On the Classification of Integral Quadratic Forms
On the Classification of Integral Quadratic Forms
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论积分二次型的分类
DOI：
10.1007/978-1-4757-6568-7_15
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
N. Sloane
中科院分区：
文献类型：
--
作者：
J. Conway;N. Sloane
这一章说明了积分二次型的分类。它是专门为那些希望能够进行显式计算的读者设计的。新的功能包括一个基本系统的合理不变量（定义不使用希尔伯特范数剩余符号），一个改进的符号属的形式，一个有效的方法来计算数量的旋量属在一个属，和一些条件，这意味着只有一个类在一个属。我们给出了具有-100 det 50的二进制形式，具有|det| 1950年，形式的属，|det| 11，所有p的p-初等形式的属，以及行列式2到18维和行列式3到17维的正定形式。
This chapter gives an account of the classification of integral quadratic forms. It is particularly designed for readers who wish to be able to do explicit calculations. Novel features include an elementary system of rational invariants (defined without using the Hilbert norm residue symbol), an improved notation for the genus of a form, an efficient way to compute the number of spinor genera in a genus, and some conditions which imply that there is only one class in a genus. We give tables of the binary forms with − 100 ⩽ det ⩽ 50, the indecomposable ternary forms with |det| ⩽ 50, the genera of forms with |det| ⩽ 11, the genera of p-elementary forms for all p, and the positive definite forms with determinant 2 up to dimension 18 and determinant 3 up to dimension 17.