Problem-specifications: pythagorean-triplet: improve readme and specification

[kytrinyx]

@yawpitch submitted this over in https://github.com/exercism/exercism.io/issues/3743

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I'm working on the Python track specifically, but I notice that across many of the language tracks the tests and examples do not reflect the description of the problem:

Pythagorean Triplet
A Pythagorean triplet is a set of three natural numbers, {a, b, c}, for which,
a**2 + b**2 = c**2
For example,
3**2 + 4**2 = 9 + 16 = 25 = 5**2.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product a * b * c.

In the Python, Rust, and Haskell tracks, for instance, there are no tests whatsoever related to the "find the product a*b*c" statement, and all three require different constructs than what's implied by the problem description and title. The Javascript track, however, does require that the work produced can calculate the product.

[petertseng]

Since we made different design choices than Project Euler and, as a result of the choices, we are not limited to validating a single numerical answer, I suggest we do away with finding the product. I suggest test suites simply check the values of a, b and c that a test case will ask for.

What test cases shall we recommend?

There are choices for how much parameterisation we want.

• Only find the single triplet where a + b + c = 1000
• Find triplets where a + b + c = N, for varying N
• Find triplets where a + b + c < N, for varying N
• Find triplets where a < N and b < N and c < N, for varying N
• I"m sure one can find more options if you just look through http://exercism.io/contribute/canonical-data/pythagorean-triplet but I'm not going to do that.
• Decide the problem is not a good fit for exercism and decide to deprecate it

"Only find the single triplet where a + b + c = 1000" is my least-preferred option. I do not see a need for me to express an ordering between any other options at this time.

[petertseng]

Hey there, just editing the initial issue description to put backticks around the asterisks, otherwise something like a*b*c turns into abc and a**2 + b**2 = c**2 turns into a2 + b2 = c**2 which is not what we want to show in this issue (it would decrease understanding)

[felix91gr]

What test cases shall we recommend?

Checking the solution is much easier if we can ask to be given a, b and c. Therefore, I'd suggest changing the exercise to something like this:

_Create a function which receives the sum of the three sides, and returns one pythagorean triplet that satisfies the equation a + b + c = N._

Testing the answers should be straightforward:

1. Check that a + b + c = N
2. Check that a² + b² = c²

Edit: I misclicked enter and posted my comment uncompleted. Now it's okay ^^

[petertseng]

Update on status of this issue: The canonical tests are created in https://github.com/exercism/problem-specifications/pull/1332.

A person who wants to close this issue should update https://github.com/exercism/problem-specifications/blob/master/exercises/pythagorean-triplet/description.md to match the new task (given N, find any pythagorean triplets whose sum is N).

Don't forget to use one of the words in https://help.github.com/articles/closing-issues-using-keywords/ in your commit message.