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- W1995676245 abstract "Let G'(~) denote the set of all equivalence classes, under proper equivalence, of binary quadratic forms over )7 of discriminant 5, and let G($) denote the subset of all primitive such form-classes. (It will be recalled that a binary quadratic form a x e + bxy + cy 2 with integral coefficients is called primitive if a, b, c have g.c.d. 1, and is called properly equivalent to any form obtained from it by a linear transformation with integral coefficients and determinant + 1.) Lagrange's theory of equivalence and reduction of quadratic forms over Z (1773) showed G'(8) to be a finite set, whence G(~) is finite; later, Gauss (1801), by a truly marvelous construction, defined on G(S) a binary operation he called composition, and verified that under this operation G(~) is an Abelian group. Two alternative ways (in addition to Gauss' original method) of constructing these composition groups were developed in the nineteenth century:" @default.
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- W1995676245 date "1980-04-01" @default.
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- W1995676245 title "Composition of oriented binary quadratic form-classes over commutative rings" @default.
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- W1995676245 doi "https://doi.org/10.1016/s0001-8708(80)80002-8" @default.
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