Titlebook: Ideals, Varieties, and Algorithms; An Introduction to C David Cox,John Little,Donal O’Shea Textbook 19972nd edition Springer Science+Busine

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The Algebra-Geometry Dictionary,em 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

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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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David Cox,John Little,Donal O’Sheallular automata modeling approach, bringing together conceptThe recent dramatic advances inbiotechnology have led to an explosion of data in the life sciences at the molecular level as well as more detailed observation and ch- acterization at the cellular and tissue levels. Itis now absolutely clear

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David Cox,John Little,Donal O’Sheallular automata modeling approach, bringing together conceptThe recent dramatic advances inbiotechnology have led to an explosion of data in the life sciences at the molecular level as well as more detailed observation and ch- acterization at the cellular and tissue levels. Itis now absolutely clear