feat(FieldTheory): X^n - t separable iff n nonzero

[dleijnse]

In a field F, for t : F and n > 0, we prove that the polynomial X ^ n - t is separable if and only if n is nonzero in F. This generalizes X_pow_sub_one_separable_iff, but the extra assumption that n > 0 is needed (for n = 0, the polynomial X ^ n - t is separable iff t is not 1).

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[github-actions[bot]]

PR summary 6626d3a1ec

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Files	Import difference

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Declarations diff

+ X_pow_sub_C_separable_iff

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.

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./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).

[Ruben-VandeVelde]

Please comment -awaiting-author when you've addressed or replied to the comments

[dleijnse]

-awaiting-author

[github-actions[bot]]

🚀 Pull request has been placed on the maintainer queue by robin-carlier.

[mathlib-bors[bot]]

:v: dleijnse can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[mathlib-bors[bot]]

:v: dleijnse can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[dleijnse]

bors r+

[mathlib-bors[bot]]

Pull request successfully merged into master.

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