feat(NumberField/Cyclotomic): splitting of the prime p in the p^k-th cyclotomic field

[xroblot]

The prime ideal above the prime p in the p^k-th cyclotomic field is totally ramified.

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[github-actions]

PR summary 1838dfbf5d

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal (new file)	2535

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Declarations diff

+ absNorm_eq_pow_inertiaDeg'
+ absNorm_span_zeta_sub_one
+ associated_map_sub_one_map_sub_one
+ associated_norm_zeta_sub_one
+ associated_sub_one_map_sub_one
+ eq_span_zeta_sub_one_of_liesOver
+ finrank
+ inertiaDeg_eq_of_prime_pow
+ inertiaDeg_span_zeta_sub_one
+ isPrime_span_zeta_sub_one
+ liesOver_span_zeta_sub_one
+ map_eq_span_zeta_sub_one_pow
+ ncard_primesOver_of_prime_pow
+ p_mem_span_zeta_sub_one
+ ramificationIdx_eq_of_prime_pow
+ ramificationIdx_span_zeta_sub_one
+ span_zeta_sub_one_ne_bot

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[riccardobrasca]

@erdOne do you know it there are plans to add a IsTotallyRamified predicate?

[riccardobrasca]

Can you put {R : Type*} [CommRing R] [Algebra R A] in a variable line? Maybe at the beginning of the file.

[riccardobrasca]

Suggested change

	(hζ : IsPrimitiveRoot ζ n) {σ τ : A ≃ₐ[R] A} :
	(hζ : IsPrimitiveRoot ζ n) (σ τ : A ≃ₐ[R] A) :

[riccardobrasca]

Suggested change

	apply hζ.associated_pow_sub_one_pow_of_coprime
	· exact ZMod.val_coe_unit_coprime ((autToPow R hζ) τ)
	· exact ZMod.val_coe_unit_coprime ((autToPow R hζ) σ)
	apply hζ.associated_pow_sub_one_pow_of_coprime <;>
	exact ZMod.val_coe_unit_coprime ((autToPow R hζ) _)

Untested.

[riccardobrasca]

Suggested change

	theorem associated_norm_zeta_sub_one : Associated (Algebra.norm ℤ (hζ.toInteger - 1)) (p : ℤ) := by
	by_cases h : p = 2
	· cases k with
	| zero =>
	rw [h, zero_add, pow_one] at hK hζ
	rw [hζ.norm_toInteger_sub_one_of_eq_two, h, Int.ofNat_two, Associated.neg_left_iff]
	| succ n =>
	rw [h, add_assoc, show 1 + 1 = 2 by rfl] at hK hζ
	rw [hζ.norm_toInteger_sub_one_of_eq_two_pow, h, Int.ofNat_two]
	· rw [hζ.norm_toInteger_sub_one_of_prime_ne_two h]
	theorem associated_norm_zeta_sub_one : Associated (Algebra.norm ℤ (hζ.toInteger - 1)) (p : ℤ) := by
	by_cases h : p = 2
	· cases k with
	| zero =>
	rw [h, zero_add, pow_one] at hK hζ
	rw [hζ.norm_toInteger_sub_one_of_eq_two, h, Int.ofNat_two, Associated.neg_left_iff]
	| succ n =>
	rw [h, add_assoc, show 1 + 1 = 2 by rfl] at hK hζ
	rw [hζ.norm_toInteger_sub_one_of_eq_two_pow, h, Int.ofNat_two]
	· rw [hζ.norm_toInteger_sub_one_of_prime_ne_two h]

Just changing the indentation.

[erdOne]

I'm not aware of any.