A note on required precision for computing numerical Groebner basis of exact input

Recently Y. Liang studied some numerical error analyses of computing Gröbner basis by floatingpoint numbers. One is for rounding errors in “Selecting lengths of floats for the computation of approximate Gröbner bases”, J. Symb. Comp., 53:40–52, 2013 and the other is for cancellation errors in “Structures of precision losses in computing approximate Gr¨obner bases”, J. Symb. Comp., 53:81– 95, 2013. In this paper, we give a short survey on his results and some notes on his approaches

厳密に与えられた系のGroebner基底を数値的に求める場合に必要な桁精度の考察

Recently Y. Liang studied some numerical error analyses of computing Gröbner basis by floatingpoint numbers. One is for rounding errors in “Selecting lengths of floats for the computation of approximate Gröbner bases”, J. Symb. Comp., 53:40–52, 2013 and the other is for cancellation errors in “Structures of precision losses in computing approximate Gr¨obner bases”, J. Symb. Comp., 53:81– 95, 2013. In this paper, we give a short survey on his results and some notes on his approaches