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Quelle all_pts.lib
Sprache: unbekannt
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////////////////////////////////////////////////
//
// 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;
*/
[ Dauer der Verarbeitung: 0.2 Sekunden
(vorverarbeitet)
]
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2026-03-28
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