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Theorems · Definition · commutative algebra

HahnSeries.ofPowerSeries

(Γ : Type u_1) →
  (R : Type u_2) →
    [inst : Semiring R] →
      [inst_1 : Semiring Γ] →
        [inst_2 : PartialOrder Γ] → [inst_3 : IsStrictOrderedRing Γ] → PowerSeries R →+* HahnSeries Γ R

Casts a power series as a Hahn series with coefficients from a strictly ordered semiring.

Defined in
Mathlib.RingTheory.HahnSeries.PowerSeries
Cited by
45 results in Mathlib
Foundations
Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringSemiringPartialOrderIsStrictOrderedRing

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LaurentSeries.coe_algebraMap · cited by 5LaurentSeries.coe_algebra…HahnSeries.ofPowerSeries_X · cited by 5HahnSeries.ofPowerSeries_XLaurentSeries.coeff_coe_powerSeries · cited by 3LaurentSeries.coeff_coe_p…LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero · cited by 3LaurentSeries.intValuatio…HahnSeries.ofPowerSeries_C · cited by 3HahnSeries.ofPowerSeries_CHahnSeries.ofPowerSeries_X_pow · cited by 3HahnSeries.ofPowerSeries_…LaurentSeries.single_order_mul_powerSeriesPart · cited by 3LaurentSeries.single_orde…LaurentSeries.powerSeries_as_subring · cited by 3LaurentSeries.powerSeries…LaurentSeries.val_le_one_iff_eq_coe · cited by 3LaurentSeries.val_le_one_…LaurentSeries.valuation_X_pow · cited by 3LaurentSeries.valuation_X…LaurentSeries.valuation_le_iff_coeff_lt_eq_zero · cited by 3LaurentSeries.valuation_l…PowerSeries.coe_pow · cited by 3PowerSeries.coe_powRatFunc.valuation_eq_LaurentSeries_valuation · cited by 2RatFunc.valuation_eq_Laur…RatFunc.coe_X · cited by 2RatFunc.coe_XLaurentSeries.coeff_zero_of_lt_valuation · cited by 2LaurentSeries.coeff_zero_…Semiring · cited by 13802SemiringRingHom · cited by 10189RingHomPartialOrder · cited by 6410PartialOrderIsStrictOrderedRing · cited by 2490IsStrictOrderedRingRingHom.comp · cited by 899RingHom.compPowerSeries · cited by 797PowerSeriesRingEquiv.symm · cited by 567RingEquiv.symmHahnSeries · cited by 528HahnSeriesRingEquiv.toRingHom · cited by 150RingEquiv.toRingHomNat.castAddMonoidHom · cited by 16Nat.castAddMonoidHomHahnSeries.toPowerSeries · cited by 10HahnSeries.toPowerSeriesHahnSeries.embDomainRingHom · cited by 2HahnSeries.embDomainRingH…HahnSeries.ofPowerSeriesCITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by47

Results whose statement or proof uses this declaration.