DirectSum 📖 | CompOp | 366 mathmath: DirectSum.decompose_sub, DirectSum.IsInternal.ofBijective_coeLinearMap_same, TensorAlgebra.ofDirectSum_of_tprod, DirectSum.mulHom_of_of, DirectSum.mker_map, addMonoidAlgebraEquivDirectSum_apply, DirectSum.bracket_apply, DirectSum.Decomposition.decompose'_eq, MvPolynomial.DirectSum.coeLinearMap_eq_dfinsuppSum, ExteriorAlgebra.GradedAlgebra.liftι_eq, DirectSum.Gmodule.smulAddMonoidHom_apply_of_of, DirectSum.component.of, DirectSum.coe_toModule_eq_coe_toAddMonoid, DirectSum.decompose_of_mem_same, DirectSum.lmap_id, qExpansionRingHom_apply, DirectSum.mrange_map, PiTensorProduct.ofDirectSumEquiv_tprod_lof, Module.Presentation.directSum_var, DirectSum.decomposeAlgEquiv_symm_apply, ModuleCat.ι_coprodIsoDirectSum_hom_apply, DirectSum.of_smul, DirectSum.fromAddMonoid_of_apply, DirectSum.lie_module_bracket_apply, DirectSum.instIsCentralScalar, TensorProduct.gradedComm_tmul_one, DirectSum.sub_apply, TensorAlgebra.toDirectSum_tensorPower_tprod, mul_apply_eq_zero, DirectSum.toAddMonoid.unique, LinearAlgebra.FreeProduct.mul_injections, AddCommGroup.equiv_directSum_zmod_of_finite', Representation.directSum_apply, TensorProduct.gradedMul_assoc, AddChar.directSum_apply, TensorProduct.directSum_lof_tmul_lof, DirectSum.lequivCongrLeft_apply, DirectSum.lmap_apply, DirectSum.toAddMonoidAlgebra_sub, DirectSum.lmap_comp, LinearMap.IsSymmetric.directSum_decompose_apply, DirectSum.coeAddMonoidHom_eq_dfinsuppSum, DirectSum.fromAddMonoid_of, rank_directSum, TensorProduct.coe_directSumRight', DirectSum.mk_smul, DirectSum.mk_injective, DirectSum.decompose_eq_mul_idempotent, Module.equiv_directSum_of_isTorsion, DirectSum.decompose_of_mem, DirectSum.coe_of_mul_apply_aux, DirectSum.decompose_symm_sub, DirectSum.Gmodule.of_smul_of, TensorProduct.gradedMul_def, DirectSum.sum_univ_of, MultilinearMap.fromDirectSumEquiv_symm_apply, DirectSum.lie_of_of_ne, GradedTensorProduct.auxEquiv_one, Module.DirectLimit.quotMk_of, IsBaseChange.directSumPow, DirectSum.lie_of, TensorProduct.gradedComm_algebraMap_tmul, TensorAlgebra.toDirectSum_ofDirectSum, DirectSum.instSMulCommClass, IsBaseChange.directSum, DirectSum.support_of, DirectSum.instLieModule, DirectSum.algebraMap_toAddMonoid_hom, AddMonoidAlgebra.toDirectSum_single, qExpansion_of_mul, DirectSum.ker_lmap, AdicCompletion.sumInv_apply, Module.Presentation.directSum_relation, DirectSum.coeLinearMap_of, AdicCompletion.sum_lof, DirectSum.coeLinearMap_eq_dfinsuppSum, ExteriorAlgebra.GradedAlgebra.ι_sq_zero, DirectSum.coe_of_mul_apply_add, AddMonoidAlgebra.decomposeAux_coe, DirectSum.ofPow, DirectSum.of_zero_smul, DirectSum.coe_congr_addEquiv, DirectSum.coe_decompose_mul_add_of_left_mem, LinearAlgebra.FreeProduct.