algebraic geometry

It has developed from two sources : algebraic geometry and algebraic member theory.

它由两个方面发展而来,代数几何和代数数论.

For commutative algebra, algebraic geometry, and singularity theory, the SINGULAR computer algebra system provides a large variety of algorithms in the package kernel as well as shared libraries.

对于交换代数、代数几何和奇点理论，SINGULAR计算机代数系统在软件包内核以及共享库中提供了大量的算法。

Manifolds occur in algebraic geometry, differential equations, and classical dynamics.

流形出现于代数几何 、 微分方程式和经典动力学中.

Lie Group Machine Learning ( LML) inherit the advantages of manifold learning method and make full use of the Lie group's structure of algebraic and geometry in mathematics.

李群机器学习（LML）既继承了流形学习的优点，又充分利用了李群的代数结构和几何结构的数学本质，自提出以来就引起了许多研究者的关注。

Since then they have found numerous and deep applications in areas ranging from theoretical physics, symplectic geometry, knot theory, and modular representations of reductive algebraic groups.

从那时开始，人们发现量子群在很多领域都有着深刻的应用，范围遍及理论物理、辛几何、扭结理论与约化代数群的模表示理论等。

Such kind of graded algebras arise naturally in representation theory and in algebraic geometry ( [ BGS ] ).

表示论中出现的许多代数(如路代数)和代数几何中出现的一些代数 ( 参见 [ BGS ] ) 是这样的正分次代数.

In the calibration of the system, a plan based on the principle of cross ratio invariance in algebraic projective geometry was used to calibrate the coded light planes.

在对编码投影光平面的标定过程中，提出利用代数射影几何中的交比不变原理对其进行标定的方案，并论述了标定原理。

Algebraic Topology; Symplectic Geometry and Topology; Ordinary and Partial Differential Equations.

代数拓扑；辛几何与拓扑；常微分和偏微分方程。

Topics covered range from computational complexity, algebraic geometry, dynamics, through to number theory and quantum groups.

直达数论和量组,题目由于计算的复杂性, 代数学的几何学, 力学包括范围.