diff --git a/src/current/summary.xsl b/src/current/summary.xsl index a4455660..400dab2d 100644 --- a/src/current/summary.xsl +++ b/src/current/summary.xsl @@ -310,6 +310,7 @@ @@ -2070,10 +2071,14 @@ -
+

N.B.

-
-
Iverson's Convention
+

+ 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. +

+
+
Iverson's Brackets

As is customary for many mathematical notations in CS, this system uses @@ -2091,37 +2096,44 @@

-
Sets
+
Arrays (Vectors, Matrices, etc.)
+

+ All sequences/arrays of values are represented as matrices. + For one-dimensional 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". +

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.

- 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).

-
Counting Sets
+
Counting Vectors
- 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:
  • - \(\sum_{k} S_k\) to count the number of one-values in boolean set - \(S\) (e.g. if \(S\) denotes properties with swimming pools, we can + \(\sum_{k} V_k\) to count the number of one-values in boolean vector + \(V\) (e.g. if \(V\) denotes properties with swimming pools, we can count the number of swimming pools).
  • - \(\sum_{k=0}^{N(S)} 1\) to count the number of values in set \(S\). + \(\sum_{k=0}^{\#V-1} 1\) to count the number of values in vector \(V\).
@@ -2136,7 +2148,7 @@
Subscript Precedence
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.