| 释义 |
algebraic, a.|ældʒɪˈbreɪɪk|
[f. prec. + -ic. Cf. the more regularly formed Fr. algébrique.]
Of or pertaining to algebra, occurring in algebra.
1662Hobbes Seven Prob. Wks. 1845 VII. 60, I have to prove..the algebraic calculation. 1673Kersey Algebra (1725) 31 Two or more Algebraic quantities. 1681Sir G. Wharton Wks. 1683, 44 The so long sought for Equation of three discontinued Numbers in Algebriaque proportion. 1684Lond. Gaz. mdcccclxxxv/4 Algebraick Arithmetick, made easie for the commonest capacity. 1827Hutton Course Math. I. 182 Algebraic Fractions have the same names and rules of operation, as numeral fractions in common arithmetic. 1858Holmes Aut. of Breakf. T. xi. 101 These expressions come to be the algebraic symbols of minds which have grown too weak to discriminate.
Add:2. Math. a. Of, pertaining to, or designating an equation or formula in which a finite number of symbols are combined using only the operations of addition, subtraction, multiplication, division, and exponentiation with constant rational exponents. Cf. transcendental a. 4.
[1728Chambers Cycl. I. 60/2 Algebraical curve, is a curve, wherein the relation of the abscisses to the semiordinates, may be defined by an algebraical equation... Algebraical curves stand contradistinguish'd to mechanical or transcendental ones.] 1738Ibid. (ed. 2) I. opp. sig. 2 Hhh, Most authors, after Des Cartes, call algebraic curves, geometrical ones. 1871Tait & Steele Treat. Dynamics of Particle (ed. 3) i. 26 When e = 1 , the corrected integral..is 2(x + a/4) = y2/2a - a log y/a . This is the only case in which we do not obtain an algebraic curve. 1902J. W. Mellor Higher Math. i. 22 An algebraic function of x is an expression containing terms which involve only the operations of addition, subtraction, multiplication, division, evolution (root extraction) or involution. 1972C. S. Ogilvy Tomorrow's Math (ed. 2) viii. 153 The famous equation connecting π and e, eπi = -1 , is not algebraic.
b. Of a number: that can be expressed as a root of a polynomial with rational coefficients.
[1893Proc. London Math. Soc. XXIV. 327 (heading) On the algebraical integers derived from an irreducible cubic equation.] 1937A. A. Albert Mod. Higher Algebra xii. 288 Let us apply this to a field 𝔉 = ℜ(ξ) which is algebraic of degree n over the field ℜ of all rational numbers. We call the quantities of 𝔉 algebraic numbers and say that 𝔉 is an algebraic number field. 1947F. G. Brown Everyman's Math. xxiii. 560 An algebraic number is any x that satisfies the equation anxn + an-1xn-1 +..+ a1x + a0 = 0 where all the coefficients are integers. 1972M. Kline Math. Thought xxv. 593 Any root, real or complex, of any algebraic (polynomial) equation with rational coefficients is called an algebraic number. 1982Sci. Amer. Dec. 130/2 For example, √2 , i (the imaginary square root of -1) and (-1 + i√3)/2 are all algebraic integers because they are roots of the algebraic equations x2 - 2 = 0 , x2 + 1 = 0 and x3 - 1 = 0 . |