Singular Manual: globalSections

| #### D.5.4.7 globalSections Procedure from library `divisors.lib` (see divisors_lib). Usage: globalSections(A); A = divisor. Assume: A is a divisor on X. Return: a list with a basis of the space of global sections of D. Theory: We assume that the qring of X satisfies the S2-condition and that X is smooth. We compute sat((f*J) : I) /f where D = (I)-(J). Example:
    LIB "divisors.lib";
    ring r=31991,(x,y,z),dp;
    ideal I = y^2*z - x*(x-z)*(x+3*z);
    qring Q = std(I);
    divisor P = makeDivisor(ideal(x,z),ideal(1));
    divisor D = multdivisor(4,P);
    globalSections(D);
    ==> [1]:
    ==>    _[1]=x2
    ==>    _[2]=z2
    ==>    _[3]=yz
    ==>    _[4]=xz
    ==> [2]:
    ==>    z2

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