Symbolic Numerical Solving - An Example

LIB "triang.lib";
ring r=0,(x,y,z),lp;
ideal i=x2+y+z-1,x+y2+z-1,x+y+z2-1;
option(redSB);
ideal j = groebner(i);
triangMH(j,2);

 
        
            
              ==> [1]: 
           
              [2]: 
           
              [3]: 
           
              [4]: 
           
           
             
              _[1]=z 
           
              _[1]=z 
           
              _[1]=z2+2z-1 
           
              _[1]=z-1
           
           
             
              _[2]=y 
           
              _[2]=y-1 
           
              _[2]=y-z 
           
              _[2]=y
           
           
              
              _[3]=x-1 
           
              _[3]=x 
           
              _[3]=x-z 
           
              _[3]=x

LIB"solve.lib";
triang_solve(triangMH(j,2),30); // accuracy of 30 digits
rlist; Returns a list of 5 solutions.

Symbolic Numerical Solving

Paris 7-2-01

http://www.singular.uni-kl.de