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D.4.14.5 collectDiv

Procedure from library reszeta.lib (see reszeta_lib).

Usage:
collectDiv(L);
L = list of rings

Assume:
L is output of resolution of singularities

Compute:
list representing the identification of the exceptional divisors in the various charts

Return:
list l, where
l[1]: intmat, entry k in position i,j implies BO[4][j] of chart i is divisor k (if k!=0)
if k==0, no divisor corresponding to i,j
l[2]: list ll, where each entry of ll is a list of intvecs entry i,j in list ll[k] implies BO[4][j] of chart i
is divisor k
l[3]: list L

Example:
 
LIB "reszeta.lib";
ring R=0,(x,y,z),dp;
ideal I=xyz+x4+y4+z4;
//we really need to blow up curves even if the generic point of
//the curve the total transform is n.c.
//this occurs here in r[2][5]
list re=resolve(I,1);
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 0
==> 1
==> 1
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x4+y4+z4+xyz
==>       
==> ==== E: 
==> empty list
==>    
==> ==== Intersection
==> 0
==>      
==> -------  Center ------------
==> _[1]=z
==> _[2]=y
==> _[3]=x
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 0
==> 4
==> 2
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(3)*y(1)^4+x(3)*y(2)^4+y(1)*y(2)+x(3)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=x(3)
==>    
==> ==== Intersection
==> 0
==>      
==> -------  Center ------------
==> _[1]=y(2)
==> _[2]=y(1)
==> _[3]=x(3)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 0
==> 6
==> 3
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(2)*y(0)^4+x(2)*y(2)^4+y(0)*y(2)+x(2)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=x(2)
==>    
==> ==== Intersection
==> 0
==>      
==> -------  Center ------------
==> _[1]=y(2)
==> _[2]=y(0)
==> _[3]=x(2)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 0
==> 8
==> 4
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(1)*y(0)^4+x(1)*y(1)^4+y(0)*y(1)+x(1)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=x(1)
==>    
==> ==== Intersection
==> 0
==>      
==> -------  Center ------------
==> _[1]=y(1)
==> _[2]=y(0)
==> _[3]=x(1)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 0
==> 10
==> 5
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(3)^4*y(1)^4*y(2)+x(3)^4*y(2)+x(3)*y(1)+y(2)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=y(2)
==> [2]:
==>    _[1]=x(3)
==>    
==> ==== Intersection
==> 0,1,
==> 0,0 
==>      
==> -------  Center ------------
==> _[1]=y(2)
==> _[2]=x(3)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 0
==> 12
==> 6
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(2)^4*y(0)^4*y(2)+x(2)^4*y(2)+x(2)*y(0)+y(2)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=y(2)
==> [2]:
==>    _[1]=x(2)
==>    
==> ==== Intersection
==> 0,1,
==> 0,0 
==>      
==> -------  Center ------------
==> _[1]=y(2)
==> _[2]=x(2)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 0
==> 14
==> 7
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(3)^4*y(1)^4*y(2)+x(3)^4*y(2)+x(3)*y(1)+y(2)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=y(2)
==> [2]:
==>    _[1]=x(3)
==>    
==> ==== Intersection
==> 0,1,
==> 0,0 
==>      
==> -------  Center ------------
==> _[1]=y(2)
==> _[2]=x(3)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 0
==> 16
==> 8
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(2)^4*y(0)^4*y(2)+x(2)^4*y(2)+x(2)*y(0)+y(2)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=y(2)
==> [2]:
==>    _[1]=x(2)
==>    
==> ==== Intersection
==> 0,1,
==> 0,0 
==>      
==> -------  Center ------------
==> _[1]=y(2)
==> _[2]=x(2)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 0
==> 18
==> 9
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(3)^4*y(1)^4*y(2)+x(3)^4*y(2)+x(3)*y(1)+y(2)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=y(2)
==> [2]:
==>    _[1]=x(3)
==>    
==> ==== Intersection
==> 0,1,
==> 0,0 
==>      
==> -------  Center ------------
