birationaladj.

/bʌɪˈraʃənəl/

Etymology: < bi- comb. form + rational adj.

Mathematics.

Applied to a transformation in which each of two sets of variables is expressed rationally in terms of the other, or to a correspondence between two sets of variables that can be so related.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > transformation > [adjective] > having specific correspondence

orthogonal1852

permutational1888

isomorphic1892

birational1894

unary1931

homomorphic1935

symplectic1939

involutory1941

injective1952

monomorphic1958

bijective1962

surjective1964

1894 C. A. Scott Introd. Plane Analyt. Geom. xi. 240 The transformations hitherto considered are birational transformations of the whole plane.

1915 R. A. P. Rogers Salmon's Analyt. Geom. (ed. 5) II. 268 Such a correspondence is called birational.

1954 W. V. D. Hodge & D. Pedoe Methods Algebraic Geom. III. xviii. 224 An irreducible correspondence between two varieties U and U′ in which to a generic point of each there corresponds a unique point of the other is called a birational correspondence.

Derivatives

biˈrationally adv.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > transformation > [adverb]

alternately1570

homographically1859

birationally1915

homoeomorphically1927

homotopically1930

isomorphically1935

homomorphically1941

isometrically1959

symplectically1959

1915 R. A. P. Rogers Salmon's Analyt. Geom. (ed. 5) II. 268 Any surface which can be birationally transformed into a unicursal surface is itself unicursal.

This entry has not yet been fully updated (first published 1933; most recently modified version published online June 2018).

单词	birational
释义	birationaladj. /bʌɪˈraʃənəl/ Etymology: < bi- comb. form + rational adj. Mathematics. Applied to a transformation in which each of two sets of variables is expressed rationally in terms of the other, or to a correspondence between two sets of variables that can be so related. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [adjective] > having specific correspondence orthogonal1852 permutational1888 isomorphic1892 birational1894 unary1931 homomorphic1935 symplectic1939 involutory1941 injective1952 monomorphic1958 bijective1962 surjective1964 1894 C. A. Scott Introd. Plane Analyt. Geom. xi. 240 The transformations hitherto considered are birational transformations of the whole plane. 1915 R. A. P. Rogers Salmon's Analyt. Geom. (ed. 5) II. 268 Such a correspondence is called birational. 1954 W. V. D. Hodge & D. Pedoe Methods Algebraic Geom. III. xviii. 224 An irreducible correspondence between two varieties U and U′ in which to a generic point of each there corresponds a unique point of the other is called a birational correspondence. Derivatives biˈrationally adv. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [adverb] alternately1570 homographically1859 birationally1915 homoeomorphically1927 homotopically1930 isomorphically1935 homomorphically1941 isometrically1959 symplectically1959 1915 R. A. P. Rogers Salmon's Analyt. Geom. (ed. 5) II. 268 Any surface which can be birationally transformed into a unicursal surface is itself unicursal. This entry has not yet been fully updated (first published 1933; most recently modified version published online June 2018). < adj.1894
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