summary: Readd N.B. section from old summary page
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<ul>


<li><a href="#testdata">Test Case</a></li>


<li><a id="loadprior" href="#prior">Prior Test Cases</a></li>


<li><a href="#__nb">N.B.</a></li>


</ul>




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<! basic summary info >


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<div class="tcontent" id="__nb">


<div class="tcontent mathtypesethover" id="__nb">


<h2 class="nb">N.B.</h2>


<dl class="mathtypesethover">


<dt>Iverson's Convention</dt>


<p>


This "Summary Page" provides both an overview of the rater as a whole


and a breakdown of all of its details on an intimate level.


</p>


<dl>


<dt>Iverson's Brackets</dt>


<dd>


<p>


As is customary for many mathematical notations in CS, this system uses



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</p>


</dd>




<dt>Sets</dt>


<dt>Arrays (Vectors, Matrices, etc.)</dt>


<dd>


<p>


All sequences/arrays of values are represented as matrices.


For onedimensional arrays, column vectors are used; written


horizontally, their notation is


\(\left[\begin{array}\\x_0 & x_1 & \ldots & x_n\end{array}\right]^T\),


where the \(T\) means "transpose".


</p>


<p>


In the equations represented above, it is to be assumed that undefined


values in a set are implicitly 0; this simplifies the representations of


values in a vector are implicitly \(0\); this simplifies the representations of


the various summations; they are not intended to be vigorous.


</p>


<p>


For example: let \( x \) = \( \{ 1, 2, 3 \} \). Given the equation \(


For example: let \( x \) = \( \left[\begin{array}\\1 & 2 & 3\end{array}\right]^T \). Given the equation \(


\sum_k x_k \), it is assumed that the solution is \( 1 + 2 + 3 = 6 \),


not undefined. Formally, the former sum is to be interpreted as: \(


\sum_{k=0}^n x_k \) where \( n \) is the length of set \( x \), or \(


\sum_{k=0}^n x_k \) where \( n \) is the length of vector \( x \), or \(


\sum_k x_k [x_k \textrm{ is defined}] \) using Iverson's convention (the


latter of which our first notation is based upon by simply omitting the


brackets and implying their existence).


</p>


</dd>




<dt>Counting Sets</dt>


<dt>Counting Vectors</dt>


<dd>


Let \(N(S)\) = the number of values within the set \(S\); this notation is


Let \(\#V\) = the number of values within the vector \(V\); this notation is


used within certain summations. You may also see the following notations:




<ul>


<li>


\(\sum_{k} S_k\) to count the number of onevalues in boolean set


\(S\) (e.g. if \(S\) denotes properties with swimming pools, we can


\(\sum_{k} V_k\) to count the number of onevalues in boolean vector


\(V\) (e.g. if \(V\) denotes properties with swimming pools, we can


count the number of swimming pools).


</li>


<li>


\(\sum_{k=0}^{N(S)} 1\) to count the number of values in set \(S\).


\(\sum_{k=0}^{\#V1} 1\) to count the number of values in vector \(V\).


</li>


</ul>


</dd>



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<dt>Subscript Precedence</dt>


<dd>


Subscripts should be applied from right to left. That is:


\(S_{x_{y_z}}\) = \(S_{(x_{(y_z)})}\). In the event where a notation may


\(V_{x_{y_z}}\) = \(V_{(x_{(y_z)})}\). In the event where a notation may


be ambiguous (e.g. \(\theta_{1_x}\), since \(1_x\) could not possibly make


sense in the context of this system), parenthesis will always be added to


clarify intent.




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