==> _[1]=y(2)
==> _[2]=x(3)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 0
==> 20
==> 10
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(2)^4*y(0)^4*y(2)+x(2)^4*y(2)+x(2)*y(0)+y(2)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=y(2)
==> [2]:
==>    _[1]=x(2)
==>    
==> ==== Intersection
==> 0,1,
==> 0,0 
==>      
==> -------  Center ------------
==> _[1]=y(2)
==> _[2]=x(2)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 0
==> 22
==> 11
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(2)^4*x(3)^4*y(1)^4+x(3)^4*y(1)^4+x(2)*y(1)+1
==>       
==> ==== E: 
==> [1]:
==>    _[1]=1
==> [2]:
==>    _[1]=y(1)
==> [3]:
==>    _[1]=x(3)
==>    
==> ==== Intersection
==> 0,1,1,
==> 0,0,1,
==> 0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(2)^4*x(3)^4*y(1)^4+x(3)^4*y(1)^4+x(2)*y(1)+1
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 1
==> 22
==> 12
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(1)^4*x(2)^4*y(0)+x(1)^4*y(0)+x(2)+y(0)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=y(0)
==> [2]:
==>    _[1]=1
==> [3]:
==>    _[1]=x(1)
==>    
==> ==== Intersection
==> 0,1,1,
==> 0,0,1,
==> 0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(1)^4*x(2)^4*y(0)+x(1)^4*y(0)+x(2)+y(0)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 2
==> 22
==> 13
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(2)^4*x(3)^4*y(1)^4+x(3)^4*y(1)^4+x(2)*y(1)+1
==>       
==> ==== E: 
==> [1]:
==>    _[1]=1
==> [2]:
==>    _[1]=y(1)
==> [3]:
==>    _[1]=x(3)
==>    
==> ==== Intersection
==> 0,1,1,
==> 0,0,1,
==> 0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(2)^4*x(3)^4*y(1)^4+x(3)^4*y(1)^4+x(2)*y(1)+1
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 3
==> 22
==> 14
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(1)^4*x(2)^4*y(0)+x(1)^4*y(0)+x(2)+y(0)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=y(0)
==> [2]:
==>    _[1]=1
==> [3]:
==>    _[1]=x(1)
==>    
==> ==== Intersection
==> 0,1,1,
==> 0,0,1,
==> 0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(1)^4*x(2)^4*y(0)+x(1)^4*y(0)+x(2)+y(0)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 4
==> 22
==> 15
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(2)^4*x(3)^4*y(1)^4+x(3)^4*y(1)^4+x(2)*y(1)+1
==>       
==> ==== E: 
==> [1]:
==>    _[1]=1
==> [2]:
==>    _[1]=y(1)
==> [3]:
==>    _[1]=x(3)
==>    
==> ==== Intersection
==> 0,1,1,
==> 0,0,1,
==> 0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(2)^4*x(3)^4*y(1)^4+x(3)^4*y(1)^4+x(2)*y(1)+1
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 5
==> 22
==> 16
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(1)^4*x(2)^4*y(0)+x(1)^4*y(0)+x(2)+y(0)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=y(0)
==> [2]:
==>    _[1]=1
==> [3]:
==>    _[1]=x(1)
==>    
==> ==== Intersection
==> 0,1,1,
==> 0,0,1,
==> 0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(1)^4*x(2)^4*y(0)+x(1)^4*y(0)+x(2)+y(0)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 6
==> 22
==> 17
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(2)^4*x(3)^4*y(1)^4+x(3)^4*y(1)^4+x(2)*y(1)+1
==>       
==> ==== E: 
==> [1]:
==>    _[1]=1
==> [2]:
==>    _[1]=y(1)
==> [3]:
==>    _[1]=x(3)
==>    
==> ==== Intersection
==> 0,1,1,
==> 0,0,1,
==> 0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(2)^4*x(3)^4*y(1)^4+x(3)^4*y(1)^4+x(2)*y(1)+1
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 7
==> 22
==> 18
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(1)^4*x(2)^4*y(0)+x(1)^4*y(0)+x(2)+y(0)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=y(0)
==> [2]:
==>    _[1]=1
==> [3]:
==>    _[1]=x(1)
==>    
==> ==== Intersection
==> 0,1,1,
==> 0,0,1,
==> 0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(1)^4*x(2)^4*y(0)+x(1)^4*y(0)+x(2)+y(0)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 8
==> 22
==> 19
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(2)^4*x(3)^4*y(1)^4+x(3)^4*y(1)^4+x(2)*y(1)+1
