algebraic geometry

In 1945 MacLane and Eilenberg introduced the concept and theories of categories, which have played a role in many branches of mathematics such as algebraic geometry, topology, differential geometry and functional theories.

自从1945年MacLane与Eilenberg提出范畴的概念和理论以来，它在数学的许多分支，例如代数几何学、拓扑学、微分几何学以及函数理论中均已有所应用。

Topology, Ergodic Theory, Real Algebraic Geometry.

拓扑，遍历理论，实代数几何。

Nowadays, our country is carrying through curricular innovation, we are gradually closed to contemporaneity geometry, it is inevitable for algebraic geometry.

现在我国正在进行课程改革，慢慢向现代几何靠拢，几何代数化是不可避免的。

The research of Wu includes the following fields: algebraic topology, algebraic geometry, game theory, history of mathematics, mathematics mechanization, and his most important contribution is to topology ( the Wu class and Wu formula), which is somewhat foundational in its field.

吴文俊的研究领域为拓扑学、代数几何、对策论、数学史、数学机械化，最重要的贡献是拓扑学（“吴示性类”、“吴公式”），在所属领域是基础性的。

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。

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。

The theory of local cohomology modules plays an important role in the study of commutative algebra and algebraic geometry.

局部上同调模在交换代数和代数几何的研究中起着重要的作用。

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。

Vector is one of the significant and basic conceptions in contemporary mathematics, which also acts as an important tool and bridge between algebraic geometry and trigonometric function.

向量是现代数学中重要和基本的数学概念之一，是沟通代数几何与三角函数的一种重要工具和桥梁，同时也是一种重要的数学语言，同时还广泛应用于物理和科技领域。

Quantity and space both play a role in analytic geometry, differential geometry, and algebraic geometry.

数量和空间在解析几何，微分几何和代数几何中都发挥作用。

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.

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.

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.

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.