Merge pull request #747 from polyadic/cartesian-product-docs

Update Out-of-date Cartesian Product Docs

Documentation/src/enumerable-extensions/cartesian-product.md

@@ -1,38 +1,61 @@
 ## CartesianProduct
 
-In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A×B, is the set of all ordered pairs (a, b) where a is in A and b is in B.
+In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A×B,
+is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B.
 
-The CartesianProduct extension function returns all possible pairs of two given IEnumerables.
-
-There are two overloads, one which lets you choose
+In other words: The Cartesian product produces all possible pairs of two given `IEnumerable`s.
 
 ![cartesian-product with marbles](cartesian-product.svg "Marble me!")
 
+### Recipe
+The Cartesian product can be easily implemented ad-hoc using LINQ's built-in `SelectMany` extension function:
+
+```cs
+using System;
+using System.Linq;
+
+// Version A: Get each pair as a tuple
+var result = sequenceA.SelectMany(_ => sequenceB, ValueTuple.Create);
+
+// Version B: Transform each pair using a selector
+var result = sequenceA.SelectMany(_ => sequenceB, (a, b) => ...);
+
+// Version C: Using LINQs declarative query syntax
+var result =
+    from a in sequenceA
+    from b in sequenceB
+    select ...;
+```
+
+
 ### Examples
 
 Two sequences as input:
 
-``` 
+```
 smiles = [😀, 😐, 🙄]
 fruits = [🍉, 🍌, 🍇, 🍓]
-``` 
+```
 
-The cartesian products of smiles and fruits:
+The Cartesian products of smiles and fruits:
 
-``` 
-smiles × fruits => [[😀, 🍉], [😀, 🍌], [😀, 🍇], [😀, 🍓], 
-                    [😐, 🍉], [😐, 🍌], [😐, 🍇], [😐, 🍓], 
+```
+smiles × fruits => [[😀, 🍉], [😀, 🍌], [😀, 🍇], [😀, 🍓],
+                    [😐, 🍉], [😐, 🍌], [😐, 🍇], [😐, 🍓],
 				    [🙄, 🍉], [🙄, 🍌], [🙄, 🍇], [🙄, 🍓]]
 ```
 
-In this C# example you see how all Playing cards are in fact a cartesian product of a suit and a value.
+In this C# example you see how all playing cards are in fact a Cartesian products of a suit and a value.
 
-This example uses the overload with our own selector, because we just want a sequence of strings.
+This example uses the overload with a selector, because we just want a sequence of strings.
 
 ```cs
-var suits = ImmutableList.Create("♠", "♣", "♥", "♦");
-var values = 
-  ImmutableList.Create("2", "3", "4", "5", "6", "7", "8", "9", "T", "J", "Q", "K", "A");
+using System;
+using System.Linq;
+using Funcky;
+
+var suits = Sequence.Return("♠", "♣", "♥", "♦");
+var values = Sequence.Return("2", "3", "4", "5", "6", "7", "8", "9", "T", "J", "Q", "K", "A");
 
-var allCards = suits.CartesianProduct(values, (suit, value) => $"{value}{suit}");
-``` 
+var deck = suits.SelectMany(_ => values, (suit, value) => $"{value}{suit}");
+```