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Volume 9, Issue 4

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T R O T T ' S C O R N E R
Michael Trott

Building Hash Tables

A more detailed version of the sample analysis just described is carried out on all 90,000 identities of the Wolfram Functions site. This one-time processing procedure takes a few hours. Then the connections identity->listOfIngredients are reversed and large hash tables of the form ingredient->listOfIdentities are constructed. While quite large, such tables allow for a very fast lookup, which is of constant time and independent of the length of the table. The ingredients are sorted into four categories: functions (such as Sin, BesselJ), constants (such as Pi, E), numbers (such as (2, 3, 1729), and operations (such as Sum, Integrate). Integrals are classified as definite versus indefinite.

Here are a few example counts.


Ingredient
Occurrences in the
Left-Hand Side
Occurrences in the
Right-Hand Side
Occurrences
in Conditions
Cos9517623466
Pi25664273012237
Hypergeometric2F140881421209
D237235839
1159621119



     
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