Engaged
发表于 2025-3-23 12:01:58
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
发表于 2025-3-23 16:01:48
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
开始从未
发表于 2025-3-23 18:25:45
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aerial
发表于 2025-3-23 22:48:26
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
发表于 2025-3-24 02:22:21
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
提名
发表于 2025-3-24 09:00:34
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
发表于 2025-3-24 12:28:03
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).
Bouquet
发表于 2025-3-24 17:46:32
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
enfeeble
发表于 2025-3-24 21:33:20
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向宇宙
发表于 2025-3-24 23:28:37
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