# Singular

#### D.10.1.7 AGcode_Omega

Procedure from library `brnoeth.lib` (see brnoeth_lib).

Usage:
AGcode_Omega( G, D, EC ); G,D intvec, EC a list

Return:
a generator matrix for the residual AG code defined by the divisors G and D.

Note:
The procedure must be called within the ring EC[1][4], where EC is the output of `extcurve(d)` (or within the ring EC[1][2] if d=1).
The entry i in the intvec D refers to the i-th rational place in EC[1][5] (i.e., to POINTS[i], etc., see extcurve).
The intvec G represents a rational divisor (see BrillNoether for more details).
The code computes the residues of a vector space basis of

at the rational places given by D.

Warnings:
G should satisfy , which is not checked by the algorithm.
G and D should have disjoint supports (checked by the algorithm).

Example:
 ```LIB "brnoeth.lib"; int plevel=printlevel; printlevel=-1; ring s=2,(x,y),lp; list HC=Adj_div(x3+y2+y); ==> The genus of the curve is 1 HC=NSplaces(1..2,HC); HC=extcurve(2,HC); ==> Total number of rational places : NrRatPl = 9 def ER=HC[1][4]; setring ER; intvec G=5; // the rational divisor G = 5*HC[3][1] intvec D=2..9; // D = sum of the rational places no. 2..9 over F_4 // let us construct the corresponding residual AG code : matrix C=AGcode_Omega(G,D,HC); ==> Vector basis successfully computed // here is a linear code of type [8,3,>=5] over F_4 print(C); ==> (a+1),(a+1),1,(a), (a),1,0,0, ==> (a+1),(a), 1,0, 1, 0,1,0, ==> 1, 0, 1,(a+1),(a),0,0,1 printlevel=plevel; ```
See also: AGcode_L; Adj_div; BrillNoether; extcurve.