Details:
Title  Intervals, syzygies, numerical Gr\"obner bases: A mixed study.  Author(s)  Marco Bodrato, Alberto Zanoni  Type  Book, Chapter in Book, Conference Proceeding  Abstract  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.  Keywords  Gröbner bases, numerical coefficients, syzygie  ISBN  9783540451822/pbk 
URL 
http://link.springer.com/chapter/10.1007%2F11870814_5 
Language  English  Pages  6476  Publisher  Berlin: Springer  Year  2006  Edition  0  Translation 
No  Refereed 
No 
