Documentation Verification Report

Basic

πŸ“ Source: Mathlib/RingTheory/PowerSeries/Basic.lean

Statistics

MetricCount
DefinitionscoeToPowerSeries, algHom, ringHom, toPowerSeries, C, X, algebraPolynomial, algebraPolynomial', algebraPowerSeries, coeff, constantCoeff, evalNegHom, instAddCommGroup, instAddCommMonoid, instAddGroup, instAddMonoid, instAlgebra, instCommRing, instCommSemiring, instInhabited, instModule, instRing, instSemiring, instZero, map, mapAlgHom, mk, monomial, rescale, toSubring, «term_⟦X⟧»
31
TheoremstoMvPowerSeries_pUnitAlgEquiv, algHom_apply, ringHom_apply, coe_C, coe_X, coe_add, coe_def, coe_eq_one_iff, coe_eq_zero_iff, coe_inj, coe_injective, coe_monomial, coe_mul, coe_neg, coe_one, coe_pow, coe_smul, coe_sub, coe_zero, coeff_coe, constantCoeff_coe, evalβ‚‚_C_X_eq_coe, pUnitAlgEquiv_symm_toPowerSeries, polynomial_map_coe, C_eq_algebraMap, C_injective, X_dvd_iff, X_eq, X_mul, X_mul_cancel, X_mul_inj, X_mul_injective, X_ne_zero, X_pow_dvd_iff, X_pow_eq, X_pow_mul, X_pow_mul_cancel, X_pow_mul_inj, X_pow_mul_injective, algebraMap_apply, algebraMap_apply', algebraMap_apply'', algebraMap_eq, coeff_C, coeff_C_mul, coeff_C_mul_X_pow, coeff_X, coeff_X_pow, coeff_X_pow_mul, coeff_X_pow_mul', coeff_X_pow_self, coeff_comp_monomial, coeff_def, coeff_map, coeff_mk, coeff_monomial, coeff_monomial_same, coeff_mul, coeff_mul_C, coeff_mul_X_pow, coeff_mul_X_pow', coeff_ne_zero_C, coeff_one, coeff_one_X, coeff_one_mul, coeff_one_pow, coeff_pow, coeff_prod, coeff_rescale, coeff_smul, coeff_succ_C, coeff_succ_X_mul, coeff_succ_mul_X, coeff_toSubring, coeff_zero_C, coeff_zero_X, coeff_zero_X_mul, coeff_zero_eq_constantCoeff, coeff_zero_eq_constantCoeff_apply, coeff_zero_mul_X, coeff_zero_one, commute_X, commute_X_pow, constantCoeff_C, constantCoeff_X, constantCoeff_comp_C, constantCoeff_mk, constantCoeff_one, constantCoeff_smul, constantCoeff_surj, constantCoeff_toSubring, constantCoeff_zero, eq_X_mul_shift_add_const, eq_shift_mul_X_add_const, evalNegHom_X, ext, ext_iff, forall_coeff_eq_zero, instIsScalarTower, instNontrivial, instNontrivialSubalgebra, instSubsingleton, isUnit_constantCoeff, mapAlgHom_apply, map_C, map_X, map_comp, map_eq_zero, map_id, map_injective, map_surjective, map_toSubring, monomial_eq_mk, monomial_mul_monomial, monomial_pow, monomial_zero_eq_C, monomial_zero_eq_C_apply, mul_X_cancel, mul_X_inj, mul_X_injective, mul_X_pow_cancel, mul_X_pow_inj, mul_X_pow_injective, not_isField, prod_monomial, rescale_X, rescale_mk, rescale_mul, rescale_neg_one_X, rescale_one, rescale_rescale, rescale_zero, rescale_zero_apply, smul_eq_C_mul, subsingleton_iff
135
Total166

MvPolynomial

Theorems

NameKindAssumesProvesValidatesDepends On
toMvPowerSeries_pUnitAlgEquiv πŸ“–mathematicalβ€”toMvPowerSeries
Polynomial.toPowerSeries
CommSemiring.toSemiring
DFunLike.coe
AlgEquiv
MvPolynomial
Polynomial
commSemiring
Polynomial.semiring
algebra
Algebra.id
Polynomial.algebraOfAlgebra
AlgEquiv.instFunLike
pUnitAlgEquiv
β€”induction_on'
Finsupp.unique_ext
Finsupp.single_eq_same
coe_monomial
pUnitAlgEquiv_monomial
Polynomial.coe_monomial
evalβ‚‚_add
Polynomial.coe_add

Polynomial

Definitions

NameCategoryTheorems
coeToPowerSeries πŸ“–CompOpβ€”
toPowerSeries πŸ“–CompOp
69 mathmath: PowerSeries.coeff_mul_eq_coeff_trunc_mul_truncβ‚‚, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_apply, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, evalβ‚‚_C_X_eq_coe, coe_eq_one_iff, PowerSeries.trunc_mul_trunc, PowerSeries.IsWeierstrassDivisorAt.div_coe_eq_zero, PowerSeries.eq_mul_weierstrassDiv_add_weierstrassMod, toPowerSeries_toMvPowerSeries, pUnitAlgEquiv_symm_toPowerSeries, PowerSeries.evalβ‚‚_coe, coe_one, coe_monomial, coe_eq_zero_iff, coe_C, PowerSeries.eq_shift_mul_X_pow_add_trunc, coe_def, RatFunc.coe_coe, PowerSeries.intValuation_eq_of_coe, PowerSeries.trunc_trunc_mul_trunc, PowerSeries.IsWeierstrassDivisionAt.eq_mul_add, IsDistinguishedAt.isWeierstrassDivisorAt, constantCoeff_coe, PowerSeries.normalized_count_X_eq_of_coe, PowerSeries.IsWeierstrassDivisorAt.mod_coe_eq_self, LaurentSeries.exists_Polynomial_intValuation_lt, PowerSeries.trunc_trunc_mul, coe_X, IsDistinguishedAt.isWeierstrassDivisorAt', PowerSeries.WithPiTopology.denseRange_toPowerSeries, coe_smul, coe_add, PowerSeries.isWeierstrassFactorizationAt_iff, PowerSeries.derivativeFun_coe, PowerSeries.eq_X_pow_mul_shift_add_trunc, PowerSeries.trunc_trunc_of_le, coeff_mul_invOneSubPow_eq_hilbertPoly_eval, PowerSeries.trunc_trunc_pow, PowerSeries.subst_coe, coeToPowerSeries.algHom_apply, PowerSeries.derivative_coe, IsDistinguishedAt.algEquivQuotient_symm_apply, PowerSeries.IsWeierstrassFactorizationAt.eq_mul, coe_mul, algebraMap_hahnSeries_apply, coeToPowerSeries.ringHom_apply, coe_sub, coe_neg, MvPolynomial.toMvPowerSeries_pUnitAlgEquiv, gaussNorm_coe_powerSeries, PowerSeries.coeff_mul_eq_coeff_trunc_mul_trunc, PowerSeries.trunc_coe_eq_self, PowerSeries.isWeierstrassDivisionAt_iff, coe_injective, coe_zero, PowerSeries.IsWeierstrassDivisorAt.mk_mod'_eq_self, PowerSeries.eq_weierstrassDistinguished_mul_weierstrassUnit, PowerSeries.trunc_trunc, PowerSeries.aeval_coe, PowerSeries.substAlgHom_coe, coe_inj, PowerSeries.WithPiTopology.tendsto_trunc_atTop, PowerSeries.algebraMap_apply', PowerSeries.coeff_coe_trunc_of_lt, polynomial_map_coe, IsDistinguishedAt.algEquivQuotient_apply, coe_pow, coeff_coe, PowerSeries.IsWeierstrassDivisionAt.coeff_f_sub_r_mem

Theorems

NameKindAssumesProvesValidatesDepends On
coe_C πŸ“–mathematicalβ€”toPowerSeries
DFunLike.coe
RingHom
Polynomial
Semiring.toNonAssocSemiring
semiring
RingHom.instFunLike
C
PowerSeries
PowerSeries.instSemiring
PowerSeries.C
β€”coe_monomial
PowerSeries.monomial_zero_eq_C_apply
coe_X πŸ“–mathematicalβ€”toPowerSeries
X
PowerSeries.X
β€”coe_monomial
coe_add πŸ“–mathematicalβ€”toPowerSeries
Polynomial
instAdd
PowerSeries
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
PowerSeries.instSemiring
β€”PowerSeries.ext
coeff_coe
coeff_add
map_add
SemilinearMapClass.toAddHomClass
LinearMap.semilinearMapClass
coe_def πŸ“–mathematicalβ€”toPowerSeries
coeff
β€”β€”
coe_eq_one_iff πŸ“–mathematicalβ€”toPowerSeries
PowerSeries
MvPowerSeries.instOne
Polynomial
instOne
β€”coe_one
coe_eq_zero_iff πŸ“–mathematicalβ€”toPowerSeries
PowerSeries
PowerSeries.instZero
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Polynomial
instZero
β€”coe_zero
coe_inj πŸ“–mathematicalβ€”toPowerSeriesβ€”coe_injective
coe_injective πŸ“–mathematicalβ€”Polynomial
PowerSeries
toPowerSeries
β€”ext
coe_monomial πŸ“–mathematicalβ€”toPowerSeries
DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
Polynomial
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
semiring
Semiring.toModule
module
LinearMap.instFunLike
monomial
PowerSeries
PowerSeries.instAddCommMonoid
PowerSeries.instModule
PowerSeries.monomial
β€”PowerSeries.ext
coeff_coe
coeff_monomial
PowerSeries.coeff_monomial
coe_mul πŸ“–mathematicalβ€”toPowerSeries
Polynomial
instMul
PowerSeries
MvPowerSeries.instMul
β€”PowerSeries.ext
coeff_coe
coeff_mul
PowerSeries.coeff_mul
Finset.sum_congr
coe_neg πŸ“–mathematicalβ€”toPowerSeries
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial
instNeg
CommRing.toRing
PowerSeries
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
PowerSeries.instAddCommGroup
Ring.toAddCommGroup
β€”RingHom.map_neg
coe_one πŸ“–mathematicalβ€”toPowerSeries
Polynomial
instOne
PowerSeries
MvPowerSeries.instOne
β€”coe_monomial
PowerSeries.monomial_zero_eq_C_apply
coe_pow πŸ“–mathematicalβ€”toPowerSeries
Polynomial
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
semiring
PowerSeries
PowerSeries.instSemiring
β€”RingHom.map_pow
coe_smul πŸ“–mathematicalβ€”toPowerSeries
Polynomial
SMulZeroClass.toSMul
instZero
smulZeroClass
DistribSMul.toSMulZeroClass
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
instDistribSMul
NonAssocSemiring.toNonUnitalNonAssocSemiring
PowerSeries
AddZero.toZero
AddZeroClass.toAddZero
PowerSeries.instAddMonoid
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
PowerSeries.instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
PowerSeries.instModule
Semiring.toModule
β€”β€”
coe_sub πŸ“–mathematicalβ€”toPowerSeries
CommSemiring.toSemiring
CommRing.toCommSemiring
Polynomial
instSub
CommRing.toRing
PowerSeries
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
PowerSeries.instAddGroup
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
β€”RingHom.map_sub
coe_zero πŸ“–mathematicalβ€”toPowerSeries
Polynomial
instZero
PowerSeries
PowerSeries.instZero
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
β€”β€”
coeff_coe πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
PowerSeries.instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
PowerSeries.instModule
Semiring.toModule
LinearMap.instFunLike
PowerSeries.coeff
toPowerSeries
coeff
β€”Finsupp.single_eq_same
constantCoeff_coe πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
PowerSeries.instSemiring
RingHom.instFunLike
PowerSeries.constantCoeff
toPowerSeries
coeff
β€”β€”
evalβ‚‚_C_X_eq_coe πŸ“–mathematicalβ€”evalβ‚‚
PowerSeries
PowerSeries.instSemiring
PowerSeries.C
PowerSeries.X
toPowerSeries
β€”evalβ‚‚_C_X
coeToPowerSeries.ringHom_apply
evalβ‚‚_eq_sum_range
map_sum
RingHomClass.toAddMonoidHomClass
RingHom.instRingHomClass
Finset.sum_congr
map_mul
NonUnitalRingHomClass.toMulHomClass
RingHomClass.toNonUnitalRingHomClass
map_pow
MonoidWithZeroHomClass.toMonoidHomClass
RingHomClass.toMonoidWithZeroHomClass
coe_C
coe_X
pUnitAlgEquiv_symm_toPowerSeries πŸ“–mathematicalβ€”toPowerSeries
CommSemiring.toSemiring
MvPolynomial.toMvPowerSeries
DFunLike.coe
AlgEquiv
Polynomial
MvPolynomial
semiring
MvPolynomial.commSemiring
algebraOfAlgebra
Algebra.id
MvPolynomial.algebra
AlgEquiv.instFunLike
AlgEquiv.symm
MvPolynomial.pUnitAlgEquiv
β€”AlgEquiv.apply_symm_apply
MvPolynomial.toMvPowerSeries_pUnitAlgEquiv
polynomial_map_coe πŸ“–mathematicalβ€”toPowerSeries
CommSemiring.toSemiring
map
DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
PowerSeries.instSemiring
RingHom.instFunLike
PowerSeries.map
β€”PowerSeries.ext
coeff_coe
coeff_map

