Computing the minimal number of equations defining an affine curve ideal-theoretically
نویسنده
چکیده
There is an algorithm which computes the minimal number of generators of the ideal of a reduced curve C in affine n-space over an algebraically closed field K, provided C is not a local complete intersection. The existence of such an algorithm follows from the fact that given d ∈ N, there exists d ∈ N, such that if a is a height n−1 radical ideal inK[X1, . . . ,Xn], generated by polynomials of degree at most d, then a admits a set of generators of minimal cardinality, with each generator having degree at most d, except possibly when K[X1, . . . ,Xn]/a is an (unmixed) local complete intersection.
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