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rational-numbers: Add ordering to spec #1736

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rational-numbers: Add ordering to spec #1736

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24 changes: 24 additions & 0 deletions exercises/rational-numbers/canonical-data.json
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Expand Up @@ -422,6 +422,30 @@
"expected": [1, 1]
}
]
},
{
"uuid": "bd1eab16-7603-4a77-ae4e-23c930fe39cd",
"description": "Ordering",
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I don't have a better alternative, but this description is fairly minimal. Maybe something like Rational numbers can be ordered or something like that?

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The name is in the style of the other names, like "absolute value" or "multiplication". Do you think it should be longer anyway?

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There is some inconsistency in the test naming. I'm fine with keeping it as is therefore, but let's see what others think.

"property": "<",
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In the diffie-hellman exercise, we experimented with using a textual description of the property. This might be useful here too.

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Interesting, didn't know about that exercise. Do you think that format would be better here? I feel like it'd need special handling in generators either way, so I'm not sure if a description like in diffie-hellman has an advantage? It would likely need the comment anyway for extra explanations.

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It would definitely need the comment. I do think a textual property might be somewhat easier to understand. What do you think @SleeplessByte?

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Special handling is required either way (see linked-list); I think written out properties are more consistent with the other exercises.

Wouldn't care here 🤷🏽‍♂️🤗

"comments": [
"Depending on your language's features, you may have to implement the following operators:",
"=, !=, <=, <, >=, >",
"",
"To test the ordering, it's recommended to iterate through a = -5..5, b = -5..5, c = -5..5, d = -5..5,",
"define rational numbers r = a / b, s = c / d,",
"and compare the result of r $op c,",
"where $op = {=, !=, <=, <, >=, >}",
"to the result of the corresponding floating point comparisons",
"a / b $op c. Analogously, compare r $op s with a / b $op c / d.",
"Skip the iteration step when a == b == 0 or c == d == 0, since 0/0 is undefined.",
"",
"Depending on your implementation of the exercise, you may need to consider",
"division by zero differently in the iteration.",
"",
"This testing method is based on Julia Base tests[1], released under the MIT licence[2].",
"[1]: https://github.com/JuliaLang/julia/blob/52bafeb981bac548afd2264edb518d8d86944dca/test/rational.jl",
"[2]: https://github.com/JuliaLang/julia/blob/52bafeb981bac548afd2264edb518d8d86944dca/LICENSE.md"
]
}
]
}
3 changes: 3 additions & 0 deletions exercises/rational-numbers/description.md
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Expand Up @@ -18,9 +18,12 @@ Exponentiation of a rational number `r = a/b` to a real (floating-point) number

Exponentiation of a real number `x` to a rational number `r = a/b` is `x^(a/b) = root(x^a, b)`, where `root(p, q)` is the `q`th root of `p`.

Ordering of rational numbers: `a/b < c/d` if and only if `a * sign(b) * |d| < |b| * c * sign(d)`.

Implement the following operations:
- addition, subtraction, multiplication and division of two rational numbers,
- absolute value, exponentiation of a given rational number to an integer power, exponentiation of a given rational number to a real (floating-point) power, exponentiation of a real number to a rational number.
- the ordering of rational numbers.

Your implementation of rational numbers should always be reduced to lowest terms. For example, `4/4` should reduce to `1/1`, `30/60` should reduce to `1/2`, `12/8` should reduce to `3/2`, etc. To reduce a rational number `r = a/b`, divide `a` and `b` by the greatest common divisor (gcd) of `a` and `b`. So, for example, `gcd(12, 8) = 4`, so `r = 12/8` can be reduced to `(12/4)/(8/4) = 3/2`.

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