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'''Partitioning on an Element'' is used in a cyclical way to order the indexing of the matrix under development. | '''Partitioning on an Element''' is used in a cyclical way to order the indexing of the matrix under development. | ||
In the process of [[Partitioning|partitioning]], data are supplied that partially fill the matrix. Each cycle may involve several parts, and each part involves the ''same four steps'': | In the process of [[Partitioning|partitioning]], data are supplied that partially fill the matrix. Each cycle may involve several parts, and each part involves the ''same four steps'': | ||
* First cycle has only one part, and four steps | * First cycle has only one part, and four steps. | ||
* Second cycle may have as many as three parts, depending on the results of the first | * Second cycle may have as many as three parts, depending on the results of the first cycle. | ||
cycle. | * Third cycle may have as many as nine parts. | ||
* Third cycle may have as many as nine parts | |||
* The nth cycle may have as many as 3<sup>n-1</sup> parts. | * The nth cycle may have as many as 3<sup>n-1</sup> parts. | ||
Experience suggests that only a few cycles will normally be needed to develop a [[Reachability Matrix]], and the number of parts will seldom be as high as the stated maxima. | Experience suggests that only a few cycles will normally be needed to develop a [[Reachability Matrix]], and the number of parts will seldom be as high as the stated maxima. | ||
:<math>\begin{pmatrix} | |||
1 & 1 & 1 & 1 \\ | |||
0 & 1 & 0 & 1 \\ | |||
0 & 0 & 1 & 0 \\ | |||
0 & 0 & 0 & 1 | |||
\end{pmatrix}</math> which includes a diagonal of ones since each number divides itself. | |||
[[Category: ISM Terminology]] | [[Category: ISM Terminology]] | ||