spielwiese
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Last change
on this file since b258984 was
b258984,
checked in by Hans Schönemann <hannes@…>, 23 years ago
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*hannes brnoeth_l
git-svn-id: file:///usr/local/Singular/svn/trunk@4871 2c84dea3-7e68-4137-9b89-c4e89433aadc
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-
Property mode set to
100644
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File size:
2.5 KB
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| 1 | LIB "tst.lib"; |
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| 2 | tst_init(); |
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| 3 | tst_ignore("CVS ID $Id: brnoeth_l.tst,v 1.1 2000-12-12 12:36:37 Singular Exp $"); |
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| 4 | |
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| 5 | // tst_status(); |
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| 6 | |
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| 7 | |
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| 8 | // killall(); |
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| 9 | |
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| 10 | LIB "brnoeth.lib"; |
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| 11 | |
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| 12 | // special CURVE over F_64 (p=2) |
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| 13 | |
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| 14 | ring r=2,(x,y),lp; |
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| 15 | poly f=y9+y8+xy6+x2y3+y2+x3; |
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| 16 | ideal I=f,jacob(f); |
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| 17 | closed_points(I); |
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| 18 | I=f,x2+x,y2+y; |
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| 19 | closed_points(I); |
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| 20 | I=f,x4+x,y4+y; |
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| 21 | closed_points(I); |
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| 22 | I=f,x8+x,y8+y; |
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| 23 | closed_points(I); |
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| 24 | I=f,x16+x,y16+y; |
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| 25 | closed_points(I); |
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| 26 | I=f,x32+x,y32+y; |
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| 27 | closed_points(I); |
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| 28 | I=f,x64+x,y64+y; |
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| 29 | closed_points(I); |
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| 30 | list CURVE=Adj_div(f); |
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| 31 | CURVE=NSplaces(4,CURVE); |
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| 32 | CURVE=extcurve(6,CURVE); |
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| 33 | CURVE; |
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| 34 | def affR=CURVE[1][1]; |
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| 35 | setring affR; |
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| 36 | listvar(); |
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| 37 | Aff_SLocus; |
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| 38 | Inf_Points; |
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| 39 | def projR=CURVE[1][2]; |
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| 40 | setring projR; |
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| 41 | CHI; |
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| 42 | Weierstrass(4,10,CURVE); |
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| 43 | tst_status(); |
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| 44 | Weierstrass(1,10,CURVE); |
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| 45 | tst_status(); |
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| 46 | Weierstrass(2,10,CURVE); |
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| 47 | tst_status(); |
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| 48 | intvec DD=2,1,1,1,0,1; |
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| 49 | BrillNoether(DD,CURVE); |
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| 50 | DD=3,0,2; |
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| 51 | BrillNoether(DD,CURVE); |
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| 52 | def RP=CURVE[1][5]; |
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| 53 | setring RP; |
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| 54 | size(POINTS); |
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| 55 | setring r; |
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| 56 | killall(); |
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| 57 | |
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| 58 | // SUZUKI curve over F_8 (p=2) |
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| 59 | |
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| 60 | ring r=2,(x,y),lp; |
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| 61 | poly f=x10+x3+y8+y; |
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| 62 | ideal I=f,jacob(f); |
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| 63 | closed_points(I); |
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| 64 | I=f,x2+x,y2+y; |
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| 65 | closed_points(I); |
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| 66 | I=f,x4+x,y4+y; |
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| 67 | closed_points(I); |
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| 68 | I=f,x8+x,y8+y; |
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| 69 | closed_points(I); |
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| 70 | I=f,x16+x,y16+y; |
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| 71 | closed_points(I); |
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| 72 | I=f,x32+x,y32+y; |
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| 73 | closed_points(I); |
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| 74 | I=f,x64+x,y64+y; |
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| 75 | closed_points(I); |
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| 76 | list SUZUKI=Adj_div(f); |
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| 77 | SUZUKI=NSplaces(2,SUZUKI); |
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| 78 | SUZUKI=extcurve(3,SUZUKI); |
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| 79 | SUZUKI; |
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| 80 | def affR=SUZUKI[1][1]; |
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| 81 | setring affR; |
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| 82 | listvar(); |
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| 83 | Aff_SLocus; |
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| 84 | Inf_Points; |
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| 85 | def projR=SUZUKI[1][2]; |
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| 86 | setring projR; |
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| 87 | CHI; |
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| 88 | Weierstrass(1,20,SUZUKI); |
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| 89 | tst_status(); |
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| 90 | intvec DD=2,1,0,0,3,3; |
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| 91 | BrillNoether(DD,SUZUKI); |
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| 92 | tst_status(); |
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| 93 | def RP=SUZUKI[1][5]; |
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| 94 | setring RP; |
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| 95 | size(POINTS); |
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| 96 | setring r; |
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| 97 | killall(); |
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| 98 | |
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| 99 | // special HYPERELLIPTIC curve over F_16 (p=2) |
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| 100 | |
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| 101 | ring r=2,(x,y),lp; |
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| 102 | intvec G,D,F; |
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| 103 | poly f=x5+y2+y; |
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| 104 | list EC=Adj_div(f); |
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| 105 | EC=NSplaces(4,EC); |
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| 106 | EC=extcurve(4,EC); |
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| 107 | def R4=EC[1][4]; |
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| 108 | setring R4; |
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| 109 | G[5]=4; |
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| 110 | D=1..33; |
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| 111 | matrix C=AGcode_Omega(G,D,EC); |
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| 112 | print(C); |
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| 113 | // the code C=AGcode_Omega(G,D) is of type [33,22,>=10] over F_16; |
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| 114 | // the basic decoding algorithm can correct up to 3 errors; |
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| 115 | // for it, we need an auxiliary divisor F of degree 5 : |
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| 116 | F[14]=1; |
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| 117 | list SV=prepSV(G,D,F,EC); |
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| 118 | matrix y[1][33]; |
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| 119 | y[1,1]=1; |
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| 120 | y[1,2]=a; |
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| 121 | y[1,3]=1; |
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| 122 | print(decodeSV(y,SV)); |
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| 123 | y[1,1]=0; |
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| 124 | y[1,2]=a; |
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| 125 | y[1,10]=a+1; |
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| 126 | y[1,3]=0; |
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| 127 | y[1,21]=1; |
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| 128 | print(decodeSV(y,SV)); |
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| 129 | y[1,4]=a; |
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| 130 | y[1,2]=0; |
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| 131 | y[1,12]=a; |
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| 132 | y[1,10]=0; |
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| 133 | y[1,21]=0; |
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| 134 | y[1,29]=a+1; |
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| 135 | print(decodeSV(y,SV)); |
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| 136 | matrix H=dual_code(C); |
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| 137 | print(H); |
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| 138 | list SC=sys_code(C); |
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| 139 | print(SC[1]); |
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| 140 | print(SC[2]); |
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| 141 | SC[3]; |
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| 142 | list SH=sys_code(H); |
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| 143 | print(SH[1]); |
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| 144 | print(SH[2]); |
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| 145 | SH[3]; |
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| 146 | setring r; |
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| 147 | killall(); |
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| 148 | |
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| 149 | |
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| 150 | tst_status(1); |
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| 151 | $ |
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