SSL rr_space.lib
Sprache: unbekannt
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// proc below computes length, dimension, and generator matrix of
// AG code associated to divisots G, D on the curve
// f(x,y)=0 over a field extension of degree d over
// the ground field for f(x,y)
///// may not work for all examples
//
// 8-9-2004,wdj
// http://cadigweb.ew.usna.edu/~wdj/gap/singular/ag_code_rr_space.sing
LIB "brnoeth.lib"; // need this
LIB "linalg.lib"; // need this
proc ag_code (poly f, int d, intvec G, intvec D)
//["
//Input: f over GF(p) in x,y, representing a curve f(x,y)=0
//over a field extension E of GF(p) degree d>0,
//divisots G, D on the curve f(x,y)=0 over E,
//Output: (generator matrix for AG code C_L(G,D),
//n = length, k = dim, rank of matrix (should = k))
//"]
{
list AD=Adj_div(f);
list nsp=NSplaces(1..d,AD);
list crv_info=extcurve(d,nsp);
def GAP_S=crv_info[1][2];
setring GAP_S;
keepring GAP_S;
matrix AGC=AGcode_L(G,D,crv_info);
int n_length=ncols(AGC);
int k_dim=nrows(AGC);
list AGC2=gaussred(AGC,1);
int ag_mat_rank=AGC2[4];
matrix ag_mat=AGC2[3];
list ans=ag_mat,n_length,k_dim,ag_mat_rank;
export(GAP_S);
return(ans);
};
/*
////////////////[example
//{
int p=11;
ring R=p,(x,y),lp;
poly f=x3y+y3+x;
int d=2;
intvec G=1,0,0,0,0,0,0,0;
intvec D=4..8;
list agc=ag_code(f,d,G,D);
//}]
/////////////////[example
//{
int p=11;
ring R=p,(x,y),lp;
poly f=x3y+y3+x;
int d=2;
intvec G=6,0,0,0,0,0,0,1;
intvec D=5..7;
list agc=ag_code(f,d,G,D);
//}]
*/
// works in Singular
proc rr_basis (poly f, intvec G)
//["
//Input: f in GF(p)[x,y], representing a curve f(x,y)=0
//over GF(p), divisot G on the curve f(x,y)=0 over GF(p),
//Output: string representing basis of Riemann-Roch space L(G)
//"]
{
list C=Adj_div(f);
list curveinfo=NSplaces(1,C);
def R=curveinfo[1][2];
setring R;
list LG=BrillNoether(G,curveinfo);
// export(GAP_curveinfo);
string s=string(LG);
// print(LG);
return(s);
}; // return(LG); doesn't work ...
/*
/////////////[example
int p=11;
ring R=p,(x,y),lp;
poly f=x3y+y3+x;
int d=2;
intvec G=6,0,0,0,0,0,0,1;
rr_basis(f,G);
//}]
*/
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2026-03-28
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