## A First Course in Computational Algebraic GeometryA First Course in Computational Algebraic Geometry is designed for young students with some background in algebra who wish to perform their first experiments in computational geometry. Originating from a course taught at the African Institute for Mathematical Sciences, the book gives a compact presentation of the basic theory, with particular emphasis on explicit computational examples using the freely available computer algebra system, Singular. Readers will quickly gain the confidence to begin performing their own experiments. |

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A First Course in Computational Algebraic Geometry Wolfram Decker,Gerhard Pfister Limited preview - 2013 |

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afﬁne algebraic set afﬁne rings algebraic geometry algebraic set associated primes bases Buchberger’s algorithm called coefﬁcients computer algebra consider coordinate change deﬁned Deﬁnition dim(I dimension element elimination ideal elliptic curves f G K ﬁeld ﬁnd ﬁnite group ﬁrst given Greuel and Pﬁster Grobner basis Hence Hilbert function Hilbert polynomial homogeneous ideal ideal H ideal quotients inﬁnite integral intersection multiplicities irreducible components leading monomial Lemma Let G Let I C K lexicographical ordering linear LM(g matrix monomial ideal monomial ordering morphism NF(f nilpotent Noether normalization nonempty nonzero normal form Nullstellensatz Permutation Group poly f polynomial f polynomial functions polynomial ring prime ideal Problem Proof quotient ring R C S radical Remark respect to 1p ring extension ring R2 sage Section SINGULAR Example solution solvable standard basis std(I subset Sudoku twisted cubic vanishing locus V(I variables vector space weakNF(h Zariski closure