monicadj.
/ˈmɒnɪk/, U.S. /ˈmɑnɪk/ Mathematics.
Of a polynomial or equation: having the coefficient of the term of highest degree equal to one.
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monic1937
1937 A. A. Albert Mod. Higher Algebra ii. 24 The coefficient an is called the leading coefficient of f and we shall call f a monic polynomial when an = 1. [Note] This notion occurs so frequently in algebra that the author believes it would be wise to adopt the above term.
1963 R. A. Beaumont & R. S. Pierce Algebraic Found. Math. ix. 328 Thus, for any nonzero polynomial g(x), there is a unique monic polynomial f(x) which is a multiple of g(x) by a nonzero element of F.
1989 W. Gellert et al. VNR Conc. Encycl. Math. (ed. 2) iv. 83 An algebraic equation of degree n with one variable and with the highest coefficient an = 1 is said to be monic or in normal form.
1994 IEEE Trans. Information Theory 40 1661/1 From a polynomial ideal point of view, the decoding problems of cyclic codes are closely related to the monic generators of certain polynomial ideals.
This entry has been updated (OED Third Edition, September 2002; most recently modified version published online March 2022).
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adj.1937