ι_apply, PiTensorProduct.ofDirectSumEquiv_symm_lof_tprod, DirectSum.toAddMonoidAlgebra_one, DirectSum.one_def, DirectSum.decompose_symm_neg, TensorProduct.directSumRight_comp_rTensor, DirectSum.addEquivProdDirectSum_symm_apply_toFun, TensorAlgebra.equivDirectSum_apply, DirectSum.of_mul_of, GradedTensorProduct.auxEquiv_symm_one, DirectSum.sigmaLcurry_apply, GradedTensorProduct.auxEquiv_comm, DirectSum.coe_decompose_mul_of_left_mem_of_le, DirectSum.coe_mul_of_apply_of_not_le, DirectSum.decompose_symm_one, DirectSum.coe_decompose_mul_of_left_mem, AddCommGroup.equiv_free_prod_directSum_zmod, DirectSum.congr_linearEquiv_toAddEquiv, addMonoidAlgebraEquivDirectSum_symm_apply, AddMonoidAlgebra.toDirectSum_mul, DirectSum.toAlgebra_apply, TensorProduct.gradedComm_algebraMap, GradedAlgebra.proj_recompose, ModuleCat.lof_coprodIsoDirectSum_inv, DirectSum.algebraMap_apply, TensorProduct.gradedComm_tmul_of_zero, Module.Relations.Solution.directSum_var, Module.Presentation.directSum_G, DirectSum.lof_eq_of, DirectSum.map_injective, DirectSum.of_zero_mul, DirectSum.lmap_eq_map, DirectSum.coe_congr_linearEquiv, AddMonoidAlgebra.toDirectSum_natCast, AddCommGroup.equiv_directSum_zmod_of_finite, TensorProduct.directSumLeft_tmul_lof, DirectSum.lieAlgebraComponent_apply, AdicCompletion.sumInv_comp_sum, DirectSum.coe_mul_apply, DirectSum.mk_apply_of_notMem, TensorProduct.algebraMap_gradedMul, MvPolynomial.DirectSum.coeAddMonoidHom_eq_support_sum, AddMonoidAlgebra.toDirectSum_zero, DirectSum.decompose_mul_add_left, DirectSum.congr_linearEquiv_toLinearMap, addMonoidAlgebraAlgEquivDirectSum_symm_apply, DirectSum.IsInternal.ofBijective_coeLinearMap_of_mem_ne, TensorProduct.gradedComm_one, DirectSum.toAddMonoidAlgebra_mul, AddMonoidAlgebra.toDirectSum_add, DirectSum.linearEquivFunOnFintype_lof, DirectSum.coeAlgHom_of, TensorProduct.gradedComm_symm, CliffordAlgebra.GradedAlgebra.ι_apply, GradedTensorProduct.auxEquiv_mul, DirectSum.congrLinearEquiv_toLinearMap, ModuleCat.lof_coprodIsoDirectSum_inv_apply, DirectSum.decompose_symm_algebraMap, DirectSum.toAddMonoidAlgebra_natCast, DirectSum.lieAlgebraOf_apply, DirectSum.map_of, DirectSum.decompose_symm_add, DirectSum.lmap_surjective, DirectSum.coe_decompose_mul_of_right_mem_of_not_le, DirectSum.coe_decompose_mul_of_left_mem_of_not_le, DirectSum.lmap_lof, DirectSum.addEquivProdDirectSum_apply, LinearAlgebra.FreeProduct.identify_one, DirectSum.coe_of_mul_apply_of_not_le, TensorAlgebra.ofDirectSum_toDirectSum, DirectSum.linearMap_ext_iff, DirectSum.addEquivProdDirectSum_symm_apply_support', AddMonoidAlgebra.toDirectSum_pow, DirectSum.mk_apply_of_mem, TensorProduct.gradedMul_one, DirectSum.ext_component_iff, DirectSum.decompose_algebraMap, Module.Relations.Solution.IsPresentation.directSum, LinearAlgebra.FreeProduct.ι_def, DirectSum.ker_map, Module.Finite.instDirectSum, GradedTensorProduct.mulHom_apply, MultilinearMap.fromDirectSumEquiv_lof, TensorProduct.directSumRight_tmul_lof, DirectSum.algHom_ext'_iff, AddMonoidAlgebra.GradesBy.decompose_single, DirectSum.IsInternal.ofBijective_coeLinearMap_of_mem, MvPolynomial.weightedHomogeneousComponent_directSum, DirectSum.range_map, GradedRing.mem_support_iff, DirectSum.coeAddMonoidHom_of, TensorProduct.directSumLeft_symm_lof_tmul, DirectSum.component.lof_self, DirectSum.of_injective, DirectSum.coe_decompose_mul_of_right_mem, DirectSum.toSemiring_apply, DirectSum.toAddMonoidAlgebra_zero, AdicCompletion.sum_of, DirectSum.mulHom_apply, DirectSum.coe_mul_of_apply_of_mem_zero, DirectSum.of_eq_same, DirectSum.single_eq_lof, DirectSum.sigmaCurry_apply, DirectSum.coeRingHom_of, MultilinearMap.fromDirectSumEquiv_apply, finsuppLEquivDirectSum_single, GradedTensorProduct.auxEquiv_tmul, TensorAlgebra.toDirectSum_comp_ofDirectSum, DirectSum.decomposeLinearEquiv_apply, TensorProduct.gradedComm_of_zero_tmul, ModuleCat.