Titlebook: Ideals, Varieties, and Algorithms; An Introduction to C David Cox,John Little,Donal O’Shea BookLatest edition Springer Science+Business Med

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David Cox,John Little,Donal O’Sheaarticular positive and Turing equivalent) to a given recursively enumerable set. These groups can be interpreted as groups of finite state machines or as subgroups of topological full groups, on effective subshifts over other torsion groups. We define a recursion-theoretic property of a set of natur

FOIL

David Cox,John Little,Donal O’Sheaarticular positive and Turing equivalent) to a given recursively enumerable set. These groups can be interpreted as groups of finite state machines or as subgroups of topological full groups, on effective subshifts over other torsion groups. We define a recursion-theoretic property of a set of natur

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

叙述

Elimination Theory,ll be given in two main theorems: the Elimination Theorem and the Extension Theorem. We will prove these results using Groebner bases and the classic theory of resultants. The geometric interpretation of elimination will also be explored when we discuss the Closure Theorem. Of the many applications

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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 §§3 and 4, where we will

Forehead-Lift

Polynomial and Rational Functions on a Variety,se objects, and especially the mappings which preserve some property of interest. For instance, in linear algebra after studying vector spaces, you also studied the properties of . between vector spaces (mappings that preserve the vector space operations of sum and scalar product).

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Robotics and Automatic Geometric Theorem Proving,nuing a theme introduced in several examples in Chapter 1, 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 o

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