Is Unit mk of is Coprime
ArkLib.Lattices.CyclotomicModulus.isUnit_mk_of_isCoprime
Plain-language statement
If a is coprime to f then Ideal.Quotient.mk (span {f}) a is a unit.
Exact Lean statement
theorem isUnit_mk_of_isCoprime {a f : (ZMod q)[X]} (h : IsCoprime a f) :
IsUnit (Ideal.Quotient.mk (Ideal.span {f}) a)Formal artifact
Lean source
theorem isUnit_mk_of_isCoprime {a f : (ZMod q)[X]} (h : IsCoprime a f) : IsUnit (Ideal.Quotient.mk (Ideal.span {f}) a) := by obtain ⟨u, v, huv⟩ := h refine IsUnit.of_mul_eq_one (Ideal.Quotient.mk (Ideal.span {f}) u) ?_ have hf : Ideal.Quotient.mk (Ideal.span {f}) f = 0 := Ideal.Quotient.eq_zero_iff_mem.mpr (Ideal.mem_span_singleton_self f) have hkey := congrArg (Ideal.Quotient.mk (Ideal.span {f})) huv rw [map_add, map_mul, map_mul, hf, mul_zero, add_zero, map_one] at hkey rw [mul_comm]; exact hkey- Project
- ArkLib
- License
- Apache-2.0
- Commit
- fad5cbf80877
- Source
- ArkLib/Data/Lattices/CyclotomicRing/NormBounds/LyubashevskySeiler.lean:126-134
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Person-level attribution pending.
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Plain-language statement
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Source project: ArkLib
Person-level attribution pending.