| 释义 |
polynomial, a. and n.|pɒlɪˈnəʊmɪəl|
[Hybrid f. poly- after binomial (irreg. f. L. nōmen name).]
A. adj.
1. Alg. Consisting of many terms; multinomial. polynomial theorem (also called multinomial theorem): an extension of the binomial theorem, for the expansion of any power of a polynomial expression.
1704J. Harris Lex. Techn. I, Polynomial, or Multinomial Roots, in Mathematicks, are such as are composed of many Nomes, Parts or Members; as, a + b + d + c. 1706in Phillips.
2. Consisting of, or characterized by, many names or terms: as the old scientific nomenclature in which species were denoted by names of more than two terms, or any modern nomenclature in which the genus, species, sub-species, variety, etc. are indicated by a number of terms (instead of only the genus and species by two terms: see binomial A. 2).
1828Webster, Polynomial, containing many names or terms. 1964Huntia I. 34 He makes the essential distinction between the old Aristotelian polynomial phrase-names and the new trivial names.
B. n.
1. Alg. An expression consisting of many terms; a multinomial. The terms are usually taken to be multiples of powers, finitely many in number.
1674S. Jeake Arith. (1696) 273 Those knit together by both Signs are called..by some Multinomials, or Polynomials, that is, many named. 1753Chambers Cycl. Suppl. s.v., To raise a polynomial to any given power, may be done by Sir Isaac Newton's binomial theorem. c1865in Circ. Sc. I. 481/1 We conclude that the polynomial is not a square. 1906Athenæum 19 May 613/3 The Expansion of Polynomials in Series of Functions. 1941,1966[see factor v. 2].
2. A scientific name consisting of many terms (see A. 2).
1885Nature XXXI. 413/1 Trinomials—that is the usage of three names, of which the last is that of the sub-species—are in great favour... Quadrinomials and Polynomials must necessarily follow. 1951G. H. M. Lawrence Taxon. Vascular Plants ix. 194 Before the middle of the eighteenth century the names of plants commonly were polynomials. 1971W. T. Stearn in W. Blunt Compleat Naturalist 248/1 Such a polynomial determines the application of the binomial.
Hence polyˈnomialism, a system of polynomial nomenclature; polyˈnomialist, one who uses or favours polynomial nomenclature.
Add:[A.] 3. Math. That may be expressed as a polynomial; spec. in polynomial time, an amount of time expressible as a polynomial in terms of the ‘size’ of a given problem whose solution is required. Freq. attrib., esp. with reference to algorithms which can be executed in polynomial time. Cf. *exponential a. 2 d.
1972R. M. Karp in Miller & Thatcher Complexity of Computer Computations 88 The class of languages recognizable by string recognition algorithms which operate in polynomial time is also invariant under a wide range of changes in the class of algorithms. 1976Garey & Johnson in J. F. Traub Algorithms & Complexity 42 There are problems for which no finite upper bound on worst-case performance is known to be satisfied for any polynomial time algorithm. 1982Papadimitriou & Steiglitz Combinatorial Optimization viii. 166 Exponential algorithms..are quickly abandoned once a polynomial-time algorithm for the same problem is discovered. |