Evaluation techniques for zero-dimensional primary decomposition
نویسنده
چکیده
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.
منابع مشابه
A Survey of Primary Decomposition using GrSbner Bases
A Survey of Primary Decomposition using GrSbner Bases MICHELLE WILSON Submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Master of Science We present a survey of primary decomposition of ideals in a noetherian commutative polynomial ring R[x] = R[xi,..., x,]. With the use of ideal operations introduced and the lexicographical Gr6bner bases of...
متن کاملInfinite-dimensional versions of the primary, cyclic and Jordan decompositions
The famous primary and cyclic decomposition theorems along with the tightly related rational and Jordan canonical forms are extended to linear spaces of infinite dimensions with counterexamples showing the scope of extensions.
متن کاملAddendum to: "Infinite-dimensional versions of the primary, cyclic and Jordan decompositions", by M. Radjabalipour
In his paper mentioned in the title, which appears in the same issue of this journal, Mehdi Radjabalipour derives the cyclic decomposition of an algebraic linear transformation. A more general structure theory for linear transformations appears in Irving Kaplansky's lovely 1954 book on infinite abelian groups. We present a translation of Kaplansky's results for abelian groups into the terminolo...
متن کاملPrimary decomposition of zero-dimensional ideals over finite fields
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...
متن کاملAlgorithms for Zero-Dimensional Ideals Using Linear Recurrent Sequences
Inspired by Faugère and Mou’s sparse FGLM algorithm, we show how using linear recurrent multi-dimensional sequences can allow one to perform operations such as the primary decomposition of an ideal, by computing the annihilator of one or several such sequences.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Symb. Comput.
دوره 44 شماره
صفحات -
تاریخ انتشار 2009