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D.5.6.9 computeN
Procedure from library reszeta.lib (see reszeta_lib).
- Usage:
- computeN(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 total transform under resolution
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=computeN(re,iden);
v;
==> 3,4,8,12,1
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