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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David Cox,John Little,Donal O’Sheaation in this digital epoch. As a consequence, they indicate a public source of evidence in our everyday life. Beside their benefits, the accessibility of them could bring a major detriment as they can be modified easily by a media processing application..Detection of tampering with digital images i

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Projective Algebraic Geometry,rojective point of view. By working in projective space, we will get a much better understanding of the Extension Theorem from Chapter 3. The chapter will end with a discussion of the geometry of quadric hypersurfaces.

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Groebner Bases,ion. The method of Groebner bases is also used in several powerful computer algebra systems to study specific polynomial ideals that arise in applications. In Chapter 1, we posed many problems concerning the algebra of polynomial ideals and the geometry of affine varieties. In this chapter and the next, we will focus on four of these problems.

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The Algebra-Geometry Dictionary,arising out of the Hilbert Basis Theorem: notably the possibility of decomposing a variety into a union of simpler varieties and the corresponding algebraic notion of writing an ideal as an intersection of simpler ideals.

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Textbook 19921st editionnvolved a lot of abstract mathematics and were only taught in graduate school. But in the 1960‘s, Buchberger and Hironaka discovered new algorithms for manipulating systems of polynomial equations. Fueled by the development of computers fast enough to run these algorithms, the last two decades have

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