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In Mathematics, a fingerprint database for theorems is any collection of theorems uniquely identified by a small canonical form which is independent of specialized notation or vocabulary[1] . Such collections were first available in book format[2], but now the web hosts the majority of such collections. A key feature of web based fingerprint databases is that anyone can access the collection and anyone can contribute. The best known fingerprint database for theorems is the On-Line Encyclopedia of Integer Sequences created by Neil Sloane. Other examples are listed below.
We note that Wikipedia, the Math ArXiv, and the searchable part of the internet also include vast collections of theorems. However, these are not considered as having fingerprints based on the key features of a small canonical language - independent fingerprint.
Definition
editA fingerprint database for theorems is a collection of mathematical information along with a method to uniquely or nearly uniquely distinguish each theorem in its collection in such a way that satisfies the following properties:
- Canonical: To each theorem in the collection, one can associate an appropriate fingerprint.
- Language Independent: The method of fingerprinting cannot depend on specialized vocabulary.
- References: The fingerprint must point the user to references in the literature where the theorem is proved or is used.
- Small: A fingerprint must be small enough that it is easily stored or computed.
- Universality: It covers a range of topics.
Examples of Fingerprint Databases for Theorems
edit- The Online Encyclopedia of Integer Sequences [1]
- The Database of Permutation Pattern Avoidance [2]
- Findstat -The Combinatorial Statistic Finder [3]
- manYPoints – Table of Curves with Many Points [4]
External links
edit- Ben Lillie's Blog "Quomodocumque"[5]
References
edit- ^ Billey, Sara; Tenner, Bridget (Sept. 2013). "Fingerprint Databases for Theorems" (PDF). Notices of the AMS. 60 (8): 1034–1039.
{{cite journal}}: Check date values in:|date=(help) - ^ Bailey, W.N. (1935). Generalized Hypergeometric Series. Cambridge: Cambridge University Press.