Appendix:English polynomial degrees
In algebra, the names for the degree of a polynomial, or of a polynomial with a given degree, are a mixture of common Latinate words for degree up to three, followed by words regularly derived from the Latin ordinal numbers (compare English ordinal numbers), suffixed with -ic for degree two and above.[1][2][3][4] Up to degree three are commonly understood, as they correspond to everyday words for spacial dimensions, while degree four and above are more technical, with words for higher degrees rarely used. The zero polynomial is a special case, and is typically just referred to as “zero”, without a special term for its degree. Grecian roots are occasionally used, such as hexic for degree 6, though this is rare.
By contrast, number of variables (arity) is named using Latinate distributive numbers, with the suffix -ary, and number of terms is named similarly, using the suffix -nomial. For example, a degree two polynomial in two variables (x and y) with two terms, such as , is called a “binary quadratic binomial”: binary due to two variables, quadratic due to degree two, binomial due to two terms. See English arities and adicities for a full list of arities, and polynomial for list of names by number of terms.
| degree | name |
|---|---|
| 0 | constant |
| 1 | linear |
| 2 | quadratic |
| 3 | cubic |
| 4 | quartic |
| 5 | quintic |
| 6 | sextic |
| 7 | septic |
| 8 | octic |
| 9 | nonic |
| 10 | decic |
References
[edit]- ^ “Names of Polynomials”, in (Please provide the book title or journal name)[1], 2012 February 5 (last accessed)
- ^ Mac Lane and Birkhoff (1999) define "linear", "quadratic", "cubic", "quartic", and "quintic". (p. 107)
- ^ King (2009) defines "quadratic", "cubic", "quartic", "quintic", "sextic", "septic", and "octic".
- ^ James Cockle proposed the names "sexic", "septic", "octic", "nonic", and "decic" in 1851. (Mechanics Magazine, Vol. LV, p. 171)