Singular Manual: blowUp2

| #### D.5.8.2 blowUp2 Procedure from library `resolve.lib` (see resolve_lib). Usage: blowUp2(J,C); J,C = ideals, Assume: C = ideal containing J Note: C the ideal of the center of the blowup and J the ideal of the variety Important differences to blowUp: - V(J) itself is blown up, not the ambient space - C is not assumed to be non-singular Compute: the blowing up of J in C, the exceptional locus and the blow-up 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 - Jnew, ideal of the blownup J - eD, ideal of the new exceptional divisor - bM, ideal corresponding to the blowup map Example:
    LIB "resolve.lib";
    ring r=0,(x,y,z),dp;
    ideal I=z2-x^3*y^2;
    ideal C=z,xy;
    list li=blowUp2(I,C);
    size(li);                  // number of charts
    ==> 2
    def S1=li[1];
    setring S1;                // chart 1
    basering;
    ==> // coefficients: QQ
    ==> // number of vars : 3
    ==> //        block   1 : ordering dp
    ==> //                  : names    x(1) x(3) y(2)
    ==> //        block   2 : ordering C
    Jnew;
    ==> Jnew[1]=x(1)*y(2)^2-1
    eD;
    ==> eD[1]=x(3)
    ==> eD[2]=x(1)*y(2)^2-1
    bM;
    ==> bM[1]=x(1)
    ==> bM[2]=x(3)*y(2)^3
    ==> bM[3]=x(3)
    def S2=li[2];
    setring S2;                // chart 2
    basering;
    ==> // coefficients: QQ
    ==> // number of vars : 2
    ==> //        block   1 : ordering dp
    ==> //                  : names    x(2) y(1)
    ==> //        block   2 : ordering C
    Jnew;
    ==> Jnew[1]=0
    eD;
    ==> eD[1]=x(2)*y(1)^2
    bM;
    ==> bM[1]=y(1)^2
    ==> bM[2]=x(2)
    ==> bM[3]=x(2)*y(1)^3

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