Explicit methods in arithmetic geometry

算术几何中的显式方法

• 批准号: 261486-2013
• 负责人: Bruin, Nils
• 金额: $ 2.11万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=594574
• 关键词: Explicit; methods; arithmetic; geometry

A large part of the mathematical sciences is concerned with developing methods for finding solutions to various types of equations. The simplest kind of equation is the polynomial equation, where the variables are combined using just addition and multiplication. This is the oldest type of equation that was ever studied. One calls such an equation a Diophantine equation if one restricts to solutions that are natural numbers, integers, or rational numbers. Equations like this come up in many practical situations, such as in resonance problems, translating election results into seat distributions, and various questions about discrete configurations.

数学科学的很大一部分关注于开发各种类型的方程的解的方法。最简单的方程是多项式方程，其中变量仅使用加法和乘法组合。这是研究过的最古老的方程类型。如果仅限于自然数、整数或有理数的解，就称这样的方程为丢番图方程。像这样的方程在许多实际情况下都会出现，例如在共振问题中，将选举结果转化为席位分配，以及关于离散配置的各种问题。