Polynomial.coeToPowerSeries

Definitions

NameCategoryTheorems
algHom πŸ“–CompOp
3 mathmath: PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_apply, algHom_apply, Polynomial.IsDistinguishedAt.algEquivQuotient_apply
ringHom πŸ“–CompOp
1 mathmath: ringHom_apply

Theorems

NameKindAssumesProvesValidatesDepends On
algHom_apply πŸ“–mathematicalβ€”DFunLike.coe
AlgHom
Polynomial
CommSemiring.toSemiring
PowerSeries
Polynomial.semiring
PowerSeries.instSemiring
Polynomial.algebraOfAlgebra
Algebra.id
PowerSeries.instAlgebra
AlgHom.funLike
algHom
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
PowerSeries.map
algebraMap
Polynomial.toPowerSeries
β€”β€”
ringHom_apply πŸ“–mathematicalβ€”DFunLike.coe
RingHom
Polynomial
PowerSeries
Semiring.toNonAssocSemiring
Polynomial.semiring
PowerSeries.instSemiring
RingHom.instFunLike
ringHom
Polynomial.toPowerSeries
β€”β€”

PowerSeries

Definitions

NameCategoryTheorems
C πŸ“–CompOp
45 mathmath: Polynomial.evalβ‚‚_C_X_eq_coe, coeff_mul_C, heval_C, coeff_ne_zero_C, rescale_X, Polynomial.coe_C, map_constantCoeff_le_self_of_X_mem, trunc_mul_C, rescale_zero_apply, rescale_zero, derivativeFun_C, C_injective, eq_X_mul_shift_add_const, constantCoeff_comp_C, coeff_succ_C, sub_const_eq_X_mul_shift, constantCoeff_C, invUnitsSub_mul_sub, monomial_zero_eq_C, sub_const_eq_shift_mul_X, trunc_C, WithPiTopology.continuous_C, coe_C, gaussNorm_C, expand_C, C_eq_algebraMap, evalβ‚‚_C, eq_shift_mul_X_add_const, coeff_zero_C, coeff_C, monomial_eq_C_mul_X_pow, algebraMap_eq, map_C, C_inv, algebraMap_apply, coeff_C_mul, derivative_C, invUnitsSub_mul_X, coeff_C_mul_X_pow, HahnSeries.ofPowerSeries_C, smul_eq_C_mul, monomial_zero_eq_C_apply, IsRestricted.C, trunc_C_mul, eq_span_insert_X_of_X_mem_of_span_eq
X πŸ“–CompOp
113 mathmath: Polynomial.evalβ‚‚_C_X_eq_coe, coeff_X_mul_largeSchroderSeries, expand_apply, trunc_X_pow_self_mul, invOneSubPow_inv_eq_one_sub_pow, coeff_succ_mul_X, X_prime, maximalIdeal_eq_span_X, HahnSeries.ofPowerSeries_X_pow, rescale_X, Nat.Partition.tendsto_order_genFun_term_atTop_nhds_top, Polynomial.bernoulli_generating_function, evalβ‚‚_X, constantCoeff_X, eq_shift_mul_X_pow_add_trunc, bernoulliPowerSeries_mul_exp_sub_one, IsWeierstrassFactorization.isWeierstrassDivision, normUnit_X, coeff_X_mul_largeSchroderSeriesSeries_sq, mk_add_choose_mul_one_sub_pow_eq_one, HasSubst.X', commute_X_pow, substAlgHom_X, Nat.Partition.hasProd_powerSeriesMk_card_countRestricted, aeval_unique, HasSubst.X_pow, largeSchroderSeries_eq_one_add_X_mul_largeSchroderSeries_add_X_mul_largeSchroderSeries_sq, bernoulli'PowerSeries_mul_exp_sub_one, mul_X_injective, trunc_X_of, normalized_count_X_eq_of_coe, HasSubst.smul_X', Nat.Partition.summable_genFun_term, eq_X_mul_shift_add_const, evalNegHom_X, X_pow_mul, Polynomial.coe_X, Nat.Partition.powerSeriesMk_card_restricted_eq_tprod, X_inv, sub_const_eq_X_mul_shift, LaurentSeries.of_powerSeries_localization, invUnitsSub_mul_sub, X_irreducible, eq_X_pow_mul_shift_add_trunc, HahnSeries.ofPowerSeries_X, X_mul_inj, one_sub_pow_add_mul_invOneSubPow_val_eq_one_sub_pow, LaurentSeries.coe_X_compare, sub_const_eq_shift_mul_X, one_sub_pow_mul_invOneSubPow_val_add_eq_invOneSubPow_val, map_X, Nat.Partition.hasProd_powerSeriesMk_card_restricted, X_eq, map_algebraMap_eq_subst_X, X_mul, X_pow_mul_injective, coeff_X, Nat.Partition.powerSeriesMk_card_countRestricted_eq_tprod, heval_X, eq_shift_mul_X_add_const, coeff_mul_X_pow', coe_X, X_pow_eq, monomial_eq_C_mul_X_pow, mul_X_pow_injective, Nat.Partition.summable_genFun_term', Nat.Partition.multipliable_powerSeriesMk_card_restricted, X_pow_order_dvd, coeff_X_pow_self, invOneSubPow_eq_inv_one_sub_pow, intValuation_X, subst_X, rescale_neg_one_X, catalanSeries_sq_mul_X_add_one, coeff_X_pow, trunc_one_X, X_pow_order_mul_divXPowOrder, coeff_succ_X_mul, span_X_isPrime, order_X, Nat.Partition.hasProd_genFun, X_pow_dvd_iff, X_pow_mul_inj, expand_X, coeff_zero_X_mul, X_dvd_iff, invUnitsSub_mul_X, coeff_C_mul_X_pow, order_eq_emultiplicity_X, coeff_X_pow_mul', binomialSeries_nat, coeff_mul_X_pow, Nat.Partition.multipliable_powerSeriesMk_card_countRestricted, WithPiTopology.multipliable_one_sub_X_pow, order_X_pow, LaurentSeries.X_order_mul_powerSeriesPart, mul_X_pow_inj, mk_one_mul_one_sub_eq_one, HasEval.X, mul_X_inj, Nat.Partition.multipliable_genFun, divXPowOrder_X, trunc_X, X_mul_injective, derivative_X, coeff_X_pow_mul, coeff_zero_mul_X, LaurentSeries.valuation_X_pow, Nat.Partition.genFun_eq_tprod, commute_X, X_eq_normalizeX, coeff_one_X, coeff_zero_X
algebraPolynomial πŸ“–CompOp
14 mathmath: RatFunc.instFaithfulSMulPolynomialLaurentSeries, RatFunc.coe_X, RatFunc.coe_coe, LaurentSeries.inducing_coe, LaurentSeries.continuous_coe, LaurentSeries.exists_ratFunc_val_lt, RatFunc.valuation_eq_LaurentSeries_valuation, RatFunc.algebraMap_apply_div, LaurentSeries.LaurentSeries_coe, Polynomial.algebraMap_hahnSeries_apply, Polynomial.algebraMap_hahnSeries_injective, LaurentSeries.valuation_coe_ratFunc, LaurentSeries.coe_range_dense, algebraMap_apply'
algebraPolynomial' πŸ“–CompOpβ€”
algebraPowerSeries πŸ“–CompOp
1 mathmath: algebraMap_apply''
coeff πŸ“–CompOp
131 mathmath: coeff_mul_eq_coeff_trunc_mul_truncβ‚‚, CuspFormClass.qExpansion_isBigO, WithPiTopology.hasSum_iff_hasSum_coeff, hasSum_aeval, coeff_mul_one_sub_of_lt_order, coeff_mul_of_lt_order, coeff_of_lt_order_toNat, constantCoeff_subst, WithPiTopology.continuous_coeff, ModularFormClass.qExpansionFormalMultilinearSeries_apply_norm, coeff_mul_C, coeff_rescale, coeff_expand_mul, catalanSeries_coeff, coeff_X_mul_largeSchroderSeries, coeff_trunc, coeff_of_lt_order, coeff_succ_mul_X, coeff_ne_zero_C, aeval_eq_sum, binomialSeries_coeff, coeff_subst, coeff_coe, eq_shift_mul_X_pow_add_trunc, IsWeierstrassDivisorAt.coeff_seq_succ_sub_seq_mem, coeff_inv_aux, WithPiTopology.tendsto_iff_coeff_tendsto, WithPiTopology.uniformContinuous_coeff, coeff_zero_one, coeff_X_mul_largeSchroderSeriesSeries_sq, coeff_invOfUnit, hasSum_of_monomials_self, coeff_derivativeFun, evalβ‚‚_eq_tsum, eq_X_mul_shift_add_const, LaurentSeries.powerSeriesPart_coeff, coeff_invUnitsSub, coeff_succ_C, IsRestricted.isRestricted_iff, coeff_mk, sub_const_eq_X_mul_shift, coeff_largeSchroderSeries, HahnSeries.ofPowerSeries_apply_coeff, eq_X_pow_mul_shift_add_trunc, ModularFormClass.qExpansion_coeff, coeff_exp, trunc_one_left, sub_const_eq_shift_mul_X, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, IsWeierstrassDivisorAt.isUnit_shift, Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval, constantCoeff_divXPowOrder, HahnSeries.toPowerSeriesAlg_symm_apply_coeff, ModularFormClass.qExpansion_coeff_zero, coeff_comp_monomial, coeff_mul, coeff_def, HahnSeries.coeff_toPowerSeries, IsWeierstrassDivisorAt.coeff_seq_mem, coeff_smul, coeff_monomial_same, trunc_apply, coeff_monomial, coeff_X, HahnSeries.coeff_toPowerSeries_symm, IsWeierstrassDivisorAt.coeff_div, as_tsum, coeff_zero_eq_constantCoeff_apply, HahnSeries.ofPowerSeriesAlg_apply_coeff, ModularFormClass.hasSum_qExpansion_of_abs_lt, coeff_map, coeff_one, eq_shift_mul_X_add_const, coeff_prod, coeff_mul_X_pow', coeff_zero_C, forall_coeff_eq_zero, coeff_C, coeff_inv, ModularFormClass.qExpansion_coeff_eq_circleIntegral, coeff_expand_of_not_dvd, coeff_zero_eq_constantCoeff, LaurentSeries.coeff_zero_of_lt_intValuation, coeff_divXPowOrder, HahnSeries.SummableFamily.powerSeriesFamily_of_orderTop_pos, ext_iff, coeff_X_pow_self, trunc_succ, ModularFormClass.qExpansion_isBigO, coeff_mul_eq_coeff_trunc_mul_trunc, qExpansion_mul_coeff_zero, coeff_derivative, coeff_subst_finite, coeff_X_pow, ModularFormClass.hasSum_qExpansion_of_norm_lt, qExpansion_coeff_unique, coeff_subst', coeff_expand, evalβ‚‚_trunc_eq_sum_range, coeff_succ_X_mul, coeff_C_mul, X_pow_dvd_iff, order_eq, coeff_zero_X_mul, coeff_C_mul_X_pow, coeff_X_pow_mul', coeff_pow, coeff_one_pow, coeff_mul_X_pow, ModularFormClass.qExpansionFormalMultilinearSeries_coeff, IsWeierstrassDivisorAt.seq_one, Nat.Partition.coeff_genFun, coeff_subst_finite', coeff_coe_trunc_of_lt, coeff_mul_prod_one_sub_of_lt_order, HahnSeries.toPowerSeries_symm_apply_coeff, LaurentSeries.coeff_coe_powerSeries, ModularFormClass.hasSum_qExpansion, qExpansion_coeff_isBigO_of_norm_isBigO, ModularFormClass.qExpansion_coeff_eq_intervalIntegral, coeff_one_mul, Polynomial.coeff_coe, IsWeierstrassDivisorAt.coeff_div_sub_seq_mem, coeff_X_pow_mul, coeff_zero_mul_X, WithPiTopology.summable_iff_summable_coeff, hasSum_evalβ‚‚, coeff_one_X, order_eq_nat, coeff_zero_X, IsWeierstrassDivisionAt.coeff_f_sub_r_mem
constantCoeff πŸ“–CompOp
49 mathmath: constantCoeff_expand, spanFinrank_le_spanFinrank_map_constantCoeff_add_one_of_X_mem, spanFinrank_le_spanFinrank_map_constantCoeff_add_one_of_isPrime, catalanSeries_constantCoeff, constantCoeff_X, isUnit_iff_constantCoeff, WithPiTopology.continuous_constantCoeff, map_constantCoeff_le_self_of_X_mem, constantCoeff_invUnitsSub, rescale_zero_apply, rescale_zero, constantCoeff_surj, constantCoeff_one, constantCoeff_invOfUnit, Polynomial.constantCoeff_coe, eq_X_mul_shift_add_const, constantCoeff_comp_C, one_le_order_iff_constCoeff_eq_zero, HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero, sub_const_eq_X_mul_shift, constantCoeff_C, constantCoeff_inv, WithPiTopology.isTopologicallyNilpotent_iff_constantCoeff_isNilpotent, spanFinrank_eq_spanFinrank_map_constantCoeff_of_X_notMem_of_fg_of_isPrime, sub_const_eq_shift_mul_X, constantCoeff_divXPowOrder, inv_eq_zero, constantCoeff_largeSchroderSeries, invOfUnit_eq, constantCoeff_divXPowOrder_eq_zero_iff, constantCoeff_zero, fg_iff_of_isPrime, coeff_zero_eq_constantCoeff_apply, constantCoeff_smul, constantCoeff_mk, eq_shift_mul_X_add_const, coeff_inv, coeff_zero_eq_constantCoeff, ker_coeff_eq_max_ideal, constantCoeff_exp, constantCoeff_toSubring, inv_eq_inv_aux, coeff_heval_zero, order_ne_zero_iff_constCoeff_eq_zero, X_dvd_iff, binomialSeries_constantCoeff, coeff_one_pow, coeff_one_mul, isUnit_constantCoeff
