Update rational-numbers tests

exercises/practice/affine-cipher/.docs/instructions.md

@@ -1,14 +1,12 @@
 # Instructions
 
-Create an implementation of the affine cipher,
-an ancient encryption system created in the Middle East.
+Create an implementation of the affine cipher, an ancient encryption system created in the Middle East.
 
-The affine cipher is a type of mono-alphabetic substitution cipher.
-Each character is mapped to its numeric equivalent, encrypted with
-a mathematical function and then converted to the letter relating to
-its new numeric value. Although all mono-alphabetic ciphers are weak,
-the affine cipher is much stronger than the atbash cipher,
-because it has many more keys.
+The affine cipher is a type of monoalphabetic substitution cipher.
+Each character is mapped to its numeric equivalent, encrypted with a mathematical function and then converted to the letter relating to its new numeric value.
+Although all monoalphabetic ciphers are weak, the affine cipher is much stronger than the atbash cipher, because it has many more keys.
+
+[comment]: # ( monoalphabetic as spelled by Merriam-Webster, compare to polyalphabetic )
 
 ## Encryption
 
@@ -18,20 +16,21 @@ The encryption function is:
 E(x) = (ai + b) mod m
 ```
 
-- where `i` is the letter's index from `0` to the length of the alphabet - 1
-- `m` is the length of the alphabet. For the Roman alphabet `m` is `26`.
+Where:
+
+- `i` is the letter's index from `0` to the length of the alphabet - 1
+- `m` is the length of the alphabet.
+  For the Roman alphabet `m` is `26`.
 - `a` and `b` are integers which make the encryption key
 
-Values `a` and `m` must be *coprime* (or, *relatively prime*) for automatic decryption to succeed,
-ie. they have number `1` as their only common factor (more information can be found in the
-[Wikipedia article about coprime integers](https://en.wikipedia.org/wiki/Coprime_integers)). In case `a` is
-not coprime to `m`, your program should indicate that this is an error. Otherwise it should
-encrypt or decrypt with the provided key.
+Values `a` and `m` must be *coprime* (or, *relatively prime*) for automatic decryption to succeed, i.e., they have number `1` as their only common factor (more information can be found in the [Wikipedia article about coprime integers][coprime-integers]).
+In case `a` is not coprime to `m`, your program should indicate that this is an error.
+Otherwise it should encrypt or decrypt with the provided key.
 
-For the purpose of this exercise, digits are valid input but they are not encrypted. Spaces and punctuation
-characters are excluded. Ciphertext is written out in groups of fixed length separated by space,
-the traditional group size being `5` letters. This is to make it harder to guess encrypted text based
-on word boundaries.
+For the purpose of this exercise, digits are valid input but they are not encrypted.
+Spaces and punctuation characters are excluded.
+Ciphertext is written out in groups of fixed length separated by space, the traditional group size being `5` letters.
+This is to make it harder to guess encrypted text based on word boundaries.
 
 ## Decryption
 
@@ -41,9 +40,10 @@ The decryption function is:
 D(y) = (a^-1)(y - b) mod m
 ```
 
-- where `y` is the numeric value of an encrypted letter, ie. `y = E(x)`
-- it is important to note that `a^-1` is the modular multiplicative inverse (MMI)
-  of `a mod m`
+Where:
+
+- `y` is the numeric value of an encrypted letter, i.e., `y = E(x)`
+- it is important to note that `a^-1` is the modular multiplicative inverse (MMI) of `a mod m`
 - the modular multiplicative inverse only exists if `a` and `m` are coprime.
 
