1 Introduction Modular arithmetic is a fundamental tool in modern algebra systems. In conjunction with the Chinese remainder theorem it serves as the workhorse in several algorithms computing the gcd, resultant etc. Moreover, it can serve as a very e…

理解: 本节主要介绍CGAL的代数结构和概念之间的互操作.与传统数论不同,CGAL的代数结构关注于实数轴的“可嵌入”特征.它没有将所有传统数的集合映射到自己的代数结构概念中,避免使用“数的类型”这一术语,由整数入手,逐步提炼,由简入繁,形成一个概念体系.最上层结构是不考虑除法的整数(IntegralDomainWithoutDivision ),它适应了所有“类型都可以由整数生成”的要求.然后向下精炼形成IntegralDomain(这一概念可能就引入了除法).IntegralDomain向下分…

1 Fundamentals A polynomial is either zero, or can be written as the sum of one or more non-zero terms. The number of terms is finite. A term consist of a constant coefficient and a monomial, that is, the product of zero or more variables. Each varia…

1 Introduction Real solving of polynomials is a fundamental problem with a wide application range. This package is targeted at providing black-box implementations of state-of-the-art algorithms to determine, compare, and approximate real roots of uni…

1 Which Programs can be Solved? This package lets you solve convex quadratic programs of the general form   in n real variables x=(x0,…,xn−1). Here, A is an m×n matrix (the constraint matrix), b is an m-dimensional vector (the right-hand side), ⋛ is…

monotone_matrix_search() and sorted_matrix_search() are techniques that deal with the problem of efficiently finding largest entries in matrices with certain structural properties. Many concrete problems can be modelled as matrix search problems, and…

1 Introduction This part of the reference manual covers the higher-dimensional kernel. The kernel contains objects of constant size, such as point, vector, direction, line, ray, segment, circle. With each type comes a set of functions which can be ap…

1 Introduction CGAL, the Computational Geometry Algorithms Library, is written in C++ and consists of three major parts. The first part is the kernel, which consists of constant-size non-modifiable geometric primitive objects and operations on these…

1 Introduction A polygon is a closed chain of edges. Several algorithms are available for polygons. For some of those algorithms, it is necessary that the polygon is simple. A polygon is simple if edges don't intersect, except consecutive edges, whic…

1 Introduction A subset S⊆R2 is convex if for any two points p and q in the set the line segment with endpoints p and q is contained in S. The convex hull of a set S is the smallest convex set containing S. The convex hull of a set of points P is a c…