`lex_hensel_gsl', `tolex_gsl', `tolex_gsl_d'
--------------------------------------------

lex_hensel_gsl(PLIST,VLIST1,ORDER,VLIST2,HOMO)
     ::Computation of an GSL form ideal basis

tolex_gsl(PLIST,VLIST1,ORDER,VLIST2)
tolex_gsl_d(PLIST,VLIST1,ORDER,VLIST2,PROCS)
     :: Computation of an GSL form ideal basis stating from a Groebner
     basis

RETURN
     list

PLIST  VLIST1  VLIST2  PROCS
     list

ORDER
     number, list or matrix

HOMO
     flag

   * `lex_hensel_gsl()' and `lex_hensel()' are variants of
     `tolex_gsl()' and `tolex()' respectively. The results are Groebner
     basis or a kind of ideal basis, called GSL form.  `tolex_gsl_d()'
     does basis computations in parallel on child processes specified
     in `procs'.

   * If the input is zero-dimensional and a lex order Groebner basis has
     the form `[f0,x1-f1,...,xn-fn]' (`f0',...,`fn' are univariate
     polynomials of `x0'; SL form), then this these functions return a
     list such as `[[x1,g1,d1],...,[xn,gn,dn],[x0,f0,f0']]' (GSL form).
     In this list `gi' is a univariate polynomial of `x0' such that
     `di*f0'*fi-gi' divides `f0' and the roots of the input ideal is
     `[x1=g1/(d1*f0'),...,xn=gn/(dn*f0')]' for `x0' such that
     `f0(x0)=0'.  If the lex order Groebner basis does not have the
     above form, these functions return a lex order Groebner basis
     computed by `tolex()'.

   * Though an ideal basis represented as GSL form is not a Groebner
     basis we can expect that the coefficients are much smaller than
     those in a Groebner basis and that the computation is efficient.
     The CPU time shown after an execution of `tolex_gsl_d()' indicates
     that of the master process, and it does not include the time in
     child processes.

     [103] K=katsura(5)$
     [104] V=[u5,u4,u3,u2,u1,u0]$
     [105] G0=gr(K,V,0)$
     [106] GSL=tolex_gsl(G0,V,0,V)$
     [107] GSL[0];
     [u1,8635837421130477667200000000*u0^31-...]
     [108] GSL[1];
     [u2,10352277157007342793600000000*u0^31-...]
     [109] GSL[5];
     [u0,11771021876193064124640000000*u0^32-...,
     376672700038178051988480000000*u0^31-...]

References
     *Note `lex_hensel lex_tl tolex tolex_d tolex_tl': lex_hensel
     lex_tl tolex tolex_d tolex_tl, *Note `Distributed computation':
     Distributed computation

