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# Normal Form

The word "normal form" is used in a variety of different ways in mathematics. In general, it refers to a way of representing objects so that, although each may have many different names, every possible name corresponds to exactly one object (Petkovšek et al. 1996, p. 7). For example, the term "normal form" is used in linear algebra to describe matrices that have been transformed into certain special forms (e.g., Hermite normal form and Smith normal form), in logic to describe statements formulated in a standard way involving so-called literals (e.g., conjunctive normal form and disjunctive normal form), and in the theory of special functions to mean the uniquely-determined holonomic function (i.e., solution of a linear homogeneous ordinary differential equation with polynomial coefficients) of lowest order up to multiplication by polynomials (Koepf 1998, p. 2).

Canonical Form, Conjunctive Normal Form, Disjunctive Normal Form, Hermite Normal Form, Holonomic Function, Literal, Normal-Form Game, Prenex Normal Form, Smith Normal Form

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## References

Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, 1998.Petkovšek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A K Peters, 1996. http://www.cis.upenn.edu/~wilf/AeqB.html.

Normal Form

## Cite this as:

Weisstein, Eric W. "Normal Form." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NormalForm.html