# Singular

#### D.5.6.8 computeV

Procedure from library `reszeta.lib` (see reszeta_lib).

Usage:
computeV(L,DL);
L = list of rings
DL = divisor list

Assume:
L has structure of output of resolve
DL has structure of output of prepEmbDiv

Return:
intvec,
i-th entry is multiplicity of i-th divisor in
pullback of volume form

Example:
 ```LIB "reszeta.lib"; ring R=0,(x,y,z),dp; ideal I=(x-y)*(x-z)*(y-z)-z4; list re=resolve(I,1); ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 1 ==> Index of the current chart in chart-tree: 1 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=-z4+x2y-xy2-x2z+y2z+xz2-yz2 ==> ==> ==== Exceptional Divisors: ==> empty list ==> ==> ==== Images of variables of original ring: ==> _[1]=x ==> _[2]=y ==> _[3]=z ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=z ==> _[2]=y ==> _[3]=x ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 4 ==> Index of the current chart in chart-tree: 2 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=y(1)^2*y(2)-y(1)*y(2)^2-y(1)^2+y(2)^2+x(3)+y(1)-y(2) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=x(3) ==> ==> ==== Images of variables of original ring: ==> _[1]=x(3)*y(2) ==> _[2]=x(3)*y(1) ==> _[3]=x(3) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=y(2)-1 ==> _[2]=y(1)-1 ==> _[3]=x(3) ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 6 ==> Index of the current chart in chart-tree: 3 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(2)*y(0)^4-y(0)^2*y(2)+y(0)*y(2)^2+y(0)^2-y(2)^2-y(0)+y(2) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=x(2) ==> ==> ==== Images of variables of original ring: ==> _[1]=x(2)*y(2) ==> _[2]=x(2) ==> _[3]=x(2)*y(0) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=y(2)-1 ==> _[2]=y(0)-1 ==> _[3]=x(2) ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 8 ==> Index of the current chart in chart-tree: 4 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(1)*y(0)^4+y(0)^2*y(1)-y(0)*y(1)^2-y(0)^2+y(1)^2+y(0)-y(1) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=x(1) ==> ==> ==== Images of variables of original ring: ==> _[1]=x(1) ==> _[2]=x(1)*y(1) ==> _[3]=x(1)*y(0) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=y(1)-1 ==> _[2]=y(0)-1 ==> _[3]=x(1) ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 10 ==> Index of the current chart in chart-tree: 5 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(3)^2*y(1)^2-x(3)^2*y(1)-2*x(3)*y(1)^2+2*x(3)*y(1)+y(1)^2-y(1)+y(2) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(2) ==> [2]: ==> _[1]=x(3)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(3)^2*y(2)-x(3)*y(2) ==> _[2]=x(3)^2*y(1)*y(2)-2*x(3)*y(1)*y(2)+x(3)*y(2)+y(1)*y(2)-y(2) ==> _[3]=x(3)*y(2)-y(2) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=y(2) ==> _[2]=x(3)-1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 12 ==> Index of the current chart in chart-tree: 6 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(2)^2*y(0)^2-x(2)^2*y(0)-2*x(2)*y(0)^2+2*x(2)*y(0)+y(0)^2-y(0)-y(2) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(2) ==> [2]: ==> _[1]=x(2)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(2)^2*y(0)*y(2)-2*x(2)*y(0)*y(2)+x(2)*y(2)+y(0)*y(2)-y(2) ==> _[2]=x(2)^2*y(2)-x(2)*y(2) ==> _[3]=x(2)*y(2)-y(2) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=y(2) ==> _[2]=x(2)-1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 14 ==> Index of the current chart in chart-tree: 7 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(3)^4*y(1)^4*y(2)-4*x(3)^3*y(1)^4*y(2)+4*x(3)^3*y(1)^3*y(2)+6*x(3)^\ 2*y(1)^4*y(2)-12*x(3)^2*y(1)^3*y(2)-4*x(3)*y(1)^4*y(2)+6*x(3)^2*y(1)^2*y(\ 2)+12*x(3)*y(1)^3*y(2)+y(1)^4*y(2)-x(3)^2*y(1)^2-12*x(3)*y(1)^2*y(2)-4*y(\ 1)^3*y(2)+x(3)^2*y(1)+2*x(3)*y(1)^2+4*x(3)*y(1)*y(2)+6*y(1)^2*y(2)-2*x(3)\ *y(1)-y(1)^2-4*y(1)*y(2)+y(1)+y(2) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(2) ==> [2]: ==> _[1]=x(3)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(3)^2*y(2)-x(3)*y(2) ==> _[2]=x(3)*y(2)-y(2) ==> _[3]=x(3)^2*y(1)*y(2)-2*x(3)*y(1)*y(2)+x(3)*y(2)+y(1)*y(2)-y(2) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=y(2) ==> _[2]=x(3)-1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 16 ==> Index of the current chart in chart-tree: 8 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(2)^4*y(2)+x(2)^2*y(0)^2-x(2)^2*y(0)-2*x(2)*y(0)^2+2*x(2)*y(0)+y(0)\ ^2-y(0) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(2) ==> [2]: ==> _[1]=x(2)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(2)^2*y(0)*y(2)-2*x(2)*y(0)*y(2)+x(2)*y(2)+y(0)*y(2)-y(2) ==> _[2]=x(2)*y(2)-y(2) ==> _[3]=x(2)^2*y(2)-x(2)*y(2) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=y(2) ==> _[2]=x(2)-1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 18 ==> Index of the current chart in chart-tree: 9 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(3)^4*y(1)^4*y(2)-4*x(3)^3*y(1)^4*y(2)+4*x(3)^3*y(1)^3*y(2)+6*x(3)^\ 2*y(1)^4*y(2)-12*x(3)^2*y(1)^3*y(2)-4*x(3)*y(1)^4*y(2)+6*x(3)^2*y(1)^2*y(\ 2)+12*x(3)*y(1)^3*y(2)+y(1)^4*y(2)+x(3)^2*y(1)^2-12*x(3)*y(1)^2*y(2)-4*y(\ 1)^3*y(2)-x(3)^2*y(1)-2*x(3)*y(1)^2+4*x(3)*y(1)*y(2)+6*y(1)^2*y(2)+2*x(3)\ *y(1)+y(1)^2-4*y(1)*y(2)-y(1)+y(2) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(2) ==> [2]: ==> _[1]=x(3)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(3)*y(2)-y(2) ==> _[2]=x(3)^2*y(2)-x(3)*y(2) ==> _[3]=x(3)^2*y(1)*y(2)-2*x(3)*y(1)*y(2)+x(3)*y(2)+y(1)*y(2)-y(2) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=y(2) ==> _[2]=x(3)-1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 20 ==> Index of the current chart in chart-tree: 10 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(2)^4*y(2)-x(2)^2*y(0)^2+x(2)^2*y(0)+2*x(2)*y(0)^2-2*x(2)*y(0)-y(0)\ ^2+y(0) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(2) ==> [2]: ==> _[1]=x(2)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(2)*y(2)-y(2) ==> _[2]=x(2)^2*y(0)*y(2)-2*x(2)*y(0)*y(2)+x(2)*y(2)+y(0)*y(2)-y(2) ==> _[3]=x(2)^2*y(2)-x(2)*y(2) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=y(2) ==> _[2]=x(2)-1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 