Singular Manual: modPrimdecGTZ

| #### D.4.14.1 modPrimdecGTZ Procedure from library `modprimdec.lib` (see modprimdec_lib). Usage: modPrimdecGTZ(I, #); I ideal, # an optional list which is either empty (not entered) or consists of precisely one integer which is 0 or 1. Assume: The basering of I is defined over the rationals. Return: A primary decomposition of I. Note: - The final result will be checked for correctness if # is either empty (not entered) or if #[1] = 1. Without the check, the functions reurns a result which is correct with high probability. - For local orderings, the result represents a primary decomposition in the localization of the polynomial ring, not in the power series ring. Example:
    LIB "modprimdec.lib";
    ring R = 0, (x,y), dp;
    ideal I = x9y2+x10, x2y7-y8;
    modPrimdecGTZ(I);
    ==> [1]:
    ==>    [1]:
    ==>       _[1]=y-1
    ==>       _[2]=x+1
    ==>    [2]:
    ==>       _[1]=y-1
    ==>       _[2]=x+1
    ==> [2]:
    ==>    [1]:
    ==>       _[1]=y2+y+1
    ==>       _[2]=x-y-1
    ==>    [2]:
    ==>       _[1]=y2+y+1
    ==>       _[2]=x-y-1
    ==> [3]:
    ==>    [1]:
    ==>       _[1]=y12
    ==>       _[2]=x2y7-y8
    ==>       _[3]=x9y2+x10
    ==>    [2]:
    ==>       _[1]=y
    ==>       _[2]=y2+10x

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