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feat(Analysis/SpecialFunctions/Complex/Log): natural number versions of exp_eq_one_iff#38015

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feat(Analysis/SpecialFunctions/Complex/Log): natural number versions of exp_eq_one_iff#38015
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@riccardobrasca riccardobrasca commented Apr 13, 2026

Add two lemmas:

  • Complex.exp_eq_one_iff_of_im_nonneg, a variant of Complex.exp_eq_one_iff that gives a natural number instead of an integer, under the hypothesis that the imaginary part is nonneg.
  • Complex.exp_two_pi_mul_I_mul_div_eq_one_iff, showing that exp (2πik/N) = 1 if and only if N ∣ k.

🤖 Generated with Claude Code

…f exp_eq_one_iff

Add `Complex.exp_eq_one_iff_of_im_nonneg`, a variant of `Complex.exp_eq_one_iff`
that produces a natural number instead of an integer, under the hypothesis that
the imaginary part is nonneg.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
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github-actions bot commented Apr 13, 2026

PR summary bdd1fc861b

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ exp_eq_one_iff_of_im_nonneg
+ exp_two_pi_mul_I_mul_div_eq_one_iff

You can run this locally as follows
## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

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

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


No changes to technical debt.

You can run this locally as

./scripts/reporting/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).

@github-actions github-actions bot added the t-analysis Analysis (normed *, calculus) label Apr 13, 2026
@riccardobrasca riccardobrasca added the WIP Work in progress label Apr 13, 2026
riccardobrasca and others added 3 commits April 13, 2026 20:55
…ff N divides k

Add `Complex.exp_two_pi_mul_I_mul_div_eq_one_iff`: for natural numbers
`k` and `N` with `N ≠ 0`, `exp (2 * π * I * k / N) = 1 ↔ N ∣ k`.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
@riccardobrasca riccardobrasca removed the WIP Work in progress label Apr 13, 2026
@riccardobrasca riccardobrasca changed the title feat(Analysis/SpecialFunctions/Complex/Log): natural number version of exp_eq_one_iff feat(Analysis/SpecialFunctions/Complex/Log): natural number versions of exp_eq_one_iff Apr 13, 2026
@grunweg grunweg added the LLM-generated PRs with substantial input from LLMs - review accordingly label Apr 14, 2026
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