Algebraic computations using Macaulay dual spaces
نویسنده
چکیده
The algebraic operations of addition, intersection, elimination, and quotient are fundamental to computational algebraic geometry. This article describes how to perform these operations on homogeneous ideals using Macaulay dual spaces. If F is a polynomial system with finitely many solutions, these operations are used to compute the homogenization of the ideal generated by F which, in particular, yields the number of solutions, counting multiplicity, of F . These computations can be performed either using exact or floating point arithmetic and are naturally parallelizable.
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تاریخ انتشار 2011