[Merged by Bors] - feat: characterize roots of unity in cyclotomic extensions #10710
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Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>
Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>
Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>
Co-authored-by: Michael Stoll <99838730+MichaelStollBayreuth@users.noreply.github.com>
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🚀 Pull request has been placed on the maintainer queue by Ruben-VandeVelde. |
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Mar 28, 2024
We add `IsPrimitiveRoot.exists_pow_or_neg_mul_pow_of_isOfFinOrder`: If `x` is a root of unity (spelled as `IsOfFinOrder x`) in an `n`-th cyclotomic extension of `ℚ`, where `n` is odd, and `ζ` is a primitive `n`-th root of unity, then there exists `r < n` such that `x = ζ^r` or `x = -ζ^r`. From flt-regular - [x] depends on: #11235
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Louddy
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Apr 15, 2024
We add `IsPrimitiveRoot.exists_pow_or_neg_mul_pow_of_isOfFinOrder`: If `x` is a root of unity (spelled as `IsOfFinOrder x`) in an `n`-th cyclotomic extension of `ℚ`, where `n` is odd, and `ζ` is a primitive `n`-th root of unity, then there exists `r < n` such that `x = ζ^r` or `x = -ζ^r`. From flt-regular - [x] depends on: #11235
atarnoam
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Apr 16, 2024
We add `IsPrimitiveRoot.exists_pow_or_neg_mul_pow_of_isOfFinOrder`: If `x` is a root of unity (spelled as `IsOfFinOrder x`) in an `n`-th cyclotomic extension of `ℚ`, where `n` is odd, and `ζ` is a primitive `n`-th root of unity, then there exists `r < n` such that `x = ζ^r` or `x = -ζ^r`. From flt-regular - [x] depends on: #11235
uniwuni
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Apr 19, 2024
We add `IsPrimitiveRoot.exists_pow_or_neg_mul_pow_of_isOfFinOrder`: If `x` is a root of unity (spelled as `IsOfFinOrder x`) in an `n`-th cyclotomic extension of `ℚ`, where `n` is odd, and `ζ` is a primitive `n`-th root of unity, then there exists `r < n` such that `x = ζ^r` or `x = -ζ^r`. From flt-regular - [x] depends on: #11235
callesonne
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Apr 22, 2024
We add `IsPrimitiveRoot.exists_pow_or_neg_mul_pow_of_isOfFinOrder`: If `x` is a root of unity (spelled as `IsOfFinOrder x`) in an `n`-th cyclotomic extension of `ℚ`, where `n` is odd, and `ζ` is a primitive `n`-th root of unity, then there exists `r < n` such that `x = ζ^r` or `x = -ζ^r`. From flt-regular - [x] depends on: #11235
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We add
IsPrimitiveRoot.exists_pow_or_neg_mul_pow_of_isOfFinOrder: Ifxis a root of unity (spelled asIsOfFinOrder x) in ann-th cyclotomic extension ofℚ, wherenis odd, andζis a primitiven-th root of unity, then there existsr < nsuch thatx = ζ^rorx = -ζ^r.From flt-regular