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D.5.9.5 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);
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
di[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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