Singular Manual: minAssGTZ

| #### D.4.27.7 minAssGTZ Procedure from library `primdec.lib` (see primdec_lib). 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 Example:
    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

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