evalNegHom πŸ“–CompOp
2 mathmath: exp_mul_exp_neg_eq_one, evalNegHom_X
instAddCommGroup πŸ“–CompOp
14 mathmath: IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, derivative_inv', IsWeierstrassDivisorAt.mod'_mk_eq_mod, evalNegHom_X, IsRestricted.neg, derivative_invOf, coe_neg, Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, Polynomial.coe_neg, qExpansion_neg, rescale_neg_one_X, order_neg, IsWeierstrassDivisorAt.mk_mod'_eq_self, derivative_inv
instAddCommMonoid πŸ“–CompOp
203 mathmath: coeff_mul_eq_coeff_trunc_mul_truncβ‚‚, CuspFormClass.qExpansion_isBigO, WithPiTopology.hasSum_iff_hasSum_coeff, hasSum_aeval, coeff_mul_one_sub_of_lt_order, coeff_mul_of_lt_order, IsRestricted.smul, coeff_of_lt_order_toNat, constantCoeff_subst, WithPiTopology.continuous_coeff, ModularFormClass.qExpansionFormalMultilinearSeries_apply_norm, coeff_mul_C, coeff_rescale, coeff_expand_mul, catalanSeries_coeff, coeff_X_mul_largeSchroderSeries, coeff_trunc, trunc_mul_trunc, trunc_X_pow_self_mul, derivative_exp, coeff_of_lt_order, coeff_succ_mul_X, gaussNorm_monomial, coeff_ne_zero_C, derivative_inv', Polynomial.coe_monomial, aeval_eq_sum, binomialSeries_coeff, coeff_subst, le_order_smul, coeff_coe, eq_shift_mul_X_pow_add_trunc, IsWeierstrassDivisorAt.coeff_seq_succ_sub_seq_mem, coeff_inv_aux, degree_trunc_lt, WithPiTopology.tendsto_iff_coeff_tendsto, coe_smul, WithPiTopology.uniformContinuous_coeff, coeff_zero_one, coeff_X_mul_largeSchroderSeriesSeries_sq, trunc_trunc_mul_trunc, coeff_invOfUnit, trunc_mul_C, hasSum_of_monomials_self, Nat.Partition.hasProd_powerSeriesMk_card_countRestricted, coeff_derivativeFun, evalβ‚‚_eq_tsum, trunc_X_of, instIsScalarTower, WithPiTopology.summable_prod_of_tendsto_order_atTop_nhds_top, order_monomial, monomial_mul_monomial, Nat.Partition.summable_genFun_term, eq_X_mul_shift_add_const, LaurentSeries.powerSeriesPart_coeff, coeff_invUnitsSub, prod_monomial, coeff_succ_C, trunc_trunc_mul, Nat.Partition.powerSeriesMk_card_restricted_eq_tprod, IsRestricted.isRestricted_iff, exp_pow_sum, coeff_mk, Polynomial.coe_smul, sub_const_eq_X_mul_shift, coeff_largeSchroderSeries, HahnSeries.ofPowerSeries_apply_coeff, monomial_zero_eq_C, monomial_pow, eq_X_pow_mul_shift_add_trunc, trunc_trunc_of_le, ModularFormClass.qExpansion_coeff, coeff_exp, trunc_one_left, sub_const_eq_shift_mul_X, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, WithPiTopology.one_sub_mul_tsum_pow_of_constantCoeff_eq_zero, derivative_invOf, HasSubst.monomial', IsWeierstrassDivisorAt.isUnit_shift, Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval, constantCoeff_divXPowOrder, monomial_eq_mk, HahnSeries.toPowerSeriesAlg_symm_apply_coeff, trunc_C, Nat.Partition.hasProd_powerSeriesMk_card_restricted, ModularFormClass.qExpansion_coeff_zero, X_eq, coeff_comp_monomial, trunc_trunc_pow, coeff_mul, HahnSeries.coeff_toPowerSeries, IsWeierstrassDivisorAt.coeff_seq_mem, coeff_smul, coeff_monomial_same, trunc_apply, coeff_monomial, coeff_X, HahnSeries.coeff_toPowerSeries_symm, IsWeierstrassDivisorAt.coeff_div, as_tsum, Nat.Partition.powerSeriesMk_card_countRestricted_eq_tprod, derivative_coe, coeff_zero_eq_constantCoeff_apply, HahnSeries.ofPowerSeriesAlg_apply_coeff, ModularFormClass.hasSum_qExpansion_of_abs_lt, coeff_map, constantCoeff_smul, coeff_one, eq_shift_mul_X_add_const, coeff_prod, coeff_mul_X_pow', coeff_zero_C, forall_coeff_eq_zero, coeff_C, coeff_inv, ModularFormClass.qExpansion_coeff_eq_circleIntegral, WithPiTopology.tsum_pow_mul_one_sub_of_constantCoeff_eq_zero, coeff_expand_of_not_dvd, coeff_zero_eq_constantCoeff, LaurentSeries.coeff_zero_of_lt_intValuation, X_pow_eq, monomial_eq_C_mul_X_pow, Nat.Partition.summable_genFun_term', Nat.Partition.multipliable_powerSeriesMk_card_restricted, coeff_divXPowOrder, trunc_one, HahnSeries.SummableFamily.powerSeriesFamily_of_orderTop_pos, ext_iff, coeff_X_pow_self, trunc_succ, ModularFormClass.qExpansion_isBigO, coeff_mul_eq_coeff_trunc_mul_trunc, qExpansion_mul_coeff_zero, trunc_coe_eq_self, coeff_derivative, coeff_subst_finite, coeff_X_pow, ModularFormClass.hasSum_qExpansion_of_norm_lt, expand_monomial, qExpansion_coeff_unique, coeff_subst', derivative_subst, IsRestricted.monomial, coeff_expand, evalβ‚‚_trunc_eq_sum_range, trunc_one_X, coeff_succ_X_mul, trunc_trunc, Nat.Partition.hasProd_genFun, coeff_C_mul, X_pow_dvd_iff, derivative_C, order_eq, coeff_zero_X_mul, WithPiTopology.tendsto_trunc_atTop, coeff_C_mul_X_pow, coeff_X_pow_mul', coeff_pow, coeff_one_pow, coeff_mul_X_pow, smul_eq_C_mul, ModularFormClass.qExpansionFormalMultilinearSeries_coeff, trunc_sub, IsWeierstrassDivisorAt.seq_one, Nat.Partition.coeff_genFun, Nat.Partition.multipliable_powerSeriesMk_card_countRestricted, trunc_derivativeFun, WithPiTopology.summable_of_tendsto_order_atTop_nhds_top, coeff_subst_finite', trunc_map, coeff_coe_trunc_of_lt, trunc_zero', coeff_mul_prod_one_sub_of_lt_order, HahnSeries.toPowerSeries_symm_apply_coeff, trunc_derivative, LaurentSeries.coeff_coe_powerSeries, ModularFormClass.hasSum_qExpansion, qExpansion_coeff_isBigO_of_norm_isBigO, ModularFormClass.qExpansion_coeff_eq_intervalIntegral, coeff_one_mul, monomial_zero_eq_C_apply, Nat.Partition.multipliable_genFun, Polynomial.coeff_coe, derivative_inv, natDegree_trunc_lt, trunc_X, derivative_X, WithPiTopology.summable_pow_of_constantCoeff_eq_zero, IsWeierstrassDivisorAt.coeff_div_sub_seq_mem, coeff_X_pow_mul, coeff_zero_mul_X, Nat.Partition.genFun_eq_tprod, order_monomial_of_ne_zero, trunc_C_mul, WithPiTopology.summable_iff_summable_coeff, hasSum_evalβ‚‚, coeff_one_X, derivative_pow, order_eq_nat, coeff_zero_X, IsWeierstrassDivisionAt.coeff_f_sub_r_mem, trunc_derivative'
instAddGroup πŸ“–CompOp
28 mathmath: coeff_mul_one_sub_of_lt_order, invOneSubPow_inv_eq_one_sub_pow, Polynomial.bernoulli_generating_function, bernoulliPowerSeries_mul_exp_sub_one, IsWeierstrassDivisorAt.coeff_seq_succ_sub_seq_mem, mk_add_choose_mul_one_sub_pow_eq_one, coe_sub, bernoulli'PowerSeries_mul_exp_sub_one, LaurentSeries.exists_Polynomial_intValuation_lt, sub_const_eq_X_mul_shift, invUnitsSub_mul_sub, one_sub_pow_add_mul_invOneSubPow_val_eq_one_sub_pow, sub_const_eq_shift_mul_X, qExpansion_sub, WithPiTopology.one_sub_mul_tsum_pow_of_constantCoeff_eq_zero, one_sub_pow_mul_invOneSubPow_val_add_eq_invOneSubPow_val, IsWeierstrassDivisorAt.coeff_seq_mem, WithPiTopology.instIsUniformAddGroup, Polynomial.coe_sub, WithPiTopology.tsum_pow_mul_one_sub_of_constantCoeff_eq_zero, invOneSubPow_eq_inv_one_sub_pow, invUnitsSub_mul_X, trunc_sub, WithPiTopology.multipliable_one_sub_X_pow, coeff_mul_prod_one_sub_of_lt_order, mk_one_mul_one_sub_eq_one, IsWeierstrassDivisorAt.coeff_div_sub_seq_mem, IsWeierstrassDivisionAt.coeff_f_sub_r_mem
instAddMonoid πŸ“–CompOp
8 mathmath: IsRestricted.smul, le_order_smul, coe_smul, instIsScalarTower, Polynomial.coe_smul, coeff_smul, constantCoeff_smul, smul_eq_C_mul
instAlgebra πŸ“–CompOp
84 mathmath: IsWeierstrassFactorizationAt.algEquivQuotient_apply, hasSum_aeval, IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, constantCoeff_expand, heval_C, coeff_expand_mul, expand_apply, derivative_exp, order_expand, mapAlgHom_apply, derivative_inv', Nat.Partition.tendsto_order_genFun_term_atTop_nhds_top, coeff_heval, aeval_eq_sum, support_expand_subset, derivativeFun_smul, support_expand, smul_weierstrassDiv, substAlgHom_X, heval_apply, expand_one_apply, LaurentSeries.algebraMap_apply, substAlgHom_comp_substAlgHom, HasSubst.smul_X', expand_smul, Nat.Partition.summable_genFun_term, IsWeierstrassDivisorAt.mod'_mk_eq_mod, smul_weierstrassMod, instNontrivialSubalgebra, derivative_invOf, HahnSeries.toPowerSeriesAlg_apply, HahnSeries.toPowerSeriesAlg_symm_apply_coeff, expand_C, C_eq_algebraMap, expand_mul, IsWeierstrassDivisorAt.mod_smul, expand_mul_eq_comp, Polynomial.coeToPowerSeries.algHom_apply, derivative_coe, HahnSeries.ofPowerSeriesAlg_apply_coeff, Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, heval_X, comp_aeval, map_expand, coeff_expand_of_not_dvd, Nat.Partition.summable_genFun_term', HasSubst.comp, algebraMap_eq, continuous_aeval, heval_unit, coeff_derivative, expand_monomial, derivative_subst, coeff_expand, algebraMap_apply, coe_aeval, expand_one, IsWeierstrassDivisorAt.mk_mod'_eq_self, aeval_coe, Nat.Partition.hasProd_genFun, coeff_heval_zero, IsWeierstrassFactorizationAt.smul, substAlgHom_coe, derivative_C, IsWeierstrassDivisorAt.div_smul, expand_X, subst_smul, IsWeierstrassDivisionAt.smul, substAlgHom_comp_substAlgHom_apply, weierstrassUnit_smul, heval_mul, smul_inv, qExpansion_smul, trunc_derivative, Polynomial.IsDistinguishedAt.algEquivQuotient_apply, Nat.Partition.multipliable_genFun, HahnSeries.SummableFamily.powerSeriesFamily_smul, derivative_inv, coe_substAlgHom, derivative_X, weierstrassDistinguished_smul, Nat.Partition.genFun_eq_tprod, derivative_pow, trunc_derivative'
instCommRing πŸ“–CompOp