ι_coprodIsoDirectSum_hom, AddMonoidAlgebra.toDirectSum_intCast, DirectSum.decomposeLinearEquiv_symm_comp_lof, DirectSum.coe_decompose_mul_add_of_right_mem, DirectSum.coe_mul_of_apply_aux, TensorProduct.directSumLeft_tmul, DirectSum.lie_of_same, DirectSum.decompose_zero, MvPolynomial.DirectSum.coeLinearMap_eq_finsum, TensorAlgebra.GradedAlgebra.ι_apply, DirectSum.toSemiring_of, DirectSum.decomposeLinearEquiv_symm_apply, DirectSum.toAddMonoidAlgebra_of, LinearAlgebra.FreeProduct.rel_id, Module.equiv_free_prod_directSum, DirectSum.decomposeAlgEquiv_apply, AddMonoidAlgebra.grade.decompose_single, TensorProduct.directSum_symm_lof_tmul, DirectSum.decompose_of_mem_ne, Submodule.IsHomogeneous.mem_iff, DirectSum.addHom_ext'_iff, DirectSum.toModule_lof, MultilinearMap.directSum_ext_iff, TensorProduct.directSumRight_tmul, TensorProduct.gradedComm_tmul_algebraMap, DirectSum.SetLike.IsHomogeneous.mem_iff, DirectSum.of_zero_pow, DirectSum.coeFnAddMonoidHom_apply, MvPolynomial.weightedDecomposition.decompose'_eq, DirectSum.of_natCast, DirectSum.sigmaLuncurry_apply, DirectSum.decompose_symm_mul, DirectSum.coe_mul_of_apply_add, finsuppLEquivDirectSum_apply, DirectSum.lof_apply, DirectSum.map_apply, DirectSum.ringHom_ext'_iff, DirectSum.map_comp, DirectSum.apply_eq_component, DirectSum.coe_of_mul_apply_of_le, DirectSum.support_of_subset, DirectSum.coe_mul_of_apply_of_le, DirectSum.coe_of_mul_apply_of_mem_zero, DirectSum.toAddMonoidAlgebra_intCast, DirectSum.equivCongrLeft_apply, TensorProduct.directSumRight'_restrict, DirectSum.of_apply, DirectSum.toAddMonoidAlgebra_add, DirectSum.of_intCast, DirectSum.mul_eq_sum_support_ghas_mul, Module.finrank_directSum, AddChar.directSum_injective, DirectSum.coeFnLinearMap_apply, AddMonoidAlgebra.toDirectSum_sub, TensorAlgebra.equivDirectSum_symm_apply, TensorProduct.gradedMul_algebraMap, AdicCompletion.sumEquivOfFintype_apply, DirectSum.liftRingHom_symm_apply_coe, Module.Flat.directSum, TensorProduct.gradedCommAux_comp_gradedCommAux, HahnEmbedding.Seed.hahnCoeff_apply, DirectSum.range_lmap, DirectSum.coe_mul_of_apply, DirectSum.mul_eq_dfinsuppSum, TensorProduct.tmul_of_gradedMul_of_tmul, DirectSum.coe_mul_apply_eq_dfinsuppSum, GradedAlgebra.proj_apply, TensorProduct.gradedComm_one_tmul, DirectSum.decomposeAddEquiv_symm_apply, GradedRing.projZeroRingHom_apply, DirectSum.of_eq_of_gradedMonoid_eq, DirectSum.support_smul, DirectSum.decompose_symm_zero, DirectSum.ofList_dProd, DirectSum.decomposeAddEquiv_apply, DirectSum.congrLinearEquiv_toAddEquiv, AddMonoidAlgebra.toDirectSum_neg, DirectSum.smul_apply, DirectSum.Decomposition.left_inv, DirectSum.support_zero, DirectSum.IsInternal.ofBijective_coeLinearMap_of_ne, DirectSum.coe_mul_apply_eq_sum_antidiagonal, DirectSum.decompose_mul, Submodule.iSup_eq_toSubmodule_range, DirectSum.Decomposition.right_inv, TensorProduct.gradedCommAux_lof_tmul, DirectSum.decompose_coe, DirectSum.sigmaUncurry_apply, AddMonoidAlgebra.decomposeAux_single, AdicCompletion.component_sumInv, DirectSum.decompose_one, DirectSum.linearEquivFunOnFintype_symm_single, LinearAlgebra.FreeProduct.lift_apply, DirectSum.decompose_mul_add_right, DirectSum.list_prod_ofFn_of_eq_dProd, Module.Presentation.directSum_R, DirectSum.toSemiring_coe_addMonoidHom, addMonoidAlgebraAddEquivDirectSum_symm_apply, DirectSum.toAddMonoidAlgebra_pow, DirectSum.coe_of_apply, AddMonoidAlgebra.decomposeAux_eq_decompose, addMonoidAlgebraRingEquivDirectSum_apply, DirectSum.coe_congrAddEquiv, DirectSum.liftRingHom_apply, addMonoidAlgebraRingEquivDirectSum_symm_apply, CliffordAlgebra.GradedAlgebra.lift_ι_eq, TensorAlgebra.toDirectSum_ι, DirectSum.lmap_of, DirectSum.coe_decompose_mul_of_left_mem_zero, addMonoidAlgebraAddEquivDirectSum_apply, DirectSum.coe_decompose_mul_of_right_mem_of_le, DirectSum.sum_support_decompose, DirectSum.lmap_injective, PiTensorProduct.ofDirectSumEquiv_tprod_apply, DirectSum.toAddMonoidAlgebra_neg, DirectSum.coe_decompose_mul_of_right_mem_zero, DirectSum.toModule.unique, TensorProduct.one_gradedMul, DirectSum.AddSubmonoidClass.IsHomogeneous.mem_iff, Module.FaithfullyFlat.directSum, TensorAlgebra.ofDirectSum_comp_toDirectSum, GradedAlgebra.mem_support_iff, lmap_finsuppLEquivDirectSum_eq, DirectSum.of_zero_one, DirectSum.decompose_symm_of, ExteriorAlgebra.GradedAlgebra.ι_apply, LinearAlgebra.FreeProduct.lof_map_one, DirectSum.sum_support_of, CliffordAlgebra.GradedAlgebra.ι_sq_scalar, TensorProduct.gradedComm_of_tmul_of, addMonoidAlgebraAlgEquivDirectSum_apply, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec.image_basicOpen_eq_basicOpen, DirectSum.toAddMonoid_injective, DirectSum.decompose_neg, qExpansion_of_pow, DirectSum.toAddMonoid_of, DirectSum.of_zero_ofNat, AdicCompletion.sumEquivOfFintype_symm_apply, Module.torsion_by_prime_power_decomposition, DirectSum.decompose_symm_sum, DirectSum.map_eq_iff, DirectSum.decompose_add, DirectSum.toLieAlgebra_apply, DirectSum.add_apply, DirectSum.decompose_sum, TensorProduct.gradedComm_gradedMul, DirectSum.toAddMonoidHom_lmap, Module.Flat.directSum_iff, DirectSum.instIsScalarTower, TensorProduct.directSumRight_symm_lof_tmul, DirectSum.coe_of_mul_apply, DirectSum.decompose_smul, DirectSum.lmap_eq_iff, AddMonoidAlgebra.toDirectSum_one, DirectSum.range_coeLinearMap, DirectSum.lequivProdDirectSum_symm_apply, DirectSum.Gmodule.smul_def, GradedRing.proj_apply, DirectSum.linearEquivFunOnFintype_symm_coe, DirectSum.linearEquivFunOnFintype_apply, OrthogonalFamily.projection_directSum_coeAddHom, GradedRing.proj_recompose, DirectSum.zero_apply, finsuppLEquivDirectSum_symm_lof, AdicCompletion.sum_comp_sumInv, Ideal.IsHomogeneous.mem_iff, DirectSum.map_surjective, MvPolynomial.decomposition.decompose'_eq, DirectSum.coe_congrLinearEquiv, DirectSum.lequivProdDirectSum_apply, DirectSum.map_id, Module.Free.directSum, DirectSum.of_eq_of_ne
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