Solving Degenerate Sparse Polynomial Systems Faster Academic Article uri icon


  • Consider a system F of n polynomial equations in n unknowns, over an algebraically closed field of arbitrary characteristic. We present a fast method to find a point in every irreducible component of the zero set Z of F. Our techniques allow us to sharpen and lower prior complexity bounds for this problem by fully taking into account the monomial term structure. As a corollary of our development we also obtain new explicit formulae for the exact number of isolated roots of F and the intersection multiplicity of the positive-dimensional part of Z. Finally, we present a combinatorial construction of non-degenerate polynomial systems, with specified monomial term structure and maximally many isolated roots, which may be of independent interest. 1999 Academic Press.

published proceedings

  • Journal of Symbolic Computation

author list (cited authors)

  • Rojas, J. M.

citation count

  • 34

complete list of authors

  • Rojas, J Maurice

publication date

  • January 1999