enhance cbrt to work on Complex and to return all cube roots

glen commented

2025-05-07 01:00:24 +00:00

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For now, we will make cbrt with return typing strategy free or full (the default) always return all three cube roots (by analogy with sqrt's default behavior of returning Complex as necessary), but under typing strategy conservative on real inputs return just the real cube root.

This is the last function needed to implement polynomialRoot.

For now, we will make `cbrt` with return typing strategy `free` or `full` (the default) always return all three cube roots (by analogy with `sqrt`'s default behavior of returning Complex as necessary), but under typing strategy `conservative` on real inputs return just the real cube root. This is the last function needed to implement polynomialRoot.

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2025-05-07 01:00:24 +00:00

glen added a new dependency

2025-05-07 01:06:39 +00:00

#30 implement polynomialRoot

glen commented

2025-12-12 10:24:14 +00:00

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Hmm, since every real number has a unique real cube root, I actually think free and conservative should return that real cube root, while full return all three, whereas on complex input, you just always get all three.

Hmm, since every real number has a unique real cube root, I actually think `free` and `conservative` should return that real cube root, while `full` return all three, whereas on complex input, you just always get all three.

glen commented

2025-12-12 15:35:20 +00:00

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The "easiest" way to find a complex cube root is to use polar form. That requires atan2, sin, and cos. Or there appears to be a formula that just uses real cube and square roots at https://mathproofs.jrensen.nl/proofs/cube-root-complex-number. That's a much lengthier formula, but won't involve starting a trigonometry category.

glen referenced this issue from a pull request that will close it,

2025-12-13 07:32:15 +00:00

feat: Fully define complex cube root #39

glen closed this issue

2025-12-13 07:34:02 +00:00

glen referenced this issue from a commit

2025-12-13 07:34:03 +00:00

feat: Fully define complex cube root (#39)

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enhance cbrt to work on Complex and to return all cube roots #29