Geodesic
Newton polyhedra and an algorithm for computing Hodge--Deligne numbers
Izvestiya. Mathematics , Tome 29 (1987) no. 2, pp. 279-298

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An algorithm is given for computing the mixed Hodge structure (more precisely, the Hodge–Deligne numbers) for cohomology of complete intersections in toric varieties in terms of Newton polyhedra specifying the complete intersection. In some particular cases the algorithm leads to explicit formulas. Bibliography: 8 titles. 
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     author = {V. I. Danilov and A. G. Khovanskii},
     title = {Newton polyhedra and an algorithm for computing {Hodge--Deligne} numbers},
     journal = {Izvestiya. Mathematics },
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     year = {1987},
     language = {en},
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V. I. Danilov; A. G. Khovanskii. Newton polyhedra and an algorithm for computing Hodge--Deligne numbers. Izvestiya. Mathematics , Tome 29 (1987) no. 2, pp. 279-298. http://geodesic.mathdoc.fr/item/IM2_1987_29_2_a1/