Singular Manual: blowUp

| #### D.5.15.1 blowUp Procedure from library `resolve.lib` (see resolve_lib). Usage: blowUp(J,C[,W][,E]); W,J,C = ideals, E = list Assume: J = ideal containing W ( W = 0 if not specified) C = ideal containing J E = list of smooth hypersurfaces (e.g. exceptional divisors) Note: W the ideal of the ambient space, C the ideal of the center of the blowup and J the ideal of the variety Important difference to blowUp2: - the ambient space V(W) is blown up and V(J) transformed in it - V(C) is assumed to be non-singular Compute: the blowing up of W in C, the exceptional locus, the strict transform of J and the blowup map Return: list, say l, of size at most size(C), l[i] is the affine ring corresponding to the i-th chart each l[i] contains the ideals - aS, ideal of the blownup ambient space - sT, ideal of the strict transform - eD, ideal of the exceptional divisor - bM, ideal corresponding to the blowup map l[i] also contains a list BO, which can best be viewed with showBO(BO) detailed information on the data type BO can be viewed via the command showDataTypes(); Example:
    LIB "resolve.lib";
    ring R=0,(x,y),dp;
    ideal J=x2-y3;
    ideal C=x,y;
    list blow=blowUp(J,C);
    def Q=blow[1];
    setring Q;
    aS;
    ==> aS[1]=0
    sT;
    ==> sT[1]=y(1)^2-x(2)
    eD;
    ==> eD[1]=x(2)
    bM;
    ==> bM[1]=x(2)*y(1)
    ==> bM[2]=x(2)

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