Evaluation techniques for zero-dimensional primary decomposition
نویسندگان
چکیده
منابع مشابه
Evaluation techniques for zero-dimensional primary decomposition
This paper presents a new algorithm that computes the local algebras of the roots of a zero-dimensional polynomial equation system, with a number of operations in the coefficient field that is polynomial in the number of variables, in the evaluation cost of the equations and in a Bézout number.
متن کاملEvaluation Techniques for Zero-dimensional Primary Decomposition Extended Abstract
In this talk, we will present an algorithm that computes the local algebra of the roots of a zero-dimensional polynomial equations system, whose cost is polynomial in the number of variables, in the evaluation cost of the equations and in the Bézout number of the input system. Let K be a field of characteristic zero, and let f1, . . . , fm, g be polynomials in K[x1, . . . , xn] such that the sy...
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A new algorithm is presented for computing primary decomposition of zero-dimensional ideals over finite fields. Like Berlekamp’s algorithm for univariate polynomials, the new method is based on the invariant subspace of the Frobenius map acting on the quotient algebra. The dimension of the invariant subspace equals the number of primary components, and a basis of the invariant subspace yields a...
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We present a zero decomposition theorem and an algorithm based on Wu’s method, which computes a zero decomposition with multiplicity for a given zerodimensional polynomial system. If the system satisfies some condition, the zero decomposition is of triangular form.
متن کاملPrimary decomposition of zero-dimensional ideals: Putting Monico’s algorithm into practice
Monico published in [Journal of Symbolic Computation, 34(5):451–459, 2002] an algorithm to compute the primary decomposition of a zero-dimensional ideal, that mostly relies on a characteristic polynomial computation modulo the input ideal, and its factorization. We revisit this algorithm, and discuss Maple and Magma implementations that contradict the somehow pessimistic conclusions of Monico’s...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2009
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2008.02.008