22 ==> Index of the current chart in chart-tree: 11 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(2)^2*x(3)*y(1)^2-x(2)*x(3)*y(1)^2+1 ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=1 ==> [2]: ==> _[1]=y(1) ==> [3]: ==> _[1]=x(3) ==> ==> ==== Images of variables of original ring: ==> _[1]=x(3)^3*y(1)^2+x(3)^2*y(1) ==> _[2]=x(2)*x(3)^3*y(1)^2+x(3)^2*y(1) ==> _[3]=x(3)^2*y(1) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(2)^2*x(3)*y(1)^2-x(2)*x(3)*y(1)^2+1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 22 ==> Index of the current chart in chart-tree: 12 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(1)*x(2)^2-x(1)*x(2)-x(2)^2+x(2)+y(0) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(0) ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=x(1)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(1)^3*y(0)-2*x(1)^2*y(0)+x(1)*y(0) ==> _[2]=x(1)^3*x(2)*y(0)-3*x(1)^2*x(2)*y(0)+x(1)^2*y(0)+3*x(1)*x(2)*y(0)-2*x\ (1)*y(0)-x(2)*y(0)+y(0) ==> _[3]=x(1)^2*y(0)-2*x(1)*y(0)+y(0) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=y(0) ==> _[2]=x(1)-1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 24 ==> Index of the current chart in chart-tree: 13 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(2)^2*x(3)*y(1)^2-x(2)*x(3)*y(1)^2-1 ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=1 ==> [2]: ==> _[1]=y(1) ==> [3]: ==> _[1]=x(3) ==> ==> ==== Images of variables of original ring: ==> _[1]=x(2)*x(3)^3*y(1)^2+x(3)^2*y(1) ==> _[2]=x(3)^3*y(1)^2+x(3)^2*y(1) ==> _[3]=x(3)^2*y(1) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(2)^2*x(3)*y(1)^2-x(2)*x(3)*y(1)^2-1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 24 ==> Index of the current chart in chart-tree: 14 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(1)*x(2)^2-x(1)*x(2)-x(2)^2+x(2)-y(0) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(0) ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=x(1)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(1)^3*x(2)*y(0)-3*x(1)^2*x(2)*y(0)+x(1)^2*y(0)+3*x(1)*x(2)*y(0)-2*x\ (1)*y(0)-x(2)*y(0)+y(0) ==> _[2]=x(1)^3*y(0)-2*x(1)^2*y(0)+x(1)*y(0) ==> _[3]=x(1)^2*y(0)-2*x(1)*y(0)+y(0) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=y(0) ==> _[2]=x(1)-1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 26 ==> Index of the current chart in chart-tree: 15 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(2)^4*x(3)^4*y(1)^4+4*x(2)^3*x(3)^3*y(1)^3+6*x(2)^2*x(3)^2*y(1)^2-x\ (2)^2*x(3)*y(1)^2+x(2)*x(3)*y(1)^2+4*x(2)*x(3)*y(1)+1 ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=1 ==> [2]: ==> _[1]=y(1) ==> [3]: ==> _[1]=x(3) ==> ==> ==== Images of variables of original ring: ==> _[1]=x(3)^3*y(1)^2+x(3)^2*y(1) ==> _[2]=x(3)^2*y(1) ==> _[3]=x(2)*x(3)^3*y(1)^2+x(3)^2*y(1) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(2)^4*x(3)^4*y(1)^4+4*x(2)^3*x(3)^3*y(1)^3+6*x(2)^2*x(3)^2*y(1)^2-x\ (2)^2*x(3)*y(1)^2+x(2)*x(3)*y(1)^2+4*x(2)*x(3)*y(1)+1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 