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D.9.1.6 AGcode_L
Procedure from library brnoeth.lib (see brnoeth_lib).
- Usage:
AGcode_L( G, D, EC ); G,D intvec, EC a list
- Return:
a generator matrix for the evaluation 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 evaluates the vector basis of L(G) 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 evaluation AG code : matrix C=AGcode_L(G,D,HC); → Vector basis successfully computed // here is a linear code of type [8,5,>=3] over F_4 print(C); → 0,0,(a), (a+1),1, 1, (a+1),(a), → 1,0,(a), (a+1),(a),(a+1),(a), (a+1), → 1,1,1, 1, 1, 1, 1, 1, → 0,0,(a+1),(a), 1, 1, (a), (a+1), → 0,0,(a+1),(a), (a),(a+1),1, 1 printlevel=plevel; |
See also: AGcode_Omega; Adj_div; BrillNoether; extcurve.