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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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