Exponentiation of rational numbers to integer powers #19883
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r^x for rational r and integer x is just r^x for natural x, or 1/(r^(-x)) for negative integers.
eric-wieser
reviewed
Dec 11, 2024
| def pow_int_exponent (q : ℚ) (n : ℤ) : ℚ := | ||
| if n ≥ 0 | ||
| then q ^ (Int.toNat n) | ||
| else q ^ (Int.toNat (-n)) |
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Didn't you mean to add a 1/ here?
Either way, your instPowInt instance below already exists in mathlib; you can find it with
import Mathlib
#synth Pow ℚ ℤThere was a problem hiding this comment.
(the name of the instance that it finds is bad though; fixed in #19884)
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Didn't you mean to add a
1/here?Either way, your
instPowIntinstance below already exists in mathlib; you can find it withimport Mathlib #synth Pow ℚ ℤ
Ack, yes, that's what I meant, of course. Curious that I wasn't able to find that instance. I think your PR is the right way to do it, so I'm happy to close this PR.
|
Closing this because the functionality I wanted already existed, though was perhaps somewhat opqaue. #19884 is the right solution. |
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r^xfor rationalrand integerxis justr^xfor natural x, or1/(r^(-x))for negative integers. To my surprise, I couldn't find this in the mathlib, though I may well have missed something. The only thing available here is a type class; if a lemma or two would be desired, I'd be happy to continue working on this.