26 ==> Index of the current chart in chart-tree: 16 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(1)^4*x(2)^4*y(0)-4*x(1)^3*x(2)^4*y(0)+4*x(1)^3*x(2)^3*y(0)+6*x(1)^\ 2*x(2)^4*y(0)-12*x(1)^2*x(2)^3*y(0)-4*x(1)*x(2)^4*y(0)+6*x(1)^2*x(2)^2*y(\ 0)+12*x(1)*x(2)^3*y(0)+x(2)^4*y(0)-12*x(1)*x(2)^2*y(0)-4*x(2)^3*y(0)-x(1)\ *x(2)^2+4*x(1)*x(2)*y(0)+6*x(2)^2*y(0)+x(1)*x(2)+x(2)^2-4*x(2)*y(0)-x(2)+\ y(0) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(0) ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=x(1)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(1)^3*y(0)-2*x(1)^2*y(0)+x(1)*y(0) ==> _[2]=x(1)^2*y(0)-2*x(1)*y(0)+y(0) ==> _[3]=x(1)^3*x(2)*y(0)-3*x(1)^2*x(2)*y(0)+x(1)^2*y(0)+3*x(1)*x(2)*y(0)-2*x\ (1)*y(0)-x(2)*y(0)+y(0) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=y(0) ==> _[2]=x(1)-1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 28 ==> Index of the current chart in chart-tree: 17 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(3)^4*y(1)^4+4*x(3)^3*y(1)^3+x(2)^2*x(3)*y(1)^2-x(2)*x(3)*y(1)^2+6*\ x(3)^2*y(1)^2+4*x(3)*y(1)+1 ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=1 ==> [2]: ==> _[1]=y(1) ==> [3]: ==> _[1]=x(3) ==> ==> ==== Images of variables of original ring: ==> _[1]=x(2)*x(3)^3*y(1)^2+x(3)^2*y(1) ==> _[2]=x(3)^2*y(1) ==> _[3]=x(3)^3*y(1)^2+x(3)^2*y(1) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(3)^4*y(1)^4+4*x(3)^3*y(1)^3+x(2)^2*x(3)*y(1)^2-x(2)*x(3)*y(1)^2+6*\ x(3)^2*y(1)^2+4*x(3)*y(1)+1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 28 ==> Index of the current chart in chart-tree: 18 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(1)^4*y(0)+x(1)*x(2)^2-x(1)*x(2)-x(2)^2+x(2) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(0) ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=x(1)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(1)^3*x(2)*y(0)-3*x(1)^2*x(2)*y(0)+x(1)^2*y(0)+3*x(1)*x(2)*y(0)-2*x\ (1)*y(0)-x(2)*y(0)+y(0) ==> _[2]=x(1)^2*y(0)-2*x(1)*y(0)+y(0) ==> _[3]=x(1)^3*y(0)-2*x(1)^2*y(0)+x(1)*y(0) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=y(0) ==> _[2]=x(1)-1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 30 ==> Index of the current chart in chart-tree: 19 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(2)^4*x(3)^4*y(1)^4+4*x(2)^3*x(3)^3*y(1)^3+6*x(2)^2*x(3)^2*y(1)^2+x\ (2)^2*x(3)*y(1)^2-x(2)*x(3)*y(1)^2+4*x(2)*x(3)*y(1)+1 ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=1 ==> [2]: ==> _[1]=y(1) ==> [3]: ==> _[1]=x(3) ==> ==> ==== Images of variables of original ring: ==> _[1]=x(3)^2*y(1) ==> _[2]=x(3)^3*y(1)^2+x(3)^2*y(1) ==> _[3]=x(2)*x(3)^3*y(1)^2+x(3)^2*y(1) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(2)^4*x(3)^4*y(1)^4+4*x(2)^3*x(3)^3*y(1)^3+6*x(2)^2*x(3)^2*y(1)^2+x\ (2)^2*x(3)*y(1)^2-x(2)*x(3)*y(1)^2+4*x(2)*x(3)*y(1)+1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 30 ==> Index of the current chart in chart-tree: 20 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(1)^4*x(2)^4*y(0)-4*x(1)^3*x(2)^4*y(0)+4*x(1)^3*x(2)^3*y(0)+6*x(1)^\ 