 The MMI of `a` is `x` such that the remainder after dividing `ax` by `m` is `1`:
@@ -52,8 +52,7 @@ The MMI of `a` is `x` such that the remainder after dividing `ax` by `m` is `1`:
 ax mod m = 1
 ```
 
-More information regarding how to find a Modular Multiplicative Inverse
-and what it means can be found in the [related Wikipedia article](https://en.wikipedia.org/wiki/Modular_multiplicative_inverse).
+More information regarding how to find a Modular Multiplicative Inverse and what it means can be found in the [related Wikipedia article][MMI].
 
 ## General Examples
 
@@ -70,3 +69,6 @@ Finding MMI for `a = 15`:
 - `(15 * x) mod 26 = 1`
 - `(15 * 7) mod 26 = 1`, ie. `105 mod 26 = 1`
 - `7` is the MMI of `15 mod 26`
+
+[MMI]: https://en.wikipedia.org/wiki/Modular_multiplicative_inverse
+[coprime-integers]: https://en.wikipedia.org/wiki/Coprime_integers

exercises/practice/book-store/.docs/instructions.md

@@ -43,8 +43,8 @@ This would give a total of:
 
 Resulting in:
 
-- 5 * (8 - 2.00) == 5 * 6.00 == $30.00
-- +3 * (8 - 0.80) == 3 * 7.20 == $21.60
+- 5 × (8 - 2.00) = 5 × 6.00 = $30.00
+- +3 × (8 - 0.80) = 3 × 7.20 = $21.60
 
 For a total of $51.60
 
@@ -60,8 +60,8 @@ This would give a total of:
 
 Resulting in:
 
-- 4 * (8 - 1.60) == 4 * 6.40 == $25.60
-- +4 * (8 - 1.60) == 4 * 6.40 == $25.60
+- 4 × (8 - 1.60) = 4 × 6.40 = $25.60
+- +4 × (8 - 1.60) = 4 × 6.40 = $25.60
 
 For a total of $51.20
 

exercises/practice/largest-series-product/.docs/instructions.md

@@ -12,3 +12,7 @@ in the input; the digits need not be *numerically consecutive*.
 
 For the input `'73167176531330624919225119674426574742355349194934'`,
 the largest product for a series of 6 digits is 23520.
+
+For a series of zero digits, the largest product is 1 because 1 is the multiplicative identity.
+(You don't need to know what a multiplicative identity is to solve this problem;
+it just means that multiplying a number by 1 gives you the same number.)

exercises/practice/pov/.docs/instructions.md

@@ -43,4 +43,4 @@ This exercise involves taking an input tree and re-orientating it from the point
 of view of one of the nodes.
 
 [wiki-graph]: https://en.wikipedia.org/wiki/Tree_(graph_theory)
-[wiki-tree]: https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)
+[wiki-tree]: https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)

exercises/practice/rational-numbers/.meta/tests.toml

@@ -84,6 +84,15 @@ description = "Exponentiation of a rational number -> Raise a positive rational
 [8168edd2-0af3-45b1-b03f-72c01332e10a]
 description = "Exponentiation of a rational number -> Raise a negative rational number to a positive integer power"
 
+[c291cfae-cfd8-44f5-aa6c-b175c148a492]
+description = "Exponentiation of a rational number -> Raise a positive rational number to a negative integer power"
+
+[45cb3288-4ae4-4465-9ae5-c129de4fac8e]
+description = "Exponentiation of a rational number -> Raise a negative rational number to an even negative integer power"
+
+[2d47f945-ffe1-4916-a399-c2e8c27d7f72]
+description = "Exponentiation of a rational number -> Raise a negative rational number to an odd negative integer power"
+
 [e2f25b1d-e4de-4102-abc3-c2bb7c4591e4]
 description = "Exponentiation of a rational number -> Raise zero to an integer power"
 

exercises/practice/rational-numbers/test/rational_numbers_test.exs

@@ -137,6 +137,21 @@ defmodule RationalNumbersTest do
       assert RationalNumbers.pow_rational({-1, 2}, 3) == {-1, 8}
     end
 
+    @tag :pending
+    test "Raise a positive rational number to a negative integer power" do
+      assert RationalNumbers.pow_rational({3, 5}, -2) == {25, 9}
+    end
+
+    @tag :pending
+    test "Raise a negative rational number to an even negative integer power" do
+      assert RationalNumbers.pow_rational({-3, 5}, -2) == {25, 9}
+    end
+
+    @tag :pending
+    test "Raise a negative rational number to an odd negative integer power" do
+      assert RationalNumbers.pow_rational({-3, 5}, -3) == {-125, 27}
+    end
+
     @tag :pending
     test "Raise zero to an integer power" do
       assert RationalNumbers.pow_rational({0, 1}, 5) == {0, 1}