Showing papers in "Journal of Symbolic Computation in 2012"

TL;DR: This work presents a hybrid symbolic-numeric algorithm for certifying a polynomial or rational function with rational coefficients to be non-negative for all real values of the variables by computing a representation for it as a fraction of twoPolynomial sum-of-squares (SOS) with rational coefficient.

TL;DR: This work counted hundreds of curves, until one was found that is suitable for cryptographic use, with a state-of-the-art security level of approximately 2^1^2^8 and desirable speed properties.

TL;DR: An overview of the key ideas which have led to either better implementation techniques or a better understanding of the underlying theory and new techniques that are essential to the recent success and for future research directions in the development of triangular decomposition methods.

TL;DR: The main idea underlying the algorithm is to substitute the repeated projection step of CAD by a single projection without carrying out a parametric existential decision over the reals, and it is found that the algorithm can tackle important and challenging problems, such as numerical stability analysis of the widely-used MacCormack's scheme.

TL;DR: The present paper is a revised version of Bachler et al. (2010) and includes the proofs of correctness and termination of the decomposition algorithm and illustrates the algorithm with further instructive examples and describes its Maple implementation.

TL;DR: This work enhances the known multi-sum algorithms to derive recurrences for sums with complicated boundary conditions, and presents new algorithms to find formal Laurent series solutions of a given recurrence relation.

TL;DR: This work constructs an associated parametric mean payoff game problem, and shows that the optimality of a given point, or the unboundedness of the problem, can be certified by exhibiting a strategy for one of the players having certain infinitesimal properties that are characterize combinatorially.

TL;DR: In this paper, the authors studied the geometry of a semialgebraic set K in R^n and showed that its boundary lies on the irreducible hypersurface defined by the discriminant @D(f) of f. Explicit formulae for these hypersurfaces and discriminants are given.

TL;DR: Two algorithms for the computation of a shifted order basis of an mxn matrix of power series over a field K with [email protected]?n are presented, one of which balances the high degree rows and computes an order basis in the case that the shift is unbalanced but satisfies the condition.

TL;DR: A partial linearization technique, that is applicable also to other problems, is developed to transform a system involving H, which may have some columns of large degrees, to an equivalent system that has degrees reduced to that of the average column degree.

TL;DR: This work provides a method to detect isolated algebraic singularities and their branching degree and appears to be the first complete purely numerical method to compute isotopic approximations of algebraic curves with isolated singularities.

TL;DR: In this article, it was shown that for a polynomial of degree n with integer coefficients bounded by 2^@r, the topology of the induced curve can be computed with O(n^8@r(n+@r)) bit operations (O@? indicates that we omit logarithmic factors).

TL;DR: A practical algorithm which computes the accepting automaton for the insertion encoding of a permutation class, whenever this insertion encoding forms a regular language.

TL;DR: D degree bounding formulas are derived which allow to estimate the degree of the output equations from creative telescoping as a function of the order, and it is shown that equations of low order have high degree, and that higher order equations have lower degree.

TL;DR: The single-factor lifting algorithm may be applied as well to accelerate the computational resolution of several global arithmetic problems in which the improvement of an approximation to a single local irreducible factor of a polynomial is required.

TL;DR: This article discusses and compares max-str strategy and min-strategy improvement algorithms for static program analysis and indicates how the general setting can be instantiated for inferring numerical invariants of programs based on non-linear templates.

TL;DR: A decision procedure is presented for a certain class of sentences of first order logic involving integral polynomials and a certain specific analytic transcendental function trans(x) in which the variables range over the real numbers.

TL;DR: An explicit algorithm to compute a closed basis of the local dual space of I=(f1,?,ft) at a given isolated singular solution x?=(x?1,,?,x?s) when the Jacobian matrix J(x?) has corank one is presented.

TL;DR: In this paper, the complexity of the SqFreeEVAL algorithm is analyzed using continuous amortization, and a simple O(d(L+lnd) bound on the size of the subdivision tree is derived.

TL;DR: In this paper, the concept of proper triangular sets is introduced and an explicit formula for the number of zeros of a proper and monic triangular set is given, and an improved zero decomposition algorithm is proposed to reduce the zero set of an equation system to the union of zero sets of monic proper triangular set.

TL;DR: A new symbolic-numeric strategy for computing efficiently and accurately floating point Puiseux series defined by a bivariate polynomial over an algebraic number field, and the size of good primes obtained with deterministic and probabilistic strategies is estimated.

TL;DR: A family of Class II RRMF quintics is thereby newly identified, that correspond to the case where a(t),b(t) are linear, and have five degrees of freedom, as with the Class I curves.

TL;DR: A root isolating algorithm for a zero-dimensional polynomial equation system can be easily derived from its linear univariate representation, which can give the exact precisions needed for isolating the roots of the univariate equations.

TL;DR: A rigorous deterministic polynomial time algorithm is given for the modular inversion hidden number problem introduced by D.A. Howgrave-Graham and answers one of their open questions.

TL;DR: TheMacsyma system arose out of research on mathematical software in the AI group at MIT in the 1960s, and the attempts in the late 70s and the 80s to develop Macsyma systems that ran on popular computer architectures are discussed.

TL;DR: A generalisation and adaptation of Kedlaya's algorithm for computing the zeta-function of a hyperelliptic curve over a finite field of odd characteristic that the author used for the implementation of the algorithm in the Magma library is described.

TL;DR: A method based on symbolic-numeric reduction to geometric involutive form to compute the primary component of and a basis of Max Noether space for a polynomial system at an isolated singular solution is presented.

TL;DR: It is proved that there exists a non-empty Zariski-open set @?@?GL"n(C) such that f(x) is positive for all x@?V@?R^n if and only if, f^A can be expressed as a sum of squares of polynomials on the truncated variety generated by the ideal.

TL;DR: In this article, the authors describe an algorithm which produces all ideals compatible with a given surjective Frobenius near-splitting, which is a special case of our algorithm.

TL;DR: This work investigates a recently-proposed strategy, the so-called “Mutant strategy”, on which a new family of algorithms is based (MXL, MXL2 and MXL3), and concludes that the MXLfamily of algorithms can be fundamentally reduced to redundant variants of F4.