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--- at:tutorial:basic [2020/02/09 21:39]
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+++ at:tutorial:basic [2020/02/09 22:03]
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-==== Multidimensional tables ====
+==== Multidimensional Tables ====
 As mentioned before, there is no special constructor for definition of multidimensional tables, a table entry can contain another table. In what follows we have a closer look to manipulations with multidimensional tables.  Consider a multidimensional table which is extensionally defined as follows:
@@ Line 122: / Line 124: @@
 </code>
+You can find later in this chapter a helper function for creating matrices  [[:at:tutorial:basic#optional_parameters|here]].
 ===== Functions =====
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 >> 21
 </code>
 ==== Optional Parameters ====
@@ Line 239: / Line 247: @@
 </code>
-As is customary in languages with the above parameter passing semantics, AmbientTalk requires mandatory parameters to be defined //before// optional parameters, which should in turn be defined //before// a variable-argument parameter, if any.
+As is customary in languages with the above optional arguments, AmbientTalk requires mandatory parameters to be defined //before// optional parameters, which should in turn be defined //before// a variable-argument parameter, if any.
+Let us show how to use optional arguments to define an auxilary function that creates matrices:
+<code>
+def makeMatrix(n, m := n, init := { |i,j| 0}){
+  def [i,j] := [0,0];
+  def makeCol(i,j) {
+     def col[m] { j := j + 1; init(i,j) }
+  };
+  def matrix[n] { i := i + 1; makeCol(i,j)}
+};
+>def c := makeMatrix(3);
+>>[[0, 0, 0], [0, 0, 0], [0, 0, 0]]
+>c[1] := [1,2,3]
+>>[1, 2, 3]
+>c
+>>[[1, 2, 3], [0, 0, 0], [0, 0, 0]]
+>def d := makeMatrix(4,4, { |i,j| if: (i == j) then: {1} else: {0}});
+>> [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]
+</code>
 ===== Closures =====

Ambient-Oriented Programming

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