2*x(2)^4*y(0)-12*x(1)^2*x(2)^3*y(0)-4*x(1)*x(2)^4*y(0)+6*x(1)^2*x(2)^2*y(\ 0)+12*x(1)*x(2)^3*y(0)+x(2)^4*y(0)-12*x(1)*x(2)^2*y(0)-4*x(2)^3*y(0)+x(1)\ *x(2)^2+4*x(1)*x(2)*y(0)+6*x(2)^2*y(0)-x(1)*x(2)-x(2)^2-4*x(2)*y(0)+x(2)+\ y(0) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(0) ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=x(1)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(1)^2*y(0)-2*x(1)*y(0)+y(0) ==> _[2]=x(1)^3*y(0)-2*x(1)^2*y(0)+x(1)*y(0) ==> _[3]=x(1)^3*x(2)*y(0)-3*x(1)^2*x(2)*y(0)+x(1)^2*y(0)+3*x(1)*x(2)*y(0)-2*x\ (1)*y(0)-x(2)*y(0)+y(0) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=y(0) ==> _[2]=x(1)-1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 32 ==> Index of the current chart in chart-tree: 21 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(3)^4*y(1)^4+4*x(3)^3*y(1)^3-x(2)^2*x(3)*y(1)^2+x(2)*x(3)*y(1)^2+6*\ x(3)^2*y(1)^2+4*x(3)*y(1)+1 ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=1 ==> [2]: ==> _[1]=y(1) ==> [3]: ==> _[1]=x(3) ==> ==> ==== Images of variables of original ring: ==> _[1]=x(3)^2*y(1) ==> _[2]=x(2)*x(3)^3*y(1)^2+x(3)^2*y(1) ==> _[3]=x(3)^3*y(1)^2+x(3)^2*y(1) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(3)^4*y(1)^4+4*x(3)^3*y(1)^3-x(2)^2*x(3)*y(1)^2+x(2)*x(3)*y(1)^2+6*\ x(3)^2*y(1)^2+4*x(3)*y(1)+1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 32 ==> Index of the current chart in chart-tree: 22 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(1)^4*y(0)-x(1)*x(2)^2+x(1)*x(2)+x(2)^2-x(2) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(0) ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=x(1)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(1)^2*y(0)-2*x(1)*y(0)+y(0) ==> _[2]=x(1)^3*x(2)*y(0)-3*x(1)^2*x(2)*y(0)+x(1)^2*y(0)+3*x(1)*x(2)*y(0)-2*x\ (1)*y(0)-x(2)*y(0)+y(0) ==> _[3]=x(1)^3*y(0)-2*x(1)^2*y(0)+x(1)*y(0) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=y(0) ==> _[2]=x(1)-1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 0 ==> Total number of charts currently in chart-tree: 34 ==> Index of the current chart in chart-tree: 23 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(2)^2*y(1)-x(2)*y(1)+1 ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=1 ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=y(1) ==> [4]: ==> _[1]=x(3) ==> ==> ==== Images of variables of original ring: ==> _[1]=x(3)^4*y(1)^3+x(3)^3*y(1)^2 ==> _[2]=x(2)*x(3)^4*y(1)^3+x(3)^3*y(1)^2 ==> _[3]=x(3)^3*y(1)^2 ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(2)^2*y(1)-x(2)*y(1)+1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 1 ==> Total number of charts currently in chart-tree: 34 ==> Index of the current chart in chart-tree: 24 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(2)^2-x(2)+y(0) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(0) ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=1 ==> [4]: ==> _[1]=x(1)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(1)^4*y(0)-3*x(1)^3*y(0)+3*x(1)^2*y(0)-x(1)*y(0) ==> _[2]=x(1)^4*x(2)*y(0)-4*x(1)^3*x(2)*y(0)+x(1)^3*y(0)+6*x(1)^2*x(2)*y(0)-3\ *x(1)^2*y(0)-4*x(1)*x(2)*y(0)+3*x(1)*y(0)+x(2)*y(0)-y(0) ==> _[3]=x(1)^3*y(0)-3*x(1)^2*y(0)+3*x(1)*y(0)-y(0) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(2)^2-x(2)+y(0) ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 2 ==> Total number of charts currently in chart-tree: 34 ==> Index of the current chart in chart-tree: 25 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(2)^2*y(1)-x(2)*y(1)-1 ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=1 ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=y(1) ==> [4]: ==> _[1]=x(3) ==> ==> ==== Images of variables of original ring: ==> _[1]=x(2)*x(3)^4*y(1)^3+x(3)^3*y(1)^2 ==> _[2]=x(3)^4*y(1)^3+x(3)^3*y(1)^2 ==> _[3]=x(3)^3*y(1)^2 ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(2)^2*y(1)-x(2)*y(1)-1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 3 ==> Total number of charts currently in chart-tree: 34 ==> Index of the current chart in chart-tree: 26 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(2)^2-x(2)-y(0) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(0) ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=1 ==> [4]: ==> _[1]=x(1)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(1)^4*x(2)*y(0)-4*x(1)^3*x(2)*y(0)+x(1)^3*y(0)+6*x(1)^2*x(2)*y(0)-3\ *x(1)^2*y(0)-4*x(1)*x(2)*y(0)+3*x(1)*y(0)+x(2)*y(0)-y(0) ==> _[2]=x(1)^4*y(0)-3*x(1)^3*y(0)+3*x(1)^2*y(0)-x(1)*y(0) ==> _[3]=x(1)^3*y(0)-3*x(1)^2*y(0)+3*x(1)*y(0)-y(0) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(2)^2-x(2)-y(0) ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 4 ==> Total number of charts currently in chart-tree: 34 ==> Index of the current chart in chart-tree: 27 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(2)^4*x(3)^4*y(1)^4+4*x(2)^3*x(3)^3*y(1)^3+6*x(2)^2*x(3)^2*y(1)^2-x\ (2)^2*y(1)+4*x(2)*x(3)*y(1)+x(2)*y(1)+1 ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=1 ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=y(1) ==> [4]: ==> _[1]=x(3) ==> ==> ==== Images of variables of original ring: ==> _[1]=x(3)^4*y(1)^3+x(3)^3*y(1)^2 ==> _[2]=x(3)^3*y(1)^2 ==> _[3]=x(2)*x(3)^4*y(1)^3+x(3)^3*y(1)^2 ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(2)^4*x(3)^4*y(1)^4+4*x(2)^3*x(3)^3*y(1)^3+6*x(2)^2*x(3)^2*y(1)^2-x\ (2)^2*y(1)+4*x(2)*x(3)*y(1)+x(2)*y(1)+1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 5 ==> Total number of charts currently in chart-tree: 34 ==> Index of the current chart in chart-tree: 28 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(1)^4*x(2)^4*y(0)-4*x(1)^3*x(2)^4*y(0)+4*x(1)^3*x(2)^3*y(0)+6*x(1)^\ 2*x(2)^4*y(0)-12*x(1)^2*x(2)^3*y(0)-4*x(1)*x(2)^4*y(0)+6*x(1)^2*x(2)^2*y(\ 0)+12*x(1)*x(2)^3*y(0)+x(2)^4*y(0)-12*x(1)*x(2)^2*y(0)-4*x(2)^3*y(0)+4*x(\ 1)*x(2)*y(0)+6*x(2)^2*y(0)-x(2)^2-4*x(2)*y(0)+x(2)+y(0) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(0) ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=1 ==> [4]: ==> _[1]=x(1)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(1)^4*y(0)-3*x(1)^3*y(0)+3*x(1)^2*y(0)-x(1)*y(0) ==> _[2]=x(1)^3*y(0)-3*x(1)^2*y(0)+3*x(1)*y(0)-y(0) ==> _[3]=x(1)^4*x(2)*y(0)-4*x(1)^3*x(2)*y(0)+x(1)^3*y(0)+6*x(1)^2*x(2)*y(0)-3\ *x(1)^2*y(0)-4*x(1)*x(2)*y(0)+3*x(1)*y(0)+x(2)*y(0)-y(0) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(1)^4*x(2)^4*y(0)-4*x(1)^3*x(2)^4*y(0)+4*x(1)^3*x(2)^3*y(0)+6*x(1)^\ 2*x(2)^4*y(0)-12*x(1)^2*x(2)^3*y(0)-4*x(1)*x(2)^4*y(0)+6*x(1)^2*x(2)^2*y(\ 0)+12*x(1)*x(2)^3*y(0)+x(2)^4*y(0)-12*x(1)*x(2)^2*y(0)-4*x(2)^3*y(0)+4*x(\ 1)*x(2)*y(0)+6*x(2)^2*y(0)-x(2)^2-4*x(2)*y(0)+x(2)+y(0) ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 6 ==> Total number of charts currently in chart-tree: 34 ==> Index of the current chart in chart-tree: 29 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(3)^4*y(1)^4+4*x(3)^3*y(1)^3+6*x(3)^2*y(1)^2+x(2)^2*y(1)-x(2)*y(1)+\ 4*x(3)*y(1)+1 ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=1 ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=y(1) ==> [4]: ==> _[1]=x(3) ==> ==> ==== Images of variables of original ring: ==> _[1]=x(2)*x(3)^4*y(1)^3+x(3)^3*y(1)^2 ==> _[2]=x(3)^3*y(1)^2 ==> _[3]=x(3)^4*y(1)^3+x(3)^3*y(1)^2 ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(3)^4*y(1)^4+4*x(3)^3*y(1)^3+6*x(3)^2*y(1)^2+x(2)^2*y(1)-x(2)*y(1)+\ 4*x(3)*y(1)+1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 7 ==> Total number of charts currently in chart-tree: 34 ==> Index of the current chart in chart-tree: 30 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(1)^4*y(0)+x(2)^2-x(2) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(0) ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=1 ==> [4]: ==> _[1]=x(1)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(1)^4*x(2)*y(0)-4*x(1)^3*x(2)*y(0)+x(1)^3*y(0)+6*x(1)^2*x(2)*y(0)-3\ *x(1)^2*y(0)-4*x(1)*x(2)*y(0)+3*x(1)*y(0)+x(2)*y(0)-y(0) ==> _[2]=x(1)^3*y(0)-3*x(1)^2*y(0)+3*x(1)*y(0)-y(0) ==> _[3]=x(1)^4*y(0)-3*x(1)^3*y(0)+3*x(1)^2*y(0)-x(1)*y(0) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(1)^4*y(0)+x(2)^2-x(2) ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 8 ==> Total number of charts currently in chart-tree: 34 ==> Index of the current chart in chart-tree: 31 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(2)^4*x(3)^4*y(1)^4+4*x(2)^3*x(3)^3*y(1)^3+6*x(2)^2*x(3)^2*y(1)^2+x\ (2)^2*y(1)+4*x(2)*x(3)*y(1)-x(2)*y(1)+1 ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=1 ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=y(1) ==> [4]: ==> _[1]=x(3) ==> ==> ==== Images of variables of original ring: ==> _[1]=x(3)^3*y(1)^2 ==> _[2]=x(3)^4*y(1)^3+x(3)^3*y(1)^2 ==> _[3]=x(2)*x(3)^4*y(1)^3+x(3)^3*y(1)^2 ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(2)^4*x(3)^4*y(1)^4+4*x(2)^3*x(3)^3*y(1)^3+6*x(2)^2*x(3)^2*y(1)^2+x\ (2)^2*y(1)+4*x(2)*x(3)*y(1)-x(2)*y(1)+1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 9 ==> Total number of charts currently in chart-tree: 34 ==> Index of the current chart in chart-tree: 32 