Singular Manual: primdecGTZ

  | #### D.4.28.2 primdecGTZ Procedure from library `primdec.lib` (see primdec_lib). Usage: primdecGTZ(I); I ideal Return: a list pr of primary ideals and their associated primes for a proper ideal I, otherwise pr = list( list( ideal(1), ideal(1) )
         pr[i][1]   the i-th primary component,
         pr[i][2]   the i-th prime component.
Note: - Algorithm of Gianni/Trager/Zacharias. - Designed for characteristic 0, works also in char k > 0, if it terminates (may result in an infinite loop in small characteristic!) - 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),lp;
    poly  p = z2+1;
    poly  q = z3+2;
    ideal i = p*q^2,y-z2;
    list pr = primdecGTZ(i);
    pr;
    ==> [1]:
    ==>    [1]:
    ==>       _[1]=z2+1
    ==>       _[2]=y-z2
    ==>    [2]:
    ==>       _[1]=z2+1
    ==>       _[2]=y-z2
    ==> [2]:
    ==>    [1]:
    ==>       _[1]=z6+4z3+4
    ==>       _[2]=y-z2
    ==>    [2]:
    ==>       _[1]=z3+2
    ==>       _[2]=y-z2

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