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ABSTRACT

In this article, we first generalize the recent notion of residual resultant of a complete intersection [4] to the case of a local complete intersection of codimension 2 in the projective plane, which is the necessary and sufficient condition for a system of three polynomials to have a solution “outside” a variety, defined here by a local complete intersection of codimension 2. We give its degree in the coefficients of each polynomial and compute it as the god of three polynomials or as a product of two determinants divided by another one. In a second part we use this new type of resultant to give a new method to compute the implicit equation of a rational surface with base points in the case where these base points are a local complete intersection of codimension 2.

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.5 Roots of Nonlinear Equations
          Subjects: Polynomials, methods for

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on polynomials

General Terms:
Algorithms, Theory, Verification