Algebraic geometry and computer vision: Polynomial systems, real and complex roots

We review the different techniques known for doing exact computations on po lynomial systems. Some are based on the use of Grobner bases and linear alg ebra, others on the more classical resultants and its modern counterparts. Many theoretical examples of the use of these techniques are given. Further more, a full set of examples of applications in the domain of artificial vi sion, where many constraints boil down to polynomial systems, are presented . Emphasis is also put on very recent methods for determining the number of (isolated) real and complex roots of such systems.