32 mathmath: IsWeierstrassFactorizationAt.algEquivQuotient_apply, HahnSeries.SummableFamily.powerSeriesFamily_add, IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, eq_mul_weierstrassDiv_add_weierstrassMod, intValuation_eq_of_coe, IsWeierstrassDivisionAt.eq_mul_add, aeval_unique, IsWeierstrassDivisorAt.mod'_mk_eq_mod, LaurentSeries.exists_Polynomial_intValuation_lt, RatFunc.valuation_eq_LaurentSeries_valuation, IsWeierstrassDivisorAt.mod_add, hasUnitMulPowIrreducibleFactorization, qExpansion_add, instIsDiscreteValuationRing, subst_add, LaurentSeries.powerSeriesRingEquiv_coe_apply, LaurentSeries.powerSeriesEquivSubring_apply, Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, IsWeierstrassDivisionAt.add, add_weierstrassMod, IsWeierstrassDivisorAt.div_add, LaurentSeries.powerSeriesEquivSubring_coe_apply, invOneSubPow_eq_inv_one_sub_pow, intValuation_X, isWeierstrassDivisionAt_iff, LaurentSeries.valuation_def, IsWeierstrassDivisorAt.mk_mod'_eq_self, WithPiTopology.multipliable_one_sub_X_pow, coeff_mul_prod_one_sub_of_lt_order, Polynomial.IsDistinguishedAt.algEquivQuotient_apply, add_weierstrassDiv, HasEval.X
instCommSemiring πŸ“–CompOp
42 mathmath: derivative_exp, algebraMap_apply'', instUniqueFactorizationMonoidOfIsPrincipalIdealRingOfIsDomain, X_prime, maximalIdeal_eq_span_X, divXPowOrder_prod, derivative_inv', LaurentSeries.coe_algebraMap, ringKrullDim_succ_le_ringKrullDim_powerseries, normUnit_X, Nat.Partition.hasProd_powerSeriesMk_card_countRestricted, WithPiTopology.summable_prod_of_tendsto_order_atTop_nhds_top, normalized_count_X_eq_of_coe, prod_monomial, instUniqueFactorizationMonoid, Nat.Partition.powerSeriesMk_card_restricted_eq_tprod, LaurentSeries.of_powerSeries_localization, derivative_invOf, Nat.Partition.hasProd_powerSeriesMk_card_restricted, Nat.Partition.powerSeriesMk_card_countRestricted_eq_tprod, derivative_coe, coeff_prod, order_prod, Nat.Partition.multipliable_powerSeriesMk_card_restricted, ker_coeff_eq_max_ideal, coeff_derivative, derivative_subst, Nat.Partition.hasProd_genFun, WithPiTopology.multipliable_one_add_of_tendsto_order_atTop_nhds_top, derivative_C, LaurentSeries.instIsFractionRingPowerSeries, Nat.Partition.multipliable_powerSeriesMk_card_countRestricted, trunc_derivative, le_order_prod, Nat.Partition.multipliable_genFun, derivative_inv, derivativeFun_mul, derivative_X, Nat.Partition.genFun_eq_tprod, X_eq_normalizeX, derivative_pow, trunc_derivative'
instInhabited πŸ“–CompOpβ€”
instModule πŸ“–CompOp
190 mathmath: coeff_mul_eq_coeff_trunc_mul_truncβ‚‚, CuspFormClass.qExpansion_isBigO, WithPiTopology.hasSum_iff_hasSum_coeff, hasSum_aeval, IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, coeff_mul_one_sub_of_lt_order, coeff_mul_of_lt_order, IsRestricted.smul, coeff_of_lt_order_toNat, constantCoeff_subst, WithPiTopology.continuous_coeff, ModularFormClass.qExpansionFormalMultilinearSeries_apply_norm, coeff_mul_C, coeff_rescale, coeff_expand_mul, catalanSeries_coeff, coeff_X_mul_largeSchroderSeries, coeff_trunc, trunc_mul_trunc, trunc_X_pow_self_mul, derivative_exp, coeff_of_lt_order, coeff_succ_mul_X, gaussNorm_monomial, coeff_ne_zero_C, derivative_inv', Polynomial.coe_monomial, aeval_eq_sum, binomialSeries_coeff, coeff_subst, le_order_smul, coeff_coe, eq_shift_mul_X_pow_add_trunc, IsWeierstrassDivisorAt.coeff_seq_succ_sub_seq_mem, coeff_inv_aux, degree_trunc_lt, WithPiTopology.tendsto_iff_coeff_tendsto, coe_smul, WithPiTopology.uniformContinuous_coeff, coeff_zero_one, coeff_X_mul_largeSchroderSeriesSeries_sq, trunc_trunc_mul_trunc, coeff_invOfUnit, trunc_mul_C, hasSum_of_monomials_self, coeff_derivativeFun, evalβ‚‚_eq_tsum, trunc_X_of, instIsScalarTower, order_monomial, monomial_mul_monomial, eq_X_mul_shift_add_const, LaurentSeries.powerSeriesPart_coeff, IsWeierstrassDivisorAt.mod'_mk_eq_mod, coeff_invUnitsSub, prod_monomial, coeff_succ_C, trunc_trunc_mul, IsRestricted.isRestricted_iff, coeff_mk, Polynomial.coe_smul, sub_const_eq_X_mul_shift, coeff_largeSchroderSeries, HahnSeries.ofPowerSeries_apply_coeff, monomial_zero_eq_C, monomial_pow, eq_X_pow_mul_shift_add_trunc, trunc_trunc_of_le, ModularFormClass.qExpansion_coeff, coeff_exp, trunc_one_left, sub_const_eq_shift_mul_X, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, derivative_invOf, HasSubst.monomial', IsWeierstrassDivisorAt.isUnit_shift, Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval, constantCoeff_divXPowOrder, monomial_eq_mk, HahnSeries.toPowerSeriesAlg_symm_apply_coeff, trunc_C, ModularFormClass.qExpansion_coeff_zero, X_eq, coeff_comp_monomial, trunc_trunc_pow, coeff_mul, HahnSeries.coeff_toPowerSeries, IsWeierstrassDivisorAt.coeff_seq_mem, coeff_smul, coeff_monomial_same, trunc_apply, coeff_monomial, coeff_X, HahnSeries.coeff_toPowerSeries_symm, IsWeierstrassDivisorAt.coeff_div, as_tsum, derivative_coe, coeff_zero_eq_constantCoeff_apply, HahnSeries.ofPowerSeriesAlg_apply_coeff, Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, ModularFormClass.hasSum_qExpansion_of_abs_lt, coeff_map, constantCoeff_smul, coeff_one, eq_shift_mul_X_add_const, coeff_prod, coeff_mul_X_pow', coeff_zero_C, forall_coeff_eq_zero, coeff_C, coeff_inv, ModularFormClass.qExpansion_coeff_eq_circleIntegral, coeff_expand_of_not_dvd, coeff_zero_eq_constantCoeff, LaurentSeries.coeff_zero_of_lt_intValuation, X_pow_eq, monomial_eq_C_mul_X_pow, coeff_divXPowOrder, trunc_one, HahnSeries.SummableFamily.powerSeriesFamily_of_orderTop_pos, ext_iff, coeff_X_pow_self, trunc_succ, ModularFormClass.qExpansion_isBigO, coeff_mul_eq_coeff_trunc_mul_trunc, qExpansion_mul_coeff_zero, trunc_coe_eq_self, coeff_derivative, coeff_subst_finite, coeff_X_pow, ModularFormClass.hasSum_qExpansion_of_norm_lt, expand_monomial, qExpansion_coeff_unique, coeff_subst', derivative_subst, IsRestricted.monomial, coeff_expand, evalβ‚‚_trunc_eq_sum_range, trunc_one_X, coeff_succ_X_mul, IsWeierstrassDivisorAt.mk_mod'_eq_self, trunc_trunc, coeff_C_mul, X_pow_dvd_iff, derivative_C, order_eq, coeff_zero_X_mul, WithPiTopology.tendsto_trunc_atTop, coeff_C_mul_X_pow, coeff_X_pow_mul', coeff_pow, coeff_one_pow, coeff_mul_X_pow, smul_eq_C_mul, ModularFormClass.qExpansionFormalMultilinearSeries_coeff, trunc_sub, IsWeierstrassDivisorAt.seq_one, Nat.Partition.coeff_genFun, trunc_derivativeFun, coeff_subst_finite', trunc_map, coeff_coe_trunc_of_lt, trunc_zero', coeff_mul_prod_one_sub_of_lt_order, HahnSeries.toPowerSeries_symm_apply_coeff, trunc_derivative, LaurentSeries.coeff_coe_powerSeries, ModularFormClass.hasSum_qExpansion, qExpansion_coeff_isBigO_of_norm_isBigO, ModularFormClass.qExpansion_coeff_eq_intervalIntegral, coeff_one_mul, monomial_zero_eq_C_apply, Polynomial.coeff_coe, derivative_inv, natDegree_trunc_lt, trunc_X, derivative_X, IsWeierstrassDivisorAt.coeff_div_sub_seq_mem, coeff_X_pow_mul, coeff_zero_mul_X, order_monomial_of_ne_zero, trunc_C_mul, WithPiTopology.summable_iff_summable_coeff, hasSum_evalβ‚‚, coeff_one_X, derivative_pow, order_eq_nat, coeff_zero_X, IsWeierstrassDivisionAt.coeff_f_sub_r_mem, trunc_derivative'
instRing πŸ“–CompOp
10 mathmath: IsWeierstrassFactorizationAt.algEquivQuotient_apply, IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, IsRestricted.add, IsWeierstrassDivisorAt.mod'_mk_eq_mod, LaurentSeries.powerSeriesEquivSubring_apply, Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, WithPiTopology.instIsTopologicalRing, IsWeierstrassDivisorAt.mk_mod'_eq_self, binomialSeries_nat, Polynomial.IsDistinguishedAt.algEquivQuotient_apply
instSemiring πŸ“–CompOp
317 mathmath: IsWeierstrassFactorizationAt.algEquivQuotient_apply, hasSum_aeval, IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, Polynomial.evalβ‚‚_C_X_eq_coe, constantCoeff_expand, coeff_mul_C, heval_C, coeff_rescale, invOneSubPow_zero, qExpansionRingHom_apply, coeff_expand_mul, expand_apply, MvPowerSeries.rescaleUnit, trunc_X_pow_self_mul, invOneSubPow_inv_eq_one_sub_pow, LaurentSeries.LaurentSeriesRingEquiv_def, algebraMap_apply'', spanFinrank_le_spanFinrank_map_constantCoeff_add_one_of_isPrime, order_expand, eq_divided_by_X_pow_order_Iff_Unit, Unit_of_divided_by_X_pow_order_zero, degree_weierstrassMod_lt, HahnSeries.ofPowerSeries_X_pow, coeff_ne_zero_C, mapAlgHom_apply, derivative_inv', instIsDomain, rescale_X, Nat.Partition.tendsto_order_genFun_term_atTop_nhds_top, coe_add, catalanSeries_constantCoeff, coeff_heval, isUnit_exp, aeval_eq_sum, LaurentSeries.ofPowerSeries_powerSeriesPart, LaurentSeries.single_order_mul_powerSeriesPart, Polynomial.coe_C, Polynomial.bernoulli_generating_function, isUnit_divided_by_X_pow_order, map_cos, coeff_coe, constantCoeff_X, eq_shift_mul_X_pow_add_trunc, LaurentSeries.coe_algebraMap, support_expand_subset, RatFunc.coe_coe, isUnit_iff_constantCoeff, subst_pow, WithPiTopology.continuous_constantCoeff, derivativeFun_smul, support_expand, IsWeierstrassFactorization.isWeierstrassDivision, smul_weierstrassDiv, coe_smul, coeff_X_mul_largeSchroderSeriesSeries_sq, LaurentSeries.val_le_one_iff_eq_coe, constantCoeff_invUnitsSub, mk_add_choose_mul_one_sub_pow_eq_one, rescale_rescale, coe_mul, trunc_mul_C, IsWeierstrassDivisionAt.degree_lt, rescale_zero_apply, commute_X_pow, substAlgHom_X, IsWeierstrassFactorizationAt.natDegree_eq_toNat_order_map_of_ne_top, heval_apply, Nat.Partition.hasProd_powerSeriesMk_card_countRestricted, coe_sub, mk_one_pow_eq_mk_choose_add, expand_one_apply, rescale_zero, le_order_map, rescale_mk, HasSubst.X_pow, constantCoeff_surj, largeSchroderSeries_eq_one_add_X_mul_largeSchroderSeries_add_X_mul_largeSchroderSeries_sq, substAlgHom_comp_substAlgHom, exp_mul_exp_neg_eq_one, constantCoeff_one, map_sin, derivativeFun_C, constantCoeff_invOfUnit, Polynomial.constantCoeff_coe, HasSubst.smul_X', expand_smul, C_injective, Nat.Partition.summable_genFun_term, eq_X_mul_shift_add_const, constantCoeff_comp_C, exp_mul_exp_eq_exp_add, IsWeierstrassDivisorAt.mod'_mk_eq_mod, evalNegHom_X, X_pow_mul, coeff_succ_C, IsWeierstrassFactorization.natDegree_eq_toNat_order_map, WithPiTopology.instIsTopologicalSemiring, Nat.Partition.powerSeriesMk_card_restricted_eq_tprod, invOneSubPow_inv_zero_eq_one, smul_weierstrassMod, exp_pow_sum, one_le_order_iff_constCoeff_eq_zero, HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero, sub_const_eq_X_mul_shift, constantCoeff_C, Polynomial.coe_add, constantCoeff_inv, isWeierstrassFactorizationAt_iff, HahnSeries.ofPowerSeries_apply_coeff, LaurentSeries.of_powerSeries_localization, invUnitsSub_mul_sub, X_irreducible, monomial_zero_eq_C, monomial_pow, instNontrivialSubalgebra, eq_X_pow_mul_shift_add_trunc, WithPiTopology.isTopologicallyNilpotent_iff_constantCoeff_isNilpotent, map_eq_zero, HahnSeries.ofPowerSeries_X, isUnit_weierstrassUnit, one_sub_pow_add_mul_invOneSubPow_val_eq_one_sub_pow, LaurentSeries.coe_X_compare, not_isField, sub_const_eq_shift_mul_X, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, IsWeierstrassFactorizationAt.isUnit, coe_divXPowOrderHom, derivative_invOf, one_sub_pow_mul_invOneSubPow_val_add_eq_invOneSubPow_val, coe_zero, IsWeierstrassDivisorAt.isUnit_shift, map_X, Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval, map_comp, constantCoeff_divXPowOrder, HahnSeries.toPowerSeriesAlg_apply, inv_eq_zero, HahnSeries.toPowerSeriesAlg_symm_apply_coeff, LaurentSeries.exists_powerSeries_of_memIntegers, trunc_C, Nat.Partition.hasProd_powerSeriesMk_card_restricted, WithPiTopology.continuous_C, coe_C, coe_neg, min_order_le_order_add, gaussNorm_C, map_subst, expand_C, map_algebraMap_eq_subst_X, trunc_trunc_pow, constantCoeff_largeSchroderSeries, C_eq_algebraMap, HahnSeries.coeff_toPowerSeries, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, invOfUnit_eq, map_surjective, map_invUnitsSub, isNoetherianRing, le_order_pow, constantCoeff_divXPowOrder_eq_zero_iff, X_pow_mul_injective, expand_mul, IsWeierstrassDivisorAt.mod_smul, HahnSeries.coeff_toPowerSeries_symm, constantCoeff_zero, expand_mul_eq_comp, invOneSubPow_add, fg_iff_of_isPrime, Polynomial.coeToPowerSeries.algHom_apply, order_pow, LaurentSeries.powerSeriesRingEquiv_coe_apply, Nat.Partition.powerSeriesMk_card_countRestricted_eq_tprod, Unit_of_divided_by_X_pow_order_nonzero, coeff_zero_eq_constantCoeff_apply, HahnSeries.ofPowerSeriesAlg_apply_coeff, LaurentSeries.powerSeriesEquivSubring_apply, Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, coeff_map, evalβ‚‚_C, constantCoeff_smul, heval_X, comp_aeval, constantCoeff_mk, eq_shift_mul_X_add_const, coeff_mul_X_pow', coeff_zero_C, Polynomial.algebraMap_hahnSeries_apply, coeff_C, coeff_inv, rescale_injective, Polynomial.coeToPowerSeries.ringHom_apply, map_expand, coeff_expand_of_not_dvd, LaurentSeries.powerSeriesEquivSubring_coe_apply, coe_evalβ‚‚Hom, coeff_zero_eq_constantCoeff, coe_X, invOneSubPow_val_eq_mk_sub_one_add_choose_of_pos, exp_pow_eq_rescale_exp, X_pow_eq, monomial_eq_C_mul_X_pow, mul_X_pow_injective, Nat.Partition.summable_genFun_term', Nat.Partition.multipliable_powerSeriesMk_card_restricted, divXPowOrder_pow, HasSubst.comp, X_pow_order_dvd, ker_coeff_eq_max_ideal, algebraMap_eq, coeff_X_pow_self, continuous_aeval, map_C, heval_unit, invOneSubPow_eq_inv_one_sub_pow, IsWeierstrassFactorization.degree_eq_coe_lift_order_map, rescale_neg_one_X, constantCoeff_exp, coe_orderHom, catalanSeries_sq_mul_X_add_one, coeff_X_pow, IsWeierstrassFactorizationAt.degree_eq_coe_lift_order_map_of_ne_top, expand_monomial, isWeierstrassDivisionAt_iff, coeff_subst', instIsLocalRing, constantCoeff_toSubring, C_inv, coeff_expand, algebraMap_apply, coe_aeval, derivativeFun_add, HahnSeries.ofPowerSeries_apply, expand_one, X_pow_order_mul_divXPowOrder, map_exp, coe_one, IsWeierstrassDivisorAt.mk_mod'_eq_self, span_X_isPrime, invOneSubPow_val_one_eq_invUnitSub_one, inv_eq_inv_aux, aeval_coe, Nat.Partition.hasProd_genFun, coeff_heval_zero, order_ne_zero_iff_constCoeff_eq_zero, HahnSeries.ofPowerSeries_injective, IsWeierstrassFactorizationAt.smul, substAlgHom_coe, WithPiTopology.multipliable_one_add_of_tendsto_order_atTop_nhds_top, coeff_C_mul, X_pow_dvd_iff, derivative_C, X_pow_mul_inj, IsWeierstrassDivisorAt.div_smul, expand_X, X_dvd_iff, order_add_of_order_ne, invUnitsSub_mul_X, subst_smul, rescale_one, IsWeierstrassDivisionAt.smul, coeff_C_mul_X_pow, order_eq_emultiplicity_X, coeff_X_pow_mul', binomialSeries_nat, algebraMap_apply', HahnSeries.ofPowerSeries_C, coe_pow, substAlgHom_comp_substAlgHom_apply, weierstrassUnit_smul, coeff_pow, LaurentSeries.mem_integers_of_powerSeries, binomialSeries_constantCoeff, coeff_one_pow, HahnSeries.toPowerSeries_apply, coeff_mul_X_pow, smul_eq_C_mul, IsWeierstrassDivisorAt.seq_one, Nat.Partition.multipliable_powerSeriesMk_card_countRestricted, map_id, WithPiTopology.multipliable_one_sub_X_pow, order_X_pow, heval_mul, rescale_neg_one_invOneSubPow, HahnSeries.algebraMap_apply', coeff_subst_finite', trunc_map, smul_inv, qExpansion_of_pow, LaurentSeries.X_order_mul_powerSeriesPart, mul_X_pow_inj, qExpansion_smul, Polynomial.polynomial_map_coe, HahnSeries.toPowerSeries_symm_apply_coeff, LaurentSeries.coeff_coe_powerSeries, Polynomial.IsDistinguishedAt.algEquivQuotient_apply, order_add_of_order_eq, coeff_one_mul, monomial_zero_eq_C_apply, map_toSubring, Nat.Partition.multipliable_genFun, Polynomial.coe_pow, IsRestricted.C, HahnSeries.SummableFamily.powerSeriesFamily_smul, derivative_inv, derivativeFun_mul, coe_substAlgHom, rescale_mul, map.isLocalHom, invOneSubPow_val_succ_eq_mk_add_choose, coeff_X_pow_mul, map_injective, weierstrassDistinguished_smul, LaurentSeries.valuation_X_pow, Nat.Partition.genFun_eq_tprod, trunc_C_mul, instIsNoetherianRing, derivative_pow
instZero πŸ“–CompOp
46 mathmath: qExpansion_eq_zero_iff, zero_weierstrassDiv, IsWeierstrassDivisorAt.div_coe_eq_zero, zero_weierstrassMod, Unit_of_divided_by_X_pow_order_zero, Polynomial.coe_eq_zero_iff, Polynomial.IsDistinguishedAt.degree_eq_coe_lift_order_map, gaussNorm_zero, derivativeFun_C, weierstrassDiv_zero, X_inv, order_zero, weierstrassDiv_zero_right, HasSubst.zero', WithPiTopology.isTopologicallyNilpotent_iff_constantCoeff_isNilpotent, map_eq_zero, coe_zero, zero_inv, inv_eq_zero, weierstrassMod_zero_left, instNoZeroDivisors, derivativeFun_one, constantCoeff_divXPowOrder_eq_zero_iff, constantCoeff_zero, forall_coeff_eq_zero, IsWeierstrassDivisorAt.mod_zero, gaussNorm_eq_zero_iff, IsWeierstrassFactorization.degree_eq_coe_lift_order_map, IsWeierstrassFactorizationAt.degree_eq_coe_lift_order_map_of_ne_top, IsWeierstrassDivisorAt.eq_zero_of_mul_eq, WithPiTopology.isTopologicallyNilpotent_of_constantCoeff_isNilpotent, Polynomial.coe_zero, order_eq_top, IsWeierstrassDivisorAt.div_zero, derivative_C, weierstrassMod_zero_right, weierstrassMod_zero, qExpansion_zero, WithPiTopology.isTopologicallyNilpotent_of_constantCoeff_zero, weierstrassDiv_zero_left, LaurentSeries.powerSeriesPart_zero, IsWeierstrassDivisorAt.seq_zero, isWeierstrassDivisionAt_zero, divXPowOrder_zero, IsRestricted.zero, LaurentSeries.powerSeriesPart_eq_zero
map πŸ“–CompOp
36 mathmath: algebraMap_apply'', degree_weierstrassMod_lt, mapAlgHom_apply, Polynomial.IsDistinguishedAt.degree_eq_coe_lift_order_map, map_cos, IsWeierstrassFactorization.isWeierstrassDivision, IsWeierstrassDivisionAt.degree_lt, IsWeierstrassFactorizationAt.natDegree_eq_toNat_order_map_of_ne_top, le_order_map, map_sin, IsWeierstrassFactorization.natDegree_eq_toNat_order_map, map_eq_zero, IsWeierstrassDivisorAt.isUnit_shift, map_X, map_comp, map_subst, map_algebraMap_eq_subst_X, map_surjective, map_invUnitsSub, Polynomial.coeToPowerSeries.algHom_apply, coeff_map, map_expand, map_C, IsWeierstrassFactorization.degree_eq_coe_lift_order_map, IsWeierstrassFactorizationAt.degree_eq_coe_lift_order_map_of_ne_top, isWeierstrassDivisionAt_iff, map_exp, algebraMap_apply', IsWeierstrassDivisorAt.seq_one, map_id, trunc_map, Polynomial.polynomial_map_coe, map_toSubring, map.isLocalHom, map_injective, Polynomial.IsDistinguishedAt.coe_natDegree_eq_order_map
mapAlgHom πŸ“–CompOp
1 mathmath: mapAlgHom_apply
mk πŸ“–CompOpβ€”
monomial πŸ“–CompOp
21 mathmath: gaussNorm_monomial, Polynomial.coe_monomial, hasSum_of_monomials_self, order_monomial, monomial_mul_monomial, prod_monomial, monomial_zero_eq_C, monomial_pow, HasSubst.monomial', monomial_eq_mk, X_eq, coeff_comp_monomial, coeff_monomial_same, coeff_monomial, as_tsum, X_pow_eq, monomial_eq_C_mul_X_pow, expand_monomial, IsRestricted.monomial, monomial_zero_eq_C_apply, order_monomial_of_ne_zero
rescale πŸ“–CompOp
15 mathmath: coeff_rescale, MvPowerSeries.rescaleUnit, rescale_X, Polynomial.bernoulli_generating_function, rescale_rescale, rescale_zero_apply, rescale_zero, rescale_mk, exp_mul_exp_eq_exp_add, rescale_injective, exp_pow_eq_rescale_exp, rescale_neg_one_X, rescale_one, rescale_neg_one_invOneSubPow, rescale_mul
toSubring πŸ“–CompOp
4 mathmath: coeff_toSubring, order_toSubring, constantCoeff_toSubring, map_toSubring
Β«term_⟦X⟧» πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
C_eq_algebraMap πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instSemiring
RingHom.instFunLike
C
algebraMap
instAlgebra
Algebra.id
β€”β€”
C_injective πŸ“–mathematicalβ€”PowerSeries
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
instSemiring
RingHom.instFunLike
C
β€”coeff_zero_C
X_dvd_iff πŸ“–mathematicalβ€”PowerSeries
semigroupDvd
SemigroupWithZero.toSemigroup
NonUnitalSemiring.toSemigroupWithZero
Semiring.toNonUnitalSemiring
