This method gives a randomized algorithm for ideal membership. If $f$ lies in the saturated ideal of each of the chains of the network, then the output is always zero. Otherwise, it returns a nonzero element with high probability.
As an example, consider the ideal of cyclically adjacent minors.
i1 : I = adjacentMinorsIdeal(QQ,2,6); o1 : Ideal of QQ[a..l] |
i2 : X = gens ring I; |
i3 : J = I + (X_0 * X_(-1) - X_1*X_(-2)); o3 : Ideal of QQ[a..l] |
i4 : f = sum gbList J; |
i5 : N = chordalNet J; |
i6 : chordalTria N; |
i7 : f % N == 0 o7 = true |
It is assumed that the base field has sufficiently many elements. For small finite fields one must work over a suitable field extension.