June 6, 2005
This file comes from
http://emmanuel.jean.briand.free.fr/publications/twoconics
Here are some explanations about the files contained in the directory PROGRAMMES

1. The formulas for the quantities involved in the study of the configurations of a pair of conics are gathered in the files :

quadratic.txt 
formulas.txt
covariants.txt

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2. TWO_CONICS is a Maple variable initialized in my .mapleinit file, which contains the (Maple) path containing the files

quadratic.txt
formulas.txt
covariants.txt
configurations.txt

For instance, my own .mapleini file contains the lines

HOME:="/user/ebriand/home/";
TWO_CONICS:=cat(HOME,"DEUXCONIQUES/PROGRAMMES/");

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3. Each of the subdirectories EX_foo contain a maple file example_foo.txt which calls formulas.txt and configurations.txt

To run the computations, I just go into the directory EX_foo and execute the command:
maple < example_foo.txt &

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4. configurations.txt makes use of Christopher Brown's simplification program SLFQ available at 
http://www.cs.usna.edu/~qepcad/SLFQ/Home.html

configurations.txt uses the UNIX path of the slfq command, for me it's 
$HOME/simplify/slfq

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5. configurations.txt produces the files
classIN.txt, classIS.txt, ...
which describe the subsets of the parameter space corresponding to the pair configurations, as well as
fDeg.txt,gDeg.txt (resp. fempty.txt, gempty.txt) which describe the subsets corresponding to  "f degenerate", "g degenerate" (resp. : "f empty", "g empty").

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6. References for the examples

-------
EX_Wang_1, EX_Wang_2

@article {Wang:Wang:Kim,
    AUTHOR = {Wang, Wenping and Wang, Jiaye and Kim, Myung-Soo},
     TITLE = {An algebraic condition for the separation of two ellipsoids},
   JOURNAL = {Comput. Aided Geom. Design},
  FJOURNAL = {Computer Aided Geometric Design},
    VOLUME = {18},
      YEAR = {2001},
    NUMBER = {6},
     PAGES = {531--539},
}

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EX_UHLIG

@article {Uhlig,
    AUTHOR = {Uhlig, Frank},
     TITLE = {A canonical form for a pair of real symmetric matrices that
              generate a nonsingular pencil},
   JOURNAL = {Linear Algebra and Appl.},
    VOLUME = {14},
      YEAR = {1976},
    NUMBER = {3},
     PAGES = {189--209}
}

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EX_DelRio

@Unpublished{E:GV:dR,
  author = 	 {Etayo, Fernando and Gonz{\'a}lez-Vega, Laureano and del Rio, Natalia},
  title = 	 {A new solution for characterizing the relative position of two ellipses},
  note = 	 {Preprint},
  year = 	 {2004}
}

-------
EX_3D

no reference, I invented the example

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7. The examples of the paper "The configurations of two real projective conics" are:
 * EX_Wang_2
 * EX_3D
 * EX_UHLIG