensorEquivSum_X_tmul_one, MvPolynomial.expand_mul_eq_comp, MvPolynomial.eval₂_pUnitAlgEquiv, MvPolynomial.killCompl_monomial, MvPolynomial.supported_eq_range_rename, MvPolynomial.trdeg_of_isDomain, LaurentPolynomial.toLaurent_reverse, MvPolynomial.rename_hsymm, MonomialOrder.sPolynomial_decomposition', addMonoidAlgebraAlgEquivDirectSum_apply, MvPolynomial.transcendental_supported_X, MvPolynomial.aeval_natDegree_le, MvPolynomial.optionEquivLeft_symm_C_C, support_gen_of_gen', C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum, Algebra.Generators.Hom.algebraMap_toAlgHom, WittVector.coeff_frobenius, Algebra.Generators.comp_σ, MvPolynomial.tensorEquivSum_C_tmul_C, MvPolynomial.IsHomogeneous.finSuccEquiv_coeff_isHomogeneous, Algebra.Presentation.instFinitePresentationQuotientOfFinite, DividedPowerAlgebra.mkRingHom_C, MvPowerSeries.subst_coe, isLocalHom_singleZeroAlgHom, MvPolynomial.mapEquivMonic_symm_map_algebraMap, MvPolynomial.coe_aeval_eq_eval, LaurentPolynomial.invert_C, exists_integral_inj_algHom_of_fg, curryAlgEquiv_single, Polynomial.Bivariate.equivMvPolynomial_C_C, DividedPowerAlgebra.mkAlgHom_C, Algebra.Generators.ker_naive, instFreeMvPolynomialKaehlerDifferential, MvPolynomial.hom_bind₁, MvPolynomial.coeff_expand_zero, Algebra.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolynomial, Matrix.mvPolynomialX_mapMatrix_aeval, MvPolynomial.supported_eq_vars_subset, DividedPowerAlgebra.embed_def, Polynomial.aeval_homogenize_of_eq_one, LaurentPolynomial.invert_comp_C, MvPolynomial.rename_eq, MvPolynomial.totalDegree_coeff_optionEquivLeft_le, MvPolynomial.derivation_ext_iff, freeAlgebra_lift_of_surjective_of_closure, mapAlgEquiv_apply, MvPolynomial.eval₂Hom_smul, MvPolynomial.mapEquivMonic_symm_map, MvPolynomial.IsHomogeneous.pderiv, Algebra.SubmersivePresentation.basisDeriv_apply, MvPolynomial.bind₁_monomial, MonomialOrder.degree_smul_of_mem_nonZeroDivisors, Algebra.Presentation.mem_ker_naive, MvPolynomial.C_eq_smul_one, MvPolynomial.coeff_killCompl, MvPolynomial.esymmAlgHom_surjective, MvPolynomial.aevalTower_ofNat, MvPolynomial.killCompl_monomial_eq_zero_of_notMem_range, MvPolynomial.esymmAlgEquiv_symm_apply, instIsPushoutFractionRingMvPolynomial_1, MvPolynomial.rename_surjective, MvPolynomial.eval₂Hom_comp_expand, Polynomial.toMvPolynomial_C, Algebra.Generators.Hom.equivAlgHom_apply_coe, MvPolynomial.universalFactorizationMapPresentation_jacobian, Polynomial.UniversalFactorizationRing.fromTensor_comp_universalFactorizationMap, LaurentPolynomial.invert_T, MvPolynomial.esymmAlgHom_injective, MvPolynomial.commAlgEquiv_C_X, MvPolynomial.expand_zero_apply, Polynomial.UniversalFactorizationRing.fromTensor_comp_universalFactorizationMap', vaddAssocClass_addMonoidAlgebra, MvPolynomial.renameSymmetricSubalgebra_apply_coe, Algebra.FinitePresentation.iff_quotient_mvPolynomial', MvPolynomial.coe_mapEquivMonic_comp, MvPolynomial.transcendental_supported_polynomial_aeval_X, instIsPushoutFractionRingMvPolynomial, LaurentPolynomial.involutive_invert, MvPolynomial.eval_polynomial_eval_finSuccEquiv, MvPolynomial.constantCoeff_comp_algebraMap, MvPolynomial.pderiv_inl_universalFactorizationMap_X, MvPolynomial.rename_id, Algebra.Presentation.tensorModelOfHasCoeffsInv_aeval_val, MvPolynomial.rTensorAlgHom_apply_eq
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