instSemiring
X
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
constantCoeff
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
β€”pow_one
X_pow_dvd_iff
coeff_zero_eq_constantCoeff_apply
zero_lt_one
Nat.instZeroLEOneClass
X_eq πŸ“–mathematicalβ€”X
DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instAddCommMonoid
Semiring.toModule
instModule
LinearMap.instFunLike
monomial
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”β€”
X_mul πŸ“–mathematicalβ€”PowerSeries
MvPowerSeries.instMul
X
β€”MvPowerSeries.X_mul
X_mul_cancel πŸ“–β€”PowerSeries
MvPowerSeries.instMul
X
β€”β€”ext_iff
coeff_succ_X_mul
X_mul_inj πŸ“–mathematicalβ€”PowerSeries
MvPowerSeries.instMul
X
β€”X_mul_injective
X_mul_injective πŸ“–mathematicalβ€”PowerSeries
MvPowerSeries.instMul
X
β€”X_mul_cancel
X_ne_zero πŸ“–β€”β€”β€”β€”coeff_one_X
map_zero
AddMonoidHomClass.toZeroHomClass
DistribMulActionSemiHomClass.toAddMonoidHomClass
SemilinearMapClass.distribMulActionSemiHomClass
LinearMap.semilinearMapClass
NeZero.one
X_pow_dvd_iff πŸ“–mathematicalβ€”PowerSeries
semigroupDvd
SemigroupWithZero.toSemigroup
NonUnitalSemiring.toSemigroupWithZero
Semiring.toNonUnitalSemiring
instSemiring
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
X
DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”Finsupp.unique_single
Finsupp.single_eq_same
MvPowerSeries.X_pow_dvd_iff
X_pow_eq πŸ“–mathematicalβ€”PowerSeries
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
X
DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instAddCommMonoid
Semiring.toModule
instModule
LinearMap.instFunLike
monomial
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”MvPowerSeries.X_pow_eq
X_pow_mul πŸ“–mathematicalβ€”PowerSeries
MvPowerSeries.instMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
X
β€”MvPowerSeries.X_pow_mul
X_pow_mul_cancel πŸ“–β€”PowerSeries
MvPowerSeries.instMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
X
β€”β€”ext_iff
coeff_X_pow_mul
X_pow_mul_inj πŸ“–mathematicalβ€”PowerSeries
MvPowerSeries.instMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
X
β€”X_pow_mul_injective
X_pow_mul_injective πŸ“–mathematicalβ€”PowerSeries
MvPowerSeries.instMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
X
β€”X_pow_mul_cancel
algebraMap_apply πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instSemiring
RingHom.instFunLike
algebraMap
instAlgebra
C
β€”MvPowerSeries.algebraMap_apply
algebraMap_apply' πŸ“–mathematicalβ€”DFunLike.coe
RingHom
Polynomial
CommSemiring.toSemiring
PowerSeries
Semiring.toNonAssocSemiring
Polynomial.commSemiring
instSemiring
RingHom.instFunLike
algebraMap
algebraPolynomial
map
Polynomial.toPowerSeries
β€”β€”
algebraMap_apply'' πŸ“–mathematicalβ€”DFunLike.coe
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NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
RingHom
instSemiring
RingHom.instFunLike
C
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
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coeff_C_mul πŸ“–mathematicalβ€”DFunLike.coe
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Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
MvPowerSeries.instMul
RingHom
instSemiring
RingHom.instFunLike
C
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
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RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
MvPowerSeries.instMul
RingHom
instSemiring
RingHom.instFunLike
C
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
X
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”X_pow_eq
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mul_ite
mul_one
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RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
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NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
X
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
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coeff_X_pow πŸ“–mathematicalβ€”DFunLike.coe
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RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
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NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
X
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”X_pow_eq
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RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
MvPowerSeries.instMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
X
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Finset.sum_eq_single
coeff_X_pow
add_right_cancel_iff
AddRightCancelSemigroup.toIsRightCancelAdd
add_comm
Finset.HasAntidiagonal.mem_antidiagonal
MulZeroClass.zero_mul
one_mul
coeff_X_pow_mul' πŸ“–mathematicalβ€”DFunLike.coe
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RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
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NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
MvPowerSeries.instMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
X
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
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Nat.instIsOrderedAddMonoid
Nat.instOrderedSub
coeff_X_pow_mul
add_tsub_cancel_right
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
coeff_mul
Finset.sum_eq_zero
coeff_X_pow
Finset.HasAntidiagonal.mem_antidiagonal
LT.lt.ne
LE.le.trans_lt
le_of_add_le_right
Eq.le
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not_le
MulZeroClass.zero_mul
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RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
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NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
X
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”coeff_X_pow
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PowerSeries
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monomial
LinearMap.id
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MvPowerSeries.coeff
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PowerSeries
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NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
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Semiring.toModule
LinearMap.instFunLike
coeff
RingHom
instSemiring
RingHom.instFunLike
map
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RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
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NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
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Semiring.toModule
LinearMap.instFunLike
coeff
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RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
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NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
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Semiring.toModule
LinearMap.instFunLike
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monomial
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”MvPowerSeries.coeff_monomial
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RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
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NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
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Semiring.toModule
LinearMap.instFunLike
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monomial
β€”MvPowerSeries.coeff_monomial_same
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RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
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NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
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Semiring.toModule
LinearMap.instFunLike
coeff
MvPowerSeries.instMul
Finset.sum
Finset.HasAntidiagonal.antidiagonal
Nat.instAddMonoid
Finset.Nat.instHasAntidiagonal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
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Finsupp.antidiagonal_single
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RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
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NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
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Semiring.toModule
LinearMap.instFunLike
coeff
MvPowerSeries.instMul
RingHom
instSemiring
RingHom.instFunLike
C
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
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RingHom.id
Semiring.toNonAssocSemiring
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instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
MvPowerSeries.instMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
X
β€”coeff_mul
Finset.sum_eq_single
coeff_X_pow
add_right_cancel_iff
AddRightCancelSemigroup.toIsRightCancelAdd
Finset.HasAntidiagonal.mem_antidiagonal
MulZeroClass.mul_zero
mul_one
coeff_mul_X_pow' πŸ“–mathematicalβ€”DFunLike.coe
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RingHom.id
Semiring.toNonAssocSemiring
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NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
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Semiring.toModule
LinearMap.instFunLike
coeff
MvPowerSeries.instMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
X
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
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CanonicallyOrderedAdd.toExistsAddOfLE
Nat.instCanonicallyOrderedAdd
