next up previous contents
Next: 4.6 Saturation Up: 4. Syzygies Previous: 4.4 Module intersection 2

4.5 Ideal quotient

Lemma 4..8   The quotient (I:J) of two ideals $\:I=(a_1,\ldots,a_r)\:$ and $\:J=(b_1,\ldots,b_s)\:$ in R is the kernel of the map

R & \longrightarrow & R/I \oplus \ldots \oplus R/I \\
1 & \longmapsto & (b_1,\ldots,b_s)

It can be computed as

\begin{displaymath}(I:J)=modulo\left((b_1\vert\ldots\vert b_s)^T\,,\:(a_1\vert\l...
...vert a_r)\oplus \ldots \oplus
(a_1\vert\ldots\vert a_r)\right) \end{displaymath}

SINGULAR example (see example in section 2.3.1):

ring R=...;
ideal I=...;
ideal J=...;

| ZCA Home | Reports |