Titlebook: Ideals, Varieties, and Algorithms; An Introduction to C David Cox,John Little,Donal O’Shea Textbook 19921st edition Springer Science+Busine

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shape and skeleton pruning based on branch analysis. In this chapter, we focus on how the skeletonization of an image can be studied in the Cellular Automata framework and, as a case study, we consider in detail the Guo and Hall skeletonizing algorithm.

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Textbook 19921st editionef that the growing importance of these computational techniques warrants their introduction into the undergraduate (and graduate) mathematics curricu- lum. Many undergraduates enjoy the concrete, almost nineteenth century, flavor that a computational emphasis brings to the subject. At the same time

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Groebner Bases,ter, 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 ideals that arise in applicat

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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

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Polynomial and Rational Functions on a Variety,e 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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