Journal of Symbolic Computation
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
An algorithm to compute floating point Gro¨bner bases
Proceedings of the Maple summer workshop and symposium on Mathematical computation with Maple V : ideas and applications: ideas and applications
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Gröbner-Bases, Gaussian elimination and resolution of systems of algebraic equations
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Numerical stability and stabilization of Groebner basis computation
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Canonical comprehensive Gröbner bases
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Computing floating-point gröbner bases stably
Proceedings of the 2007 international workshop on Symbolic-numeric computation
A speed-up of the algorithm for computing comprehensive Gröbner systems
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Fast optimal three view triangulation
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
Term cancellations in computing floating-point Gröbner bases
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
Solvability of bivariate polynomial systems under perturbation
ACM Communications in Computer Algebra
Computing a structured Gröbner basis approximately
Proceedings of the 36th international symposium on Symbolic and algebraic computation
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Gröbner basis is one of the most important tools in recent symbolic algebraic computations. However, computing a Gröbner basis for the given polynomial ideal is not easy and it is not numerically stable if polynomials have inexact coefficients. In this paper, we study what we should get for computing a Gröbner basis with inexact coefficients and introduce a naive method to compute a Gröbner basis by reduced row echelon form, for the ideal generated by the given polynomial set having a priori errors on their coefficients.