QI 1.0 released - Intersection of quadrics

Sylvain Petitjean Sylvain.Petitjean at loria.fr
Wed Jun 16 12:07:42 PDT 2004

We are pleased to announce the first release of QI, our software for 
computing near-optimal parameterizations of the intersection of implicit 
quadrics. It is available from the QI web site


QI has the following features:

    * it computes an exact parameterization of the intersection of two
      quadrics with integer coefficients of arbitrary size;
    * it correctly identifies, separates and parameterizes all the
      connected components of the intersection and gives all the
      relevant topological information;
    * the parameterization is rational when one exists; otherwise the
      intersection is a smooth quartic and the parameterization involves
      the square root of a polynomial;
    * the parameterization is either optimal in the degree of the
      extension of the integers on which its coefficients are defined
      or, in a small number of well-identified cases, involves one extra
      possibly unnecessary square root;
    * it is fast and efficient and can routinely compute
      parameterizations of the intersection of quadrics with input
      coefficients having ten digits in less than 50 milliseconds on a
      mainstream PC.

QI is available free of charge for non-commercial use. It was developed 
at the LORIA laboratory, Nancy, France. It is based on research work led 
by Laurent Dupont, Daniel Lazard, Sylvain Lazard and Sylvain Petitjean.

Comments and questions should be addressed to Sylvain.Petitjean at loria.fr 
and Sylvain.Lazard at loria.fr.

	- Sylvain Petitjean and Sylvain Lazard

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