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

$$\begin{array}{ccc} R & \longrightarrow & R/I \oplus \ldots \oplus R/I \\ 1 & \longmapsto & (b_1,\ldots,b_s) \end{array}$$

It can be computed as

$$(I:J)=modulo\left((b_1\vert\ldots\vert b_s)^T\,,\:(a_1\vert\l... ...vert a_r)\oplus \ldots \oplus (a_1\vert\ldots\vert a_r)\right)$$

SINGULAR example (see example in section 2.3.1):

ring R=...;
ideal I=...;
ideal J=...;
quotient(I,J)