Vol 40, No. 2, June 2006 ISSAC 2006 Poster Abstracts We write C = C1 ª C2 with C1 = V(a x1 , b c) \ V(an b) and C2 = V(a c, b x2 ) \ V(an b). To compute a (C), we can apply Theorem 3.1 to C1 and C2 , separately. In the following the tilde has the same notational meaning as in Theorem 3.1. First we compute (note that Gr¨bner bases can easily be computed by hand) o a (V(a x1 , b c, t(an b) 1)) = V(b c, t(c xn ) + 1). Ë 1 Then by Theorem 3.1 To eliminate the variable b we compute b (V(b c, t(c xn ) 1)) = V(t(c xn ) 1) Ë 1 1 and again by Theorem 3.1 we obtain b ( a (C1 )) = A2 \ V(c xn ). 1 b ( a (C2 )) = A2 \ V(x2 cn ). Since {c xn , x2 cn , xn x2 } is a Gr¨bner bases, we ï¬nally obtain o 1
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Hensel fan
Osoekawa, Takeshi; Sasaki, Tateaki
Follow ACM Communications in Computer Algebra
, Volume 40 (2)
Association for Computing Machinery – Jun 1, 2006
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