Showing papers in "Journal of Symbolic Computation in 2013"

TL;DR: It is shown that if the leading coefficient tensor of a polynomial system is a triangular tensor with nonzero diagonal elements, then the system definitely has a solution in the complex space.

TL;DR: This work explicitly decomposes a cubic polynomial in three variables as the sum of five cubes (Sylvester Pentahedral Theorem), and discusses some algorithms to compute the Waring decomposition.

TL;DR: In this paper, the authors combine some new theoretical results with computer calculations to determine all cubic vertex-transitive graphs of order at most 1280, and also all tetravalent arctransitive graph of order with valency 3 at most 640.

TL;DR: By allowing for Hermitian matrices instead, this work shows that a matrix of linear forms is definite if and only if its co-maximal minors interlace its determinant and extends a classical construction of determinantal representations of Dixon from 1902.

TL;DR: This paper proposes a formulation of the problem of Gian-Carlo Rota's problem using the framework of operated algebras and viewing an associative algebra with a linear operator as one that satisfies a certain operated polynomial identity, and allows to apply theories of rewriting systems and Grobner-Shirshov bases.

TL;DR: The tensor decomposition addressed in this paper may be seen as a generalization of Singular Value Decomposition of matrices and how the decomposition can be recovered from eigenvector computation.

TL;DR: Under the assumption that a tight superset of the support of the product is known, the benefit of asymptotically fast arithmetic for sparse multivariate polynomials and power series is observed, which might lead to speed-ups in several areas of symbolic and numeric computation.

TL;DR: It is proved that the smallest degree of an apolar 0-dimensional scheme of a general cubic form in n+1 variables is at most 2n+2, when n>=8, and therefore smaller than the rank of the form.

TL;DR: In this paper, the complexity of solving the generalized min-rank problem has been studied, i.e., computing the set of points where the evaluation of a polynomial matrix has rank at most 1.

TL;DR: In this article, regular chains and triangular decompositions are adapted for semi-algebraic solutions of polynomial systems, and two specifications (full and lazy) of such a decomposition are proposed.

TL;DR: In this paper, the authors exploit the symmetries of Hilbert polynomials to obtain a new open cover, consisting of marked schemes over Borel-fixed ideals, whose number is significantly smaller than the number of Plucker coordinates.

TL;DR: Two constructions of a basis F of a polynomial ideal I in K[x"1,...,x"n] with degrees deg(F)@?d are modified in order to give worst case bounds depending on the ideal dimension proving that deg(G)=d^n^^^@Q^^^(^^^1^^^)^2^^^ @Q^^+1 for r-dimensional ideals (in the worst case).

TL;DR: A new efficient algorithm for computing a comprehensive Grobnersystem of a parametric polynomial ideal over k[U][X] is presented, which has been implemented in Magma and Singular, and experimented with a number of examples from different applications.

TL;DR: This paper first derive an algebraizable sufficient condition for the existence of a polynomial Lyapunov function, then applies a real root classification based method step by step to under-approximate this derived condition as a semi-algebraic system such that the semi-Al algebraic system only involves the coefficients of the pre-assumed polynometric.

TL;DR: This paper presents an algorithm to compute the CUP decomposition of a matrix, adapted from the LSP algorithm of Ibarra, Moran and Hui (1982), and shows reductions from the other most common Gaussian elimination based matrix transformations and decompositions to the Cup decomposition.

TL;DR: The cyclic Bergman fan of a matroid M is defined, which is a simplicial polyhedral fan supported on the tropical linear space T(M) of M and is amenable to computational purposes.

TL;DR: Two new algorithms are presented that could, for the first time even though probabilistic, compute the Grobner basis of the famous ideal of cyclic 9-roots over the rationals with Singular.

TL;DR: In this article, an algebra embedding @i:K->S from the free associative algebra K generated by a finite or countable set X into the skew monoid ring [email protected][email protected] defined by the commutative polynomial ring P=K[XxN^@?] and by the monoid @S= generated by suitable endomorphism @s:P->P.

TL;DR: New methods to compute the radical of an ideal, assuming its complex (resp. real) variety is finite, are described, which combines the strength of existing algorithms and provides a unified treatment for the computation of border bases for the ideal, the radical ideal and the real radical ideal.

TL;DR: Using Las Vegas algorithms, it is proved that one can perform such operations as change of order, equiprojectable decomposition, or quasi-inverse computation with a cost that is essentially that of modular composition.

TL;DR: Given a reduced affine algebra A over a perfect field K, parallel algorithms to compute the normalization A@?

TL;DR: In this paper, a superminimal reduction relation was proposed to obtain an embedding of a monomial strongly stable ideal in an affine space of low dimension, which is called a J-marked family.

TL;DR: A more generalized theorem is presented to give a more generalized stable condition for parametric polynomial systems and two efficient algorithms for computing comprehensive Grobner bases are proposed.

TL;DR: The spline space C"k^r(@D) attached to a subdivided domain @D of R^d is the vector space of functions of class C^r which are polynomials of degree ==4r+1, and the same method used in this proof yields the dimension straightaway for many other cases.

TL;DR: This paper compute explicitly, in a more general setting and using an algorithmic approach, the connection and linearization coefficients of the Askey-Wilson orthogonal polynomial families and presents an algorithm to deduce the inversion coefficients for the basis B"n(a,x) in terms of the ASK-Wilson polynomials.

TL;DR: In this article, an algorithm is given for determining the topology of an algebraic space curve and to compute a certified G^1 rational parametric approximation of the space curve, which works by extending to dimension one the local generic position method for solving zero-dimensional polynomial equation systems.

TL;DR: In this paper, the authors studied the equidimensional decomposition of affine varieties defined by sparse polynomial systems and gave combinatorial conditions for the existence of positive dimensional components.

TL;DR: An algorithm is given for explicitly constructing stabilization generators for a family of Laurent toric ideals involved in applications to algebraic statistics and a theorem is proved which says that these chains locally stabilize.

TL;DR: The method is used to classify the nilpotent Lie algebras in this class in dimensions 7 and 8 that admit nilsoliton inner products, and it is presented that all such nilsolon metric Lie alagbras are classified.

TL;DR: The main purpose of this paper is to present algorithms for computing a holonomic system for the definite integral of aholonomic function with parameters over a domain defined by polynomial inequalities.