کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4625569 1631763 2017 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Unification and extension of intersection algorithms in numerical algebraic geometry
ترجمه فارسی عنوان
ادغام و گسترش الگوریتم های تقاطع در هندسه جبری
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی

The solution set of a system of polynomial equations, called an algebraic set, can be decomposed into finitely many irreducible components. In numerical algebraic geometry, irreducible algebraic sets are represented by witness sets, whereas general algebraic sets allow a numerical irreducible decomposition comprising a collection of witness sets, one for each irreducible component. We denote the solution set of any system of polynomials f:NC→nCf:CN→Cn as V(f)⊂NCV(f)⊂CN. Given a witness set for some algebraic set Z⊂NCZ⊂CN and a system of polynomials f:NC→nC,f:CN→Cn, the algorithms of this paper compute a numerical irreducible decomposition of the set Z∩V(f)Z∩V(f). While extending the types of intersection problems that can be solved via numerical algebraic geometry, this approach is also a unification of two existing algorithms: the diagonal intersection algorithm and the homotopy membership test. The new approach includes as a special case the “extension problem” where one wishes to intersect an irreducible component A   of V(g(x))V(g(x)) with V(f(x,y)),V(f(x,y)), where f introduces new variables, y. For example, this problem arises in computing the singularities of A when the singularity conditions are expressed in terms of new variables associated to the tangent space of A. Several examples are included to demonstrate the effectiveness of our approach applied in a variety of scenarios.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 293, 15 January 2017, Pages 226–243
نویسندگان
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