Singular Manual: sat

| #### D.4.7.7 sat Procedure from library `elim.lib` (see elim_lib). Usage: sat(id,j); id=ideal/module, j=ideal Return: list of an ideal/module [1] and an integer [2]: [1] = saturation of id with respect to j (= union_(k=1...) of id:j^k) [2] = saturation exponent (= min( k | id:j^k = id:j^(k+1) )) Note: [1] is a standard basis in the basering Display: saturation exponent during computation if printlevel >=1 Example:
    LIB "elim.lib";
    int p      = printlevel;
    ring r     = 2,(x,y,z),dp;
    poly F     = x5+y5+(x-y)^2*xyz;
    ideal j    = jacob(F);
    sat(j,maxideal(1));
    ==> [1]:
    ==>    _[1]=x3+x2y+xy2+y3
    ==>    _[2]=y4+x2yz+y3z
    ==>    _[3]=x2y2+y4
    ==> [2]:
    ==>    4
    printlevel = 2;
    sat(j,maxideal(2));
    ==> // compute quotient 1
    ==> // compute quotient 2
    ==> // compute quotient 3
    ==> // saturation becomes stable after 2 iteration(s)
    ==>
    ==> [1]:
    ==>    _[1]=x3+x2y+xy2+y3
    ==>    _[2]=y4+x2yz+y3z
    ==>    _[3]=x2y2+y4
    ==> [2]:
    ==>    2
    printlevel = p;
See also: modSat.

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