[4f7d76] | 1 | echo = 2; |
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| 2 | |
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| 3 | LIB("syzextra.so"); |
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| 4 | |
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| 5 | noop(); |
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| 6 | |
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| 7 | system("--min-time", "0.01"); |
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| 8 | system("--ticks-per-sec", 100); |
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| 9 | |
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| 10 | LIB "poly.lib"; // for numerator & denominator |
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| 11 | |
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| 12 | option(redSB); option(redTail); // assumed for the results of kStd! |
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| 13 | option(prot); |
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| 14 | option(mem); |
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| 15 | option(notWarnSB); |
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| 16 | |
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| 17 | |
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| 18 | // option(noloadLib); option(noredefine); |
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| 19 | |
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| 20 | LIB "teachstd.lib"; |
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| 21 | |
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| 22 | int reduce_time = 0; |
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| 23 | |
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| 24 | /////////////////////////////////////////////////////////////////////////////// |
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| 25 | proc MyReduce(f, G) |
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| 26 | { |
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| 27 | int t = timer; |
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| 28 | def g = reduce_syz(f, G, 0); |
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| 29 | int tt = timer; |
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| 30 | |
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| 31 | reduce_time = reduce_time + (tt - t); |
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| 32 | |
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| 33 | return(g); |
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| 34 | }; |
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| 35 | |
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| 36 | proc separateSyzGB( module J, int c ) |
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| 37 | { |
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| 38 | module II, G; vector v; int i; |
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| 39 | |
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| 40 | J = simplify(J, 2); |
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| 41 | |
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| 42 | for( i = ncols(J); i > 0; i-- ) |
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| 43 | { |
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| 44 | v = J[i]; |
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| 45 | if( leadcomp(v) > c ) |
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| 46 | { |
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| 47 | II[i] = v; |
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| 48 | } else |
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| 49 | { |
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| 50 | G[i] = v; // leave only gen(i): i <= c |
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| 51 | } |
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| 52 | } |
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| 53 | |
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| 54 | II = simplify(II, 2); |
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| 55 | G = simplify(G, 2); |
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| 56 | |
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| 57 | return (list(G, II)); |
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| 58 | } |
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| 59 | |
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| 60 | |
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| 61 | |
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| 62 | proc splitSyzGB( module J, int c ) |
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| 63 | { |
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| 64 | module JJ; vector v, vv; int i; |
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| 65 | |
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| 66 | for( i = ncols(J); i > 0; i-- ) |
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| 67 | { |
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| 68 | v = J[i]; |
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| 69 | |
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| 70 | vv = 0; |
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| 71 | |
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| 72 | while( leadcomp(v) <= c ) |
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| 73 | { |
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| 74 | vv = vv + lead(v); |
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| 75 | v = v - lead(v); |
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| 76 | } |
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| 77 | |
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| 78 | J[i] = vv; |
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| 79 | JJ[i] = v; |
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| 80 | } |
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| 81 | |
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| 82 | J = simplify(J, 2); |
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| 83 | JJ = simplify(JJ, 2); |
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| 84 | |
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| 85 | return (list(J, JJ)); |
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| 86 | } |
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| 87 | |
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| 88 | |
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| 89 | |
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| 90 | proc prepareSyz( module I, list # ) |
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| 91 | { |
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| 92 | int i; |
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| 93 | int k = 0; |
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| 94 | int r = nrows(I); |
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| 95 | int c = ncols(I); |
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| 96 | |
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| 97 | |
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| 98 | if( size(#) > 0 ) |
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| 99 | { |
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| 100 | if( typeof(#[1]) == "int" || typeof(#[1]) == "bigint" ) |
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| 101 | { |
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| 102 | k = #[1]; |
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| 103 | } |
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| 104 | } |
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| 105 | |
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| 106 | if( k < r ) |
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| 107 | { |
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| 108 | "// *** Wrong k: ", k, " < nrows: ", r, " => setting k = r = ", r; |
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| 109 | k = r; |
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| 110 | } |
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| 111 | |
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| 112 | // "k: ", k; "c: ", c; "I: ", I; |
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| 113 | |
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| 114 | for( i = c; i > 0; i-- ) |
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| 115 | { |
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| 116 | I[i] = I[i] + gen(k + i); |
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| 117 | } |
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| 118 | |
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| 119 | // DetailedPrint(I); |
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| 120 | |
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| 121 | return(I); |
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| 122 | } |
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| 123 | |
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| 124 | |
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| 125 | /// is p - permissible? |
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| 126 | proc myPrimeTest(def I, int p) |
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| 127 | { |
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| 128 | int i; def v; number c; |
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| 129 | |
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| 130 | for(i = ncols(I); i > 0; i--) |
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| 131 | { |
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| 132 | v = I[i]; |
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| 133 | while(v != 0) |
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| 134 | { |
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| 135 | c = leadcoef(v); |
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| 136 | |
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| 137 | if( (numerator(c) mod p) == 0) { return(0); } |
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| 138 | if( (denominator(c) mod p) == 0) { return(0); } |
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| 139 | |
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| 140 | v = v - lead(v); |
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| 141 | } |
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| 142 | } |
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| 143 | return(1); |
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| 144 | } |
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| 145 | |
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| 146 | proc myPrimeList(module I, int n, list #) |
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| 147 | { |
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| 148 | intvec L; |
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| 149 | int i,p; |
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| 150 | |
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| 151 | if(size(#) == 0) |
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| 152 | { |
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| 153 | p = 2147483647; |
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| 154 | |
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| 155 | while(myPrimeTest(I,p)==0) |
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| 156 | { |
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| 157 | p = prime(p-1); |
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| 158 | if(p == 2) { ERROR("no more primes"); } |
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| 159 | } |
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| 160 | L[1] = p; |
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| 161 | } |
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| 162 | else |
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| 163 | { |
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| 164 | L = #[1]; |
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| 165 | p = prime(L[size(L)]-1); |
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| 166 | while(!myPrimeTest(I,p)) |
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| 167 | { |
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| 168 | p = prime(p-1); |
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| 169 | if(p == 2) { ERROR("no more primes"); } |
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| 170 | } |
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| 171 | L[size(L)+1] = p; |
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| 172 | } |
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| 173 | |
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| 174 | if(p == 2) { ERROR("no more primes"); } |
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| 175 | for(i = 2; i <= n; i++) |
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| 176 | { |
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| 177 | p = prime(p-1); |
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| 178 | while(!myPrimeTest(I,p)) |
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| 179 | { |
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| 180 | p = prime(p-1); |
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| 181 | if(p == 2) { ERROR("no more primes"); } |
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| 182 | } |
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| 183 | L[size(L)+1] = p; |
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| 184 | } |
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| 185 | |
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| 186 | return(L); |
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| 187 | } |
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| 188 | |
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| 189 | |
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| 190 | |
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| 191 | //////////////////////////////////////////////////////////////////////////////// |
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| 192 | |
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| 193 | // int try = 0; |
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| 194 | |
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| 195 | proc GBCandidate0( module M, def P) |
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| 196 | { |
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| 197 | |
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| 198 | def Q = basering; |
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| 199 | |
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| 200 | int iComp = attrib(basering, "SyzComp"); |
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| 201 | |
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| 202 | setring P; |
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| 203 | module M = imap(Q, M); |
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| 204 | |
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| 205