Titlebook: Ideals, Varieties, and Algorithms; An Introduction to C David A. Cox,John Little,Donal O’Shea Textbook 2015Latest edition Springer Internat

Redundant

Hiatal-Hernia

Adulate

密切關(guān)系

Geometry, Algebra, and Algorithms,her dimensional objects) defined by polynomial equations. To understand affine varieties, we will need some algebra, and in particular, we will need to study . in the polynomial ring .[.,?.,?.]. Finally, we will discuss polynomials in one variable to illustrate the role played by ..

Common-Migraine

,Gr?bner Bases,er, we will study the method of Gr?bner bases, which will allow us to solve problems about polynomial ideals in an algorithmic or computational fashion. The method of Gr?bner bases is also used in several powerful computer algebra systems to study specific polynomial ideals that arise in application

消耗

,The Algebra–Geometry Dictionary,m which identifies exactly which ideals correspond to varieties. This will allow us to construct a “dictionary” between geometry and algebra, whereby any statement about varieties can be translated into a statement about ideals (and conversely). We will pursue this theme in §§. and?., where we will

Reservation

pester

Robotics and Automatic Geometric Theorem Proving, theme introduced in several examples in Chapter?., we will develop a systematic approach that uses algebraic varieties to describe the space of possible configurations of mechanical linkages such as robot “arms.” We will use this approach to solve the forward and inverse kinematic problems of robot

混沌

Projective Algebraic Geometry, create .-dimensional projective space .. We will then define projective varieties in . and study the projective version of the algebra–geometry dictionary. The relation between affine and projective varieties will be considered in §.; in §., we will study elimination theory from a projective point

刀鋒