/* a few sample plots */

  
numer:true;  
  
/* some nice figures.   fig1.ps from fig1.mac
  shows the units of a quadratic number field
    as lying on the yx= +- 1
  */    
  
viewps("fig1.ps");
  
/* REal part of z ^ 1/3 */

viewps("maxout-3.ps");  
  
plot2d(sin(x),[-%pi,%pi]);  
plot2d(3*sin(x),[-%pi,%pi]);  
  
block([ps_scale:[40,20],ps_translate:[5,15]],
  psaxes(4,10),
  plot2d(3*x^2*sin(x),[-%pi,%pi]));  
  
viewps("fig21.ps");  
  
/* REal part of z ^ 1/3 */
  
block([ps_scale:[200,200],
  ps_translate:[1.5,1.5],
  colour_z:true,transform_xy:polar_to_xy],
  closeps(),
  plot3d(r^.3333*cos(th/3),[1,1,1.4],[0,1,0,6*%pi],[12,81]),
  closeps(),viewps());
    
    
    
/* REal part of z ^ 1/6 */  
block([ps_scale:[200,200],
  ps_translate:[1.5,1.5],
  colour_z:true,transform_xy:polar_to_xy],
  plot3d(r^(1/6.0)*cos(th/6),[1,1,1.4],[0,1,0,2*6*%pi],[12,121]),
  closeps(),viewps()
  );
  
    


display2d:false;
set_up_dot_simplifications([z.z+y.y+y.x+x.y,-a*z.z+y.x+x.y+x.x,a*z.y,z.x-a*y.z-x.z],4);
centrals:fast_central_elements([x,y,z],3);
centrals4:  fast_central_elements([x,y,z],4);
set_up_dot_simplifications(append(centrals,centrals4,[z.z+y.y+y.x+x.y,-a*z.z+y.x+x.y+x.x,a*z.y,z.x-a*y.z-x.z]),8);
monomial_dimensions(8);