Add gcd/lcm functions

[kiedtl]

This PR adds the gcd and lcm functions.

>> gcd(12, 18)
6
>> lcm(12, 18)
36

GCD is calculated with the modified Euclidean algorithm, and LCM is
calculated with:

             ⎛           ⎞
             ⎜    ⎜a⎜     ⎟
lcm(a, b) =  ⎜ ───────── ⎟ × ⎜b⎜
             ⎜ gcd(a, b) ⎟
             ⎝           ⎠

[kiedtl]

Hmm, what's the proper way to throw a non-terminating error from a
function?

[PaddiM8]

This is a great addition!

Hmm, what's the proper way to throw a non-terminating error from a
function?

Hmm, calculator functions (like the ones you made) currently don't have a lot of options for error handling. It is assumed that any function will return a value. However, I believe some functions simply return NaN when a calculation isn't possible. You could do something like KalkNum::from(f64::NAN), I believe.

Now that I think about it, being able to throw error messages from inside these functions should probably be possible in the future. Then errors would be thrown by returning eg. CalcError::ErrorType(info) like in the rest of the code.

[kiedtl]

Now that I think about it, being able to throw error messages from inside these functions should probably be possible in the future. Then errors would be thrown by returning eg. CalcError::ErrorType(info) like in the rest of the code.

Definitely, it's better UX to throw an informative error message instead of silently returning NaN, which could be annoying to debug if the gcd/lcm call was part of a larger calculation/function call. However, I'll use the NaN solution for now :)

[kiedtl]

Alright, this is ready for review.

[kiedtl]

Oops, wrong button

[PaddiM8]

Great! Would be good if you could also run rustfmt on the file (this should've been mentioned in the README, I'll add that now). Also, I noticed that, when you give it complex numbers, it differs a bit from what eg. WolframAlpha and MathWorks are saying. It gives a result like 10 - 5i while WolframAlpha says 5 + 10i. Would the latter maybe be more of an expected result by users?

[kiedtl]

On 21-10-05 07:14 , PaddiM8 wrote: Also, I noticed that, when you give it complex numbers, it differs a bit from what eg. WolframAlpha and MathWorks are saying. It gives a result like `10 - 5i` while WolframAlpha says `5 + 10i`. Would the latter maybe be more of an expected result by users?

I'm honestly not sure. I had spent some time trying to wrap my head around number domains and other number theory stuff, but then gave up and copied something from SO, which I'm only beginning to feel like I understand. I do know, though, that there can be multiple factorizations for polynomials, so I'm assuming that both of those answers are correct... but I don't know which one would be *preferred*. (Could you double-check that the answer returned by my algorithm is correct and not an edge-case?)

[PaddiM8]

I'm assuming that both of those answers are correct... but I don't know
which one would be preferred.

Yeah this is what I'm thinking as well. When comparing to WolframAlpha, it seems to consistently give the same numbers, but often with the real and imaginary ones swapped, and the sign inverted. From what I can tell, it seems to give correct answers though, so it's probably good enough for now at least!

[PaddiM8]

The "0" constants need to be specified as f64 for it to work when not using rug. Eg. x.value.clone().fract() != 0f64. You can test this by running something like cargo test --no-default-features I believe.

[kiedtl]

Alright, working now

[PaddiM8]

Nice! This looks good now, I'll go ahead and merge it. Excited to have this in kalker.

[PaddiM8]

These can now be used on https://kalker.xyz!