GVW算法在Gr\"{o}bner 基的理论与计算中是非常重要与有效的.文章引入一种新的$S$-多项式,利用GVW算法中的``top-约化"来约化$S$-多项式,进而给出同时计算
理想的Gr\"{o}bner 基及理想合冲模的首项的Gr\"{o}bner 基的一种新算法,并且得到了一些有趣的结果.

GVW algorithm is very important and effective in the theory and the calculation of Gr¨obner basis. In this paper, a new S-polynomial is introduced, and the “top - reduction” is used in the GVW algorithm to reduce the new S-polynomial. Then a new algorithm is given, which can be used to compute simultaneously the Gr¨obner basis for the ideal generated by the polynomials and the Gr¨obner basis for the leading terms of the syzygy module of the polynomial, and some interesting results are obtained.