Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Stabilization of polynomial systems solving with Groebner bases
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Efficient algorithms for ideal operations (extended abstract)
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Numerical stability and stabilization of Groebner basis computation
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Numerical Polynomial Algebra
Floating-Point Gröbner Basis Computation with Ill-conditionedness Estimation
Computer Mathematics
Term cancellations in computing floating-point Gröbner bases
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
Structures of precision losses in computing approximate Gröbner bases
Journal of Symbolic Computation
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In Gröbner bases computation, as in other algorithms in commutative algebra, a general open question is how to guide the calculations coping with numerical coefficients and/or not exact input data. It often happens that, due to error accumulation and/or insufficient working precision, the obtained result is not one expects from a theoretical derivation. The resulting basis may have more or less polynomials, a different number of solution, roots with different multiplicity, another Hilbert function, and so on. Augmenting precision we may overcome algorithmic errors, but one does not know in advance how much this precision should be, and a trial–and–error approach is often the only way to follow. Coping with initial errors is an even more difficult task. In this experimental work we propose the combined use of syzygies and interval arithmetic to decide what to do at each critical point of the algorithm. AMS Subject Classification: 13P10, 65H10, 90C31.