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(1)^4*x(2)^4*y(0)-4*x(1)^3*x(2)^4*y(0)+4*x(1)^3*x(2)^3*y(0)+6*x(1)^\ 2*x(2)^4*y(0)-12*x(1)^2*x(2)^3*y(0)-4*x(1)*x(2)^4*y(0)+6*x(1)^2*x(2)^2*y(\ 0)+12*x(1)*x(2)^3*y(0)+x(2)^4*y(0)-12*x(1)*x(2)^2*y(0)-4*x(2)^3*y(0)+4*x(\ 1)*x(2)*y(0)+6*x(2)^2*y(0)+x(2)^2-4*x(2)*y(0)-x(2)+y(0) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(0) ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=1 ==> [4]: ==> _[1]=x(1)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(1)^3*y(0)-3*x(1)^2*y(0)+3*x(1)*y(0)-y(0) ==> _[2]=x(1)^4*y(0)-3*x(1)^3*y(0)+3*x(1)^2*y(0)-x(1)*y(0) ==> _[3]=x(1)^4*x(2)*y(0)-4*x(1)^3*x(2)*y(0)+x(1)^3*y(0)+6*x(1)^2*x(2)*y(0)-3\ *x(1)^2*y(0)-4*x(1)*x(2)*y(0)+3*x(1)*y(0)+x(2)*y(0)-y(0) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(1)^4*x(2)^4*y(0)-4*x(1)^3*x(2)^4*y(0)+4*x(1)^3*x(2)^3*y(0)+6*x(1)^\ 2*x(2)^4*y(0)-12*x(1)^2*x(2)^3*y(0)-4*x(1)*x(2)^4*y(0)+6*x(1)^2*x(2)^2*y(\ 0)+12*x(1)*x(2)^3*y(0)+x(2)^4*y(0)-12*x(1)*x(2)^2*y(0)-4*x(2)^3*y(0)+4*x(\ 1)*x(2)*y(0)+6*x(2)^2*y(0)+x(2)^2-4*x(2)*y(0)-x(2)+y(0) ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 10 ==> Total number of charts currently in chart-tree: 34 ==> Index of the current chart in chart-tree: 33 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(3)^4*y(1)^4+4*x(3)^3*y(1)^3+6*x(3)^2*y(1)^2-x(2)^2*y(1)+x(2)*y(1)+\ 4*x(3)*y(1)+1 ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=1 ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=y(1) ==> [4]: ==> _[1]=x(3) ==> ==> ==== Images of variables of original ring: ==> _[1]=x(3)^3*y(1)^2 ==> _[2]=x(2)*x(3)^4*y(1)^3+x(3)^3*y(1)^2 ==> _[3]=x(3)^4*y(1)^3+x(3)^3*y(1)^2 ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(3)^4*y(1)^4+4*x(3)^3*y(1)^3+6*x(3)^2*y(1)^2-x(2)^2*y(1)+x(2)*y(1)+\ 4*x(3)*y(1)+1 ==> ---------------------------------------------------------------- ==> ++++++++++++++ Overview of Current Chart +++++++++++++++++++++++ ==> Current number of final charts: 11 ==> Total number of charts currently in chart-tree: 34 ==> Index of the current chart in chart-tree: 34 ==> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ==> ==> ==== Ambient Space: ==> _[1]=0 ==> ==> ==== Ideal of Variety: ==> _[1]=x(1)^4*y(0)-x(2)^2+x(2) ==> ==> ==== Exceptional Divisors: ==> [1]: ==> _[1]=y(0) ==> [2]: ==> _[1]=1 ==> [3]: ==> _[1]=1 ==> [4]: ==> _[1]=x(1)-1 ==> ==> ==== Images of variables of original ring: ==> _[1]=x(1)^3*y(0)-3*x(1)^2*y(0)+3*x(1)*y(0)-y(0) ==> _[2]=x(1)^4*x(2)*y(0)-4*x(1)^3*x(2)*y(0)+x(1)^3*y(0)+6*x(1)^2*x(2)*y(0)-3\ *x(1)^2*y(0)-4*x(1)*x(2)*y(0)+3*x(1)*y(0)+x(2)*y(0)-y(0) ==> _[3]=x(1)^4*y(0)-3*x(1)^3*y(0)+3*x(1)^2*y(0)-x(1)*y(0) ==> ==> -------------------------- Upcoming Center --------------------- ==> _[1]=x(1)^4*y(0)-x(2)^2+x(2) ==> ---------------------------------------------------------------- ==> ============= result will be tested ========== ==> ==> the number of charts obtained: 12 ==> ============= result is o.k. ========== list iden=prepEmbDiv(re); intvec v=computeV(re, iden); v; ==> 3,5,8,11,1 ```