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
Nat.instOrderedSub
coeff_mul_X_pow
add_tsub_cancel_right
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
coeff_mul
Finset.sum_eq_zero
coeff_X_pow
LT.lt.ne
LE.le.trans_lt
le_of_add_le_right
Eq.le
Finset.HasAntidiagonal.mem_antidiagonal
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MulZeroClass.mul_zero
coeff_ne_zero_C πŸ“–mathematicalβ€”DFunLike.coe
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RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
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NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
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Semiring.toModule
LinearMap.instFunLike
coeff
RingHom
instSemiring
RingHom.instFunLike
C
MulZeroClass.toZero
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PowerSeries
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NonUnitalNonAssocSemiring.toAddCommMonoid
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Semiring.toModule
LinearMap.instFunLike
coeff
MvPowerSeries.instOne
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
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NonUnitalNonAssocSemiring.toMulZeroClass
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PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
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Semiring.toModule
LinearMap.instFunLike
coeff
X
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AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”coeff_X
coeff_one_mul πŸ“–mathematicalβ€”DFunLike.coe
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Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
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Semiring.toModule
LinearMap.instFunLike
coeff
MvPowerSeries.instMul
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
Distrib.toMul
RingHom
instSemiring
RingHom.instFunLike
constantCoeff
β€”coeff_mul
Finset.sum_insert
Finset.sum_singleton
coeff_zero_eq_constantCoeff
mul_comm
add_comm
coeff_one_pow πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
CommSemiring.toSemiring
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
RingHom
RingHom.instFunLike
constantCoeff
β€”pow_zero
coeff_one
Nat.cast_zero
MulZeroClass.zero_mul
zero_tsub
Nat.instCanonicallyOrderedAdd
Nat.instOrderedSub
mul_one
coeff_mul
Finset.sum_insert
Finset.sum_singleton
coeff_zero_eq_constantCoeff
map_pow
MonoidWithZeroHomClass.toMonoidHomClass
RingHomClass.toMonoidWithZeroHomClass
RingHom.instRingHomClass
Nat.cast_add
Nat.cast_one
add_tsub_cancel_right
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
Mathlib.Meta.NormNum.IsNat.to_eq
Mathlib.Meta.NormNum.isNat_add
Mathlib.Meta.NormNum.isNat_natCast
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one_mul
add_zero
mul_comm
mul_assoc
mul_left_comm
pow_one
pow_add
Mathlib.Tactic.Ring.of_eq
Mathlib.Tactic.Ring.add_congr
Mathlib.Tactic.Ring.mul_congr
Mathlib.Tactic.Ring.pow_congr
Mathlib.Tactic.Ring.atom_pf
Mathlib.Tactic.Ring.pow_add
Mathlib.Tactic.Ring.single_pow
Mathlib.Tactic.Ring.mul_pow
Mathlib.Tactic.Ring.mul_pf_right
Mathlib.Tactic.Ring.one_mul
Mathlib.Tactic.Ring.one_pow
Mathlib.Tactic.Ring.pow_zero
Mathlib.Tactic.Ring.add_mul
Mathlib.Tactic.Ring.mul_add
Mathlib.Tactic.Ring.mul_pf_left
Mathlib.Tactic.Ring.mul_zero
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Mathlib.Tactic.Ring.zero_mul
Mathlib.Tactic.Ring.add_pf_add_lt
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coeff_pow πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
CommSemiring.toSemiring
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Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
Finset.sum
Finsupp
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Nat.instAddCommMonoid
Finset.finsuppAntidiag
Finset.Nat.instHasAntidiagonal
Finset.range
Finset.prod
CommSemiring.toCommMonoid
Finsupp.instFunLike
β€”Finset.prod_range_induction
coeff_prod
coeff_prod πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
CommSemiring.toSemiring
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
Finset.prod
CommSemiring.toCommMonoid
instCommSemiring
Finset.sum
Finsupp
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Nat.instAddCommMonoid
Finset.finsuppAntidiag
Finset.Nat.instHasAntidiagonal
Finsupp.instFunLike
β€”Finset.sum_congr
Finset.prod_congr
MvPowerSeries.coeff_prod
AddEquiv.finsuppUnique_symm
Finset.mapRange_finsuppAntidiag_eq
Finset.sum_map
coeff_rescale πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
CommSemiring.toSemiring
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
RingHom
instSemiring
RingHom.instFunLike
rescale
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
β€”β€”
coeff_smul πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
instAddMonoid
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
β€”β€”
coeff_succ_C πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
RingHom
instSemiring
RingHom.instFunLike
C
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”coeff_ne_zero_C
coeff_succ_X_mul πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
MvPowerSeries.instMul
X
β€”add_comm
Finsupp.single_add
one_mul
MvPowerSeries.coeff_add_monomial_mul
coeff_succ_mul_X πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
MvPowerSeries.instMul
X
β€”Finsupp.single_add
mul_one
MvPowerSeries.coeff_add_mul_monomial
coeff_toSubring πŸ“–mathematicalSubring
SetLike.instMembership
Subring.instSetLike
DFunLike.coe
LinearMap
Ring.toSemiring
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
Subring.toRing
toSubring
β€”toSubring.eq_1
coeff_zero_C πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
RingHom
instSemiring
RingHom.instFunLike
C
β€”coeff_C
coeff_zero_X πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
X
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”coeff.eq_1
Finsupp.single_zero
X.eq_1
MvPowerSeries.coeff_zero_X
coeff_zero_X_mul πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
MvPowerSeries.instMul
X
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”coeff_zero_eq_constantCoeff
map_mul
NonUnitalRingHomClass.toMulHomClass
RingHomClass.toNonUnitalRingHomClass
RingHom.instRingHomClass
constantCoeff_X
MulZeroClass.zero_mul
coeff_zero_eq_constantCoeff πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
RingHom
instSemiring
RingHom.instFunLike
constantCoeff
β€”coeff.eq_1
Finsupp.single_zero
coeff_zero_eq_constantCoeff_apply πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
RingHom
instSemiring
RingHom.instFunLike
constantCoeff
β€”coeff_zero_eq_constantCoeff
coeff_zero_mul_X πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
MvPowerSeries.instMul
X
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”coeff_zero_eq_constantCoeff
map_mul
NonUnitalRingHomClass.toMulHomClass
RingHomClass.toNonUnitalRingHomClass
RingHom.instRingHomClass
constantCoeff_X
MulZeroClass.mul_zero
coeff_zero_one πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
MvPowerSeries.instOne
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”coeff_zero_C
commute_X πŸ“–mathematicalβ€”Commute
PowerSeries
MvPowerSeries.instMul
X
β€”MvPowerSeries.commute_X
commute_X_pow πŸ“–mathematicalβ€”Commute
PowerSeries
MvPowerSeries.instMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
X
β€”MvPowerSeries.commute_X_pow
constantCoeff_C πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
instSemiring
RingHom.instFunLike
constantCoeff
C
β€”β€”
constantCoeff_X πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
instSemiring
RingHom.instFunLike
constantCoeff
X
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
β€”MvPowerSeries.coeff_zero_X
constantCoeff_comp_C πŸ“–mathematicalβ€”RingHom.comp
PowerSeries
Semiring.toNonAssocSemiring
instSemiring
constantCoeff
C
RingHom.id
β€”β€”
constantCoeff_mk πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
instSemiring
RingHom.instFunLike
constantCoeff
β€”β€”
constantCoeff_one πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
instSemiring
RingHom.instFunLike
constantCoeff
MvPowerSeries.instOne
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”β€”
constantCoeff_smul πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
instSemiring
RingHom.instFunLike
constantCoeff
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
instAddMonoid
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
β€”β€”
constantCoeff_surj πŸ“–mathematicalβ€”PowerSeries
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
instSemiring
RingHom.instFunLike
constantCoeff
β€”constantCoeff_C
constantCoeff_toSubring πŸ“–mathematicalSubring
SetLike.instMembership
Subring.instSetLike
DFunLike.coe
LinearMap
Ring.toSemiring
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
RingHom
instSemiring
Subring.toRing
RingHom.instFunLike
constantCoeff
toSubring
β€”coeff_zero_eq_constantCoeff_apply
constantCoeff_zero πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
instSemiring
RingHom.instFunLike
constantCoeff
instZero
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
β€”β€”
eq_X_mul_shift_add_const πŸ“–mathematicalβ€”PowerSeries
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiring
MvPowerSeries.instMul
X
DFunLike.coe
LinearMap
RingHom.id
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
RingHom
RingHom.instFunLike
C
constantCoeff
β€”ext
coeff_zero_eq_constantCoeff
map_add
SemilinearMapClass.toAddHomClass
LinearMap.semilinearMapClass
map_mul
NonUnitalRingHomClass.toMulHomClass
RingHomClass.toNonUnitalRingHomClass
