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Description

A resultant complex must first be determined for this command. Its terms are modules over the coefficient ring of the sparse polynomials. They are determined by the lattice points inside sums of Newton polytopes shifted by the Canny Emiris vector, which are stored in mon. The second list choice specifies admissible sub-modules required for the Cayley formula. Finally, a system with two essential sub-families is considered. Even in such cases, the definition of toric resultant complexes and their admissible sub-modules is valid. Evaluating the Cayley formula yields the unit, without checking for exceptions.

i1 : supp = { {{2,0,0},{1,2,2},{0,4,4}}, {{1,0,0},{0,2,2}}, {{0,5,3}}, {{0,0,0},{1,3,2},{4,1,3}} };

i2 : A = QQ[c_1..c_(#flatten supp)];

i3 : (complexRes, mon, choice) = resultantComplex( A, supp, {{0,-4},{-2,-1},{-5},{-13,0,-3}}, {-1/8,1/3,4/7} );

i4 : complexRes 27 54 27 o4 = A <-- A <-- A <-- 0 0 1 2 3 o4 : Complex

i5 : Res = CayleyFormula(complexRes, mon, choice) o5 = 1 o5 : A

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