> <\body> solvers> of >> Several polynomial solvers are provided. They differ from the coefficient type used during the borderbasis computation. <\itemize-dot> : coefficients in > >: coefficients in > with . The polynomial solver can be used as follows: <\verbatim-code> solver_bb_rational exp1 where > is a file containing the polynomials, of the form: <\cpp-code> 3*x0^2*x1-1;\ 2*x0^3+x1^2-1; The polynomials are separated by a The variables are The output result is the dimension of the quotient space: <\verbatim-code> Number of solutions (with multiplicity): 7 You can also use it with additional arguments to store the solution: <\verbatim-code> solver_bb_rational expl quotient The monomial basis and the table of multiplications are then stored in the file tient>: <\verbatim-code> basis:=[1,x0,x1,x0^2,x0*x1,x1^2,x0*x1^2];\ m0:=[ \ [0,0,0,1/2,1/3,0,0], [1,0,0,0,0,0,0], [0,0,0,0,0,0,1/3], \ [0,1,0,0,0,0,0], [0,0,1,0,0,0,0], [0,0,0,-1/2,0,0,0], [0,0,0,0,0,1,0] ]; m1:=[ \ [0,0,0,1/3,0,0,0], [0,0,0,0,0,-2/3,0], [1,0,0,0,0,1,0], \ [0,0,0,0,0,0,-2/3], [0,1,0,0,0,0,1], [0,0,1,0,0,0,0], [0,0,0,0,1,0,0] ]; If an additional file argument is given,\ <\verbatim-code> solver_bb_rational expl quotient sol then numerical approximations of the complex roots are computed and stored in the file : <\verbatim-code> sol:=[\ \ [0.0428035262163119+(-0.5580279186159117)*I,-1.0517405084461988+(0.1623024230495026)*I], \ [0.0428035262163119+(0.5580279186159117)*I,-1.0517405084461988+(-0.1623024230495026)*I], \ [-0.5392836762227580+(-0.0000000000000000)*I,1.1461572238101630+(0.0000000000000000)*I], \ [0.6794478081883069+(-0.1011278450437246)*I,0.6757807989652637+(0.2057214199313530)*I], \ [0.6794478081883069+(0.1011278450437246)*I,0.6757807989652637+(-0.2057214199313530)*I], \ [-0.4526094962932398+(0.7015185419968863)*I,-0.1971189024241464+(0.4357389800666190)*I], \ [-0.4526094962932398+(-0.7015185419968863)*I,-0.1971189024241464+(-0.4357389800666190)*I] ]; . If you don't have this file, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.>