Computation of Variant Resultants
In this paper, we give a new method for computing two variants of resultants, namely the trace resultants and the slope resultants. These two variants were introduced in (Hong 1993d) while devising quantifier elimination algorithms for a certain fragment of the elementary theory of the reals, where the input formulas are required to contain at least one quadratic polynomial equation. Hong (1993d) also gave a method for computing these two variant resultants. The method is based on expanding certain determinants whose entries come directly from the coefficients of the involved polynomials. In this paper, we provide a theoretical computing time analysis of the method. More importantly, we give a new and faster method, as well as modular algorithms for the computation of the variant resultants.
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