RingHom.instRingHomClass
constantCoeff_X
MulZeroClass.zero_mul
coeff_zero_C
zero_add
coeff_succ_X_mul
coeff_C
add_zero
eq_shift_mul_X_add_const πŸ“–mathematicalβ€”PowerSeries
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiring
MvPowerSeries.instMul
DFunLike.coe
LinearMap
RingHom.id
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
X
RingHom
RingHom.instFunLike
C
constantCoeff
β€”ext
coeff_zero_eq_constantCoeff
map_add
SemilinearMapClass.toAddHomClass
LinearMap.semilinearMapClass
map_mul
NonUnitalRingHomClass.toMulHomClass
RingHomClass.toNonUnitalRingHomClass
RingHom.instRingHomClass
constantCoeff_X
MulZeroClass.mul_zero
coeff_zero_C
zero_add
coeff_succ_mul_X
coeff_C
add_zero
evalNegHom_X πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
instSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
evalNegHom
X
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
instAddCommGroup
Ring.toAddCommGroup
CommRing.toRing
β€”rescale_neg_one_X
ext πŸ“–β€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
β€”β€”MvPowerSeries.ext
coeff_def
ext_iff πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
β€”ext
forall_coeff_eq_zero πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
instZero
β€”ext
map_zero
AddMonoidHomClass.toZeroHomClass
DistribMulActionSemiHomClass.toAddMonoidHomClass
SemilinearMapClass.distribMulActionSemiHomClass
LinearMap.semilinearMapClass
instIsScalarTower πŸ“–mathematicalβ€”IsScalarTower
PowerSeries
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
instAddMonoid
AddCommMonoid.toAddMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
instAddCommMonoid
instModule
β€”Pi.isScalarTower
instNontrivial πŸ“–mathematicalβ€”Nontrivial
PowerSeries
β€”MvPowerSeries.instNontrivial
instNontrivialSubalgebra πŸ“–mathematicalβ€”Nontrivial
Subalgebra
PowerSeries
instSemiring
CommSemiring.toSemiring
instAlgebra
Algebra.id
β€”MvPowerSeries.instNontrivialSubalgebraOfNonempty
instSubsingleton πŸ“–mathematicalβ€”PowerSeriesβ€”β€”
isUnit_constantCoeff πŸ“–mathematicalIsUnit
PowerSeries
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
constantCoeff
β€”MvPowerSeries.isUnit_constantCoeff
mapAlgHom_apply πŸ“–mathematicalβ€”DFunLike.coe
AlgHom
PowerSeries
instSemiring
instAlgebra
AlgHom.funLike
mapAlgHom
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
map
RingHomClass.toRingHom
AlgHomClass.toRingHomClass
AlgHom.algHomClass
β€”MvPowerSeries.mapAlgHom_apply
map_C πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
instSemiring
RingHom.instFunLike
map
C
β€”ext
coeff_C
map_zero
MonoidWithZeroHomClass.toZeroHomClass
RingHomClass.toMonoidWithZeroHomClass
RingHom.instRingHomClass
map_X πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
instSemiring
RingHom.instFunLike
map
X
β€”ext
coeff_X
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
RingHomClass.toMonoidWithZeroHomClass
RingHom.instRingHomClass
map_zero
MonoidWithZeroHomClass.toZeroHomClass
map_comp πŸ“–mathematicalβ€”map
RingHom.comp
Semiring.toNonAssocSemiring
PowerSeries
instSemiring
β€”β€”
map_eq_zero πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
instSemiring
DivisionSemiring.toSemiring
RingHom.instFunLike
map
instZero
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
β€”MvPowerSeries.map_eq_zero
map_id πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
instSemiring
RingHom.instFunLike
map
RingHom.id
β€”β€”
map_injective πŸ“–mathematicalDFunLike.coe
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
PowerSeries
instSemiring
map
β€”ext
coeff_map
map_surjective πŸ“–mathematicalDFunLike.coe
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
PowerSeries
instSemiring
map
β€”ext
map_toSubring πŸ“–mathematicalSubring
SetLike.instMembership
Subring.instSetLike
DFunLike.coe
LinearMap
Ring.toSemiring
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
LinearMap.instFunLike
coeff
RingHom
instSemiring
Subring.toRing
RingHom.instFunLike
map
Subring.subtype
toSubring
β€”ext
coeff_toSubring
monomial_eq_mk πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instAddCommMonoid
Semiring.toModule
instModule
LinearMap.instFunLike
monomial
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”ext
coeff_monomial
monomial_mul_monomial πŸ“–mathematicalβ€”PowerSeries
MvPowerSeries.instMul
DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instAddCommMonoid
Semiring.toModule
instModule
LinearMap.instFunLike
monomial
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”Finsupp.single_add
MvPowerSeries.monomial_mul_monomial
monomial_pow πŸ“–mathematicalβ€”PowerSeries
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
CommSemiring.toSemiring
DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instAddCommMonoid
Semiring.toModule
instModule
LinearMap.instFunLike
monomial
β€”Finsupp.smul_single
MvPowerSeries.monomial_pow
monomial_zero_eq_C πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instAddCommMonoid
Semiring.toModule
instModule
LinearMap.instFunLike
monomial
RingHom
instSemiring
RingHom.instFunLike
C
β€”monomial.eq_1
Finsupp.single_zero
MvPowerSeries.monomial_zero_eq_C
monomial_zero_eq_C_apply πŸ“–mathematicalβ€”DFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
PowerSeries
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instAddCommMonoid
Semiring.toModule
instModule
LinearMap.instFunLike
monomial
RingHom
instSemiring
RingHom.instFunLike
C
β€”monomial_zero_eq_C
mul_X_cancel πŸ“–β€”PowerSeries
MvPowerSeries.instMul
X
β€”β€”ext_iff
coeff_succ_mul_X
mul_X_inj πŸ“–mathematicalβ€”PowerSeries
MvPowerSeries.instMul
X
β€”mul_X_injective
mul_X_injective πŸ“–mathematicalβ€”PowerSeries
MvPowerSeries.instMul
X
β€”mul_X_cancel
mul_X_pow_cancel πŸ“–β€”PowerSeries
MvPowerSeries.instMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
X
β€”β€”ext_iff
coeff_mul_X_pow
mul_X_pow_inj πŸ“–mathematicalβ€”PowerSeries
MvPowerSeries.instMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
X
β€”mul_X_pow_injective
mul_X_pow_injective πŸ“–mathematicalβ€”PowerSeries
MvPowerSeries.instMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
X
β€”mul_X_pow_cancel
not_isField πŸ“–mathematicalβ€”IsField
PowerSeries
instSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
β€”not_isField_of_subsingleton
instSubsingleton
Mathlib.Tactic.Nontriviality.subsingleton_or_nontrivial_elim
Ring.not_isField_iff_exists_ideal_bot_lt_and_lt_top
instNontrivial
bot_lt_iff_ne_bot
Ideal.span_singleton_eq_bot
X_ne_zero
lt_top_iff_ne_top
Ideal.eq_top_iff_one
Ideal.mem_span_singleton
X_dvd_iff
constantCoeff_one
one_ne_zero
NeZero.one
prod_monomial πŸ“–mathematicalβ€”Finset.prod
PowerSeries
CommSemiring.toCommMonoid
instCommSemiring
DFunLike.coe
LinearMap
CommSemiring.toSemiring
RingHom.id
Semiring.toNonAssocSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instAddCommMonoid
Semiring.toModule
instModule
LinearMap.instFunLike
monomial
Finset.sum
Nat.instAddCommMonoid
β€”Finset.prod_congr
Finsupp.single_finset_sum
MvPowerSeries.prod_monomial
rescale_X πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
instSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
rescale
X
MvPowerSeries.instMul
C
β€”ext
coeff_rescale
coeff_X
coeff_C_mul
pow_one
mul_one
MulZeroClass.mul_zero
rescale_mk πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
instSemiring
CommSemiring.toSemiring
RingHom.instFunLike
rescale
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
β€”ext
coeff_rescale
rescale_mul πŸ“–mathematicalβ€”rescale
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
RingHom.comp
PowerSeries
instSemiring
β€”RingHom.ext
ext
coeff_rescale
rescale_neg_one_X πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
instSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
rescale
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
CommRing.toRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
X
instAddCommGroup
β€”rescale_X
map_neg
RingHomClass.toAddMonoidHomClass
RingHom.instRingHomClass
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
RingHomClass.toMonoidWithZeroHomClass
neg_one_mul
rescale_one πŸ“–mathematicalβ€”rescale
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
RingHom.id
PowerSeries
instSemiring
β€”RingHom.ext
ext
coeff_rescale
one_pow
one_mul
rescale_rescale πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
instSemiring
CommSemiring.toSemiring
RingHom.instFunLike
rescale
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
β€”ext
coeff_rescale
mul_pow
mul_comm
mul_assoc
rescale_zero πŸ“–mathematicalβ€”rescale
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
RingHom.comp
PowerSeries
instSemiring
C
constantCoeff
β€”RingHom.ext
ext
coeff_C
pow_zero
coeff_zero_eq_constantCoeff
one_mul
zero_pow
MulZeroClass.zero_mul
rescale_zero_apply πŸ“–mathematicalβ€”DFunLike.coe
RingHom
PowerSeries
Semiring.toNonAssocSemiring
instSemiring
CommSemiring.toSemiring
RingHom.instFunLike
rescale
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
C
constantCoeff
β€”rescale_zero
smul_eq_C_mul πŸ“–mathematicalβ€”PowerSeries
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
instAddMonoid
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
instAddCommMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
instModule
Semiring.toModule
MvPowerSeries.instMul
DFunLike.coe
RingHom
instSemiring
RingHom.instFunLike
C
β€”ext
map_smul
SemilinearMapClass.toMulActionSemiHomClass
LinearMap.semilinearMapClass
coeff_C_mul
subsingleton_iff πŸ“–mathematicalβ€”PowerSeriesβ€”subsingleton_iff
C_injective
instSubsingleton

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