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D.5.14.1 intersectionDiv

Procedure from library reszeta.lib (see reszeta_lib).

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

Assume:
L is output of resolution of singularities
(only case of isolated surface singularities)

Compute:
intersection matrix and genera of the exceptional divisors (considered as curves on the strict transform)

Return:
list l, where
l[1]: intersection matrix of exceptional divisors
l[2]: intvec, genera of exceptional divisors
l[3]: divisorList, encoding the identification of the divisors

Example:
 
LIB "reszeta.lib";
ring r = 0,(x(1..3)),dp(3);
ideal J=x(3)^5+x(2)^4+x(1)^3+x(1)*x(2)*x(3);
list re=resolve(J);
list di=intersectionDiv(re);
di;
==> [1]:
==>    -3,1,1,
==>    1,-4,1,
==>    1,1,-2 
==> [2]:
==>    0,0,0
==> [3]:
==>    [1]:
==>       [1]:
==>          3,1,1
==>       [2]:
==>          5,1,1
==>    [2]:
==>       [1]:
==>          3,1,2
==>       [2]:
==>          4,1,1
==>       [3]:
==>          5,1,2
==>    [3]:
==>       [1]:
==>          4,2,1
==>       [2]:
==>          5,2,1
==> [4]:
==>    1,1,1