GC_Readme.txt  for the grobcov.lib library
Release L

After unzipping file "grobcovL.zip", 
  - rename grobcov.sg as grobcov.lib;
  - place all unzipped files in your Singular directory
  - the remaining files *.sg are executable files using grobcov.lib
  - the files *.sgw are the result of executing them.
  - you do not need to execute .sg files and can consult its result in the corresponding 
     .sgw file, but you can execute them to verify that your installation is correct.

You will find pairs of files:

GC_HELPS.sg		and  GC_HELPS.sgw			shows the helps included in grobcov.lib
GC_EXAMPLES.sg	and  GC.EXAMPLES.sgw		shows the examples included in grobcov.lib
GC_grobcov.sg		and  GC_grobcov..sgw		tutorial for grobcov
GC_ConsLevels.sg	and  GC_ConsLevels.sgw
GC_locus.sg		and  GC_locus.sgw
GC_envelop.sg		and  GC_envelop.sgw
GC5_Test.sg		and  GC5_Test.sgw

that are tutorial files in which you will find interesting examples and tutorials 
that show most of the characteristics of the use of the library.

This file is written to facilitate the use of the Singular
library grobcov.lib, programmed by Antonio Montes and containing the
Montes-Wibmer algorithm for computing the Groebner cover a o parametric ideal.
You can download the file grobcob.zip from the web:
www-ma2.upc.edu/montes/
containing all the files described here. The basic routines are:

             grobcov, cgsdr, extend,
             pdivi, pnormalf, setglobalrings, Crep, Prep, PtoCrep,
             ConsLevels,
             locus, lodusdg, locusto, envelop, envelopdg. 

The new version includes procedures for computing:
  - Comprehensive Groebner System (CGS) (Kapur-Sun-Wang),
  - canonical Groebner Cover of a parametric ideal (grobcov) (Montes-Wibmer),
  - canonical union and representation of constructible sets (Brunat-Montes)
  - loci computation and taxonomy (Abanades, Botana, Montes, Recio) and applications to dynamic geometry,
  - envelop computation and taxonomy (Montes et al.) and applications to dynamic geometry.

The different algorithms are described in:

  - Comprehensive Groebner System (GCS) (KSW  algorithm):

            D. Kapur, Y. Sun, and D.K. Wang. 
            "A New Algorithm for Computing Comprehensive Groebner Systems".
            Proceedings of ISSAC'2010, ACM Press, (2010), 29-36.

  - Groebner Cover of a parametric ideal :

             A. Montes, M. Wibmer. 
             "Groebner Bases for Polynomial Systems with Parameters."
             Journal of Symbolic Computation 45 (2010) 1391 - 1425.
             
  - Loci computation:
  
            Abanades, Botana, Montes, Recio:
            ''An Algebraic Taxonomy for Locus Computation in Dynamic Geometry''. 
            Computer-Aided Design 56 (2014) 22-33.

  - Canonical representation of consructible sets:
  
             A. Montes, J.M. Brunat,
            "Computing the vanonical representations of constructible sets". 
            J.M. Brunat, A. Montes
            submitted to
            Mathematics in Computer Science
                     
  - Envelop computation:
  
            Abanades, Botana, Montes, Recio:
             ''Envelops in Dynamic Geometry using the Groebner cover''. (to be published)