Solving systems of algebraic equations by a general elimination method
Journal of Symbolic Computation
Some algebraic and geometric computations in PSPACE
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Computing primitive elements of extension fields
Journal of Symbolic Computation
Efficient computation of zero-dimensional Gro¨bner bases by change of ordering
Journal of Symbolic Computation
A tangent-secant method for polynomial complex root calculation
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Zeros, multiplicities, and idempotents for zero-dimensional systems
Algorithms in algebraic geometry and applications
A Global Bisection Algorithm for Computing the Zeros of Polynomials in the Complex Plane
Journal of the ACM (JACM)
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
An Exact Method for Finding the Roots of a Complex Polynomial
ACM Transactions on Mathematical Software (TOMS)
A Gröbner free alternative for polynomial system solving
Journal of Complexity
Algebraic Solution of Systems of Polynomial Equations Using Groebner Bases
AAECC-5 Proceedings of the 5th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Complete numerical isolation of real roots in zero-dimensional triangular systems
Journal of Symbolic Computation
Root isolation for bivariate polynomial systems with local generic position method
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
An efficient algorithm for the stratification and triangulation of an algebraic surface
Computational Geometry: Theory and Applications
The DMM bound: multivariate (aggregate) separation bounds
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Determining the topology of real algebraic surfaces
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Local generic position for root isolation of zero-dimensional triangular polynomial systems
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Journal of Symbolic Computation
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In this paper, a linear univariate representation for the roots of a zero-dimensional polynomial equation system is presented, where the complex roots of the polynomial system are represented as linear combinations of the roots of several univariate polynomial equations. An algorithm is proposed to compute such a representation for a given zero-dimensional polynomial equation system based on Grobner basis computation. The main advantage of this representation is that the precision of the roots of the system can be easily controlled. In fact, based on the linear univariate representation, we can give the exact precisions needed for isolating the roots of the univariate equations in order to obtain roots of the polynomial system with a given precision. As a consequence, a root isolating algorithm for a zero-dimensional polynomial equation system can be easily derived from its linear univariate representation.