Real Algebraic and Analytic Geometry |

The Membership Problem for quadratic modules.

e-mail:

Submission: 2009, May 22.

*Abstract:
We prove that the Membership Problem is solvable
affirmatively for every finitely generated quadratic module Q of IR[X_1]. For the
case that the associated semialgebraic set S is bounded we show
that a polynomial f is an element of Q if and only if f is
nonnegative on S and fulfills certain order conditions in the
boundary points of S. This leads us to the definition of
generalized natural generators of Q and an algorithm which
produces at most three generators of Q.*

Mathematics Subject Classification (2000): 12E05, 12L12, 12Y05, 14P10.

Keywords and Phrases: quadratic modules, membership problem, positive polynomials and sums of squares, definability.

**Full text**, 27p.:
dvi 193k,
ps.gz 243k,
pdf 358k.

Server Home Page