MattOates at 14:28, 22 September 2012

2012-09-22T14:28:43Z

MattOates at 14:07, 22 September 2012

2012-09-22T14:07:25Z

Francis Tyers: Created page with '

 i = 0; for(n = 0; n < 10; n++) {   i = i + i; }

\sum_{i=0}^{10} i

2012-09-22T11:13:21Z

Created page with '<pre> i = 0; for(n = 0; n < 10; n++) { i = i + i; } </pre> <math>\sum_{i=0}^{10} i</math>'

New page

@@ Line 16: / Line 16: @@
 <math>
 \delta_{ij} = \left\{\begin{matrix}
-, & \mbox{if } i \ne j   \\
+, & \mbox{if } i = j   \\
-, & \mbox{if } i=j
+, & \mbox{if } i \ne j
 \end{matrix}\right.
 </math>

@@ Line 8: / Line 8: @@
 <math>\sum_{i=0}^{10} i</math>
+== Kronecker Delta and Iverson Notation ==
+The [http://en.wikipedia.org/wiki/Kronecker_delta Kronecker Delta] function below allows you to transform logical expressions into 0 and 1 integer values available for summing over sets, or for removing terms from an equation where you multiply a given term by the delta to keep it in or not dependent on some logical restriction.
+<math>
+\delta_{ij} = \left\{\begin{matrix}
+, & \mbox{if } i \ne j   \\
+, & \mbox{if } i=j
+\end{matrix}\right.
+</math>
+In computer science this function became so useful for expressing algorithms it's frequently described using a more lightweight and intuitive notation called the [http://en.wikipedia.org/wiki/Iverson_bracket Iverson bracket] popularised by [http://en.wikipedia.org/wiki/Kenneth_E._Iverson Kenneth E. Iverson]. The Iverson bracket is similarly defined as the Kronecker Delta:
+<math>
+[f] = \left\{\begin{matrix}
+, & \text{if } f \text{ is true;}   \\
+, & \text{otherwise.}
+\end{matrix}\right.
+</math>
+Imagine we wish to count the total number of instances of "the" in an array of words from a piece of text:
+<pre>
+count = 0
+for word in words
+    count += 1 if word == "the"
+print count
+</pre>
+With Iverson bracket notation we would write this thusly:
+<pre>
+let W be a set of sequences of characters from the English alphabet
+let c be the sum of sequences w that are equal to (t,h,e)
+</pre>
+<math>
+c = \sum_{w \in{} W}^{} [w = (t,h,e)]
+</math>

User:Francis Tyers/Maths - Revision history

MattOates at 14:28, 22 September 2012

MattOates at 14:07, 22 September 2012

Francis Tyers: Created page with '
i = 0; for(n = 0; n < 10; n++) { i = i + i; }
$\sum_{i=0}^{10} i$ '

User:Francis Tyers/Maths - Revision history

MattOates at 14:28, 22 September 2012

MattOates at 14:07, 22 September 2012

Francis Tyers: Created page with ' i = 0; for(n = 0; n < 10; n++) { i = i + i; } \sum_{i=0}^{10} i'

Francis Tyers: Created page with '
i = 0; for(n = 0; n < 10; n++) { i = i + i; }
$\sum_{i=0}^{10} i$ '