Singular

D.4.22.6 minAssGTZ

Usage:

minAssGTZ(I[, l]); I ideal, l list (optional)
Optional parameters in list l (can be entered in any order):
0, "facstd" -> uses facstd to first decompose the ideal (default)
1, "noFacstd" -> does not use facstd
"GTZ" -> the original algorithm by Gianni, Trager and Zacharias is used
"SL" -> GTZ algorithm with modificiations by Laplagne is used (default)

Return:

a list, the minimal associated prime ideals of proper ideal I, otherwise ideal(1)

Note:

- Designed for characteristic 0, works also in char k > 0 based on an algorithm of Yokoyama
- For local orderings, the result is considered in the localization of the polynomial ring, not in the power series ring
- For local and mixed orderings, the decomposition in the corresponding global ring is returned if the string 'global' is specified as second argument

LIB "primdec.lib";
ring  r = 0,(x,y,z),dp;
poly  p = z2+1;
poly  q = z3+2;
ideal i = p*q^2,y-z2;
list pr = minAssGTZ(i);
pr;
==> [1]:
==>    _[1]=z3+2
==>    _[2]=-z2+y
==> [2]:
==>    _[1]=z2+1
==>    _[2]=-z2+y