Quelle all_pts.lib Sprache: unbekannt

////////////////////////////////////////////////
//
// functions to help with the ag_code routine
//
// ag_code_all_pts.sing, 8-2004,wdj
// http://cadigweb.ew.usna.edu/~wdj/gap/singular/ag_code_all_pts.sing
////////////////////////////////////////////////

LIB "brnoeth.lib";  // need this

proc pts_on_curve (poly f, int d)
{
  list AD=Adj_div(f);
  list nsp=NSplaces(1..d,AD);
return(nsp);
};

/*

// example:
ring R=11,(x,y),lp;
poly f=x3y+y3+x;
int d=2;
list pts=pts_on_curve(f,d);
pts; // especially need pts[3] - to determine the
     // possibilities for G and D in the ag_code
     // procedure. NSplaces computes rational
     // places but does not identify them(!), as
     // far as I can see.

// example 2:
ring R=7,(x,y),lp;
poly f=x7-y2-x;
int d=1;
list pts=pts_on_curve(f,d);
pts;

*/

// f is a polynomial in x,y
// (belonging to) ring R = p,(x,y),lp;
// defining an affine curve
// C defined over a finite field F = GF(p)
// proc finds pts of degree 1 over F
// with x-coord = pt
proc ratl_pts_on_curve (poly f, int p)
{
list pts=list();
ideal I;
list C;
for (int pt=0; pt<p; pt=pt+1)
  {
   I = f,x-pt;
   C = closed_points( I );
   pts = pts+C;
  };
return(pts);
};

/*

//         example:
int p=11;
int pt=3;
ring R=p,(x,y),lp;
poly f=x3y+y3+x;
ideal I=f,x-pt;
list C=closed_points( I );
C;
list all_pts=ratl_pts_on_curve(f,p);
all_pts;

*/

Quelle all_pts.lib Sprache: unbekannt

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