==>       
==> ==== E: 
==> [1]:
==>    _[1]=1
==> [2]:
==>    _[1]=y(1)
==> [3]:
==>    _[1]=x(3)
==>    
==> ==== Intersection
==> 0,1,1,
==> 0,0,1,
==> 0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(2)^4*x(3)^4*y(1)^4+x(3)^4*y(1)^4+x(2)*y(1)+1
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 9
==> 22
==> 20
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(1)^4*x(2)^4*y(0)+x(1)^4*y(0)+x(2)+y(0)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=y(0)
==> [2]:
==>    _[1]=1
==> [3]:
==>    _[1]=x(1)
==>    
==> ==== Intersection
==> 0,1,1,
==> 0,0,1,
==> 0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(1)^4*x(2)^4*y(0)+x(1)^4*y(0)+x(2)+y(0)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 10
==> 22
==> 21
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(2)^4*x(3)^4*y(1)^4+x(3)^4*y(1)^4+x(2)*y(1)+1
==>       
==> ==== E: 
==> [1]:
==>    _[1]=1
==> [2]:
==>    _[1]=y(1)
==> [3]:
==>    _[1]=x(3)
==>    
==> ==== Intersection
==> 0,1,1,
==> 0,0,1,
==> 0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(2)^4*x(3)^4*y(1)^4+x(3)^4*y(1)^4+x(2)*y(1)+1
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 11
==> 22
==> 22
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(1)^4*x(2)^4*y(0)+x(1)^4*y(0)+x(2)+y(0)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=y(0)
==> [2]:
==>    _[1]=1
==> [3]:
==>    _[1]=x(1)
==>    
==> ==== Intersection
==> 0,1,1,
==> 0,0,1,
==> 0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(1)^4*x(2)^4*y(0)+x(1)^4*y(0)+x(2)+y(0)
==> ----------------------------
==> ============= result will be tested ==========
==>                                               
==> the number of charts obtained: 12
==> =============     result is o.k.    ==========
list di=collectDiv(re);
di;
==> [1]:
==>    0,0,0,
==>    1,0,0,
==>    1,0,0,
==>    1,0,0,
==>    1,2,0,
==>    1,2,0,
==>    1,3,0,
==>    1,3,0,
==>    1,4,0,
==>    1,4,0,
==>    0,2,5,
==>    1,0,5,
==>    0,2,5,
==>    1,0,5,
==>    0,3,6,
==>    1,0,6,
==>    0,3,6,
==>    1,0,6,
==>    0,4,7,
==>    1,0,7,
==>    0,4,7,
==>    1,0,7 
==> [2]:
==>    [1]:
==>       [1]:
==>          2,1
==>       [2]:
==>          3,1
==>       [3]:
==>          4,1
==>       [4]:
==>          5,1
==>       [5]:
==>          6,1
==>       [6]:
==>          7,1
==>       [7]:
==>          8,1
==>       [8]:
==>          9,1
==>       [9]:
==>          10,1
==>       [10]:
==>          12,1
==>       [11]:
==>          14,1
==>       [12]:
==>          16,1
==>       [13]:
==>          18,1
==>       [14]:
==>          20,1
==>       [15]:
==>          22,1
==>    [2]:
==>       [1]:
==>          5,2
==>       [2]:
==>          6,2
==>       [3]:
==>          11,2
==>       [4]:
==>          13,2
==>    [3]:
==>       [1]:
==>          7,2
==>       [2]:
==>          8,2
==>       [3]:
==>          15,2
==>       [4]:
==>          17,2
==>    [4]:
==>       [1]:
==>          9,2
==>       [2]:
==>          10,2
==>       [3]:
==>          19,2
==>       [4]:
==>          21,2
==>    [5]:
==>       [1]:
==>          11,3
==>       [2]:
==>          12,3
==>       [3]:
==>          13,3
==>       [4]:
==>          14,3
==>    [6]:
==>       [1]:
==>          15,3
==>       [2]:
==>          16,3
==>       [3]:
==>          17,3
==>       [4]:
==>          18,3
==>    [7]:
==>       [1]:
==>          19,3
==>       [2]:
==>          20,3
==>       [3]:
==>          21,3
==>       [4]:
==>          22,3
==>    [8]:
==>       [1]:
==>          11,0
==>       [2]:
==>          12,0
==>       [3]:
==>          13,0
==>       [4]:
==>          14,0
==>       [5]:
==>          15,0
==>       [6]:
==>          16,0
==>       [7]:
==>          17,0
==>       [8]:
==>          18,0
==>       [9]:
==>          19,0
==>       [10]:
==>          20,0
==>       [11]:
==>          21,0
==>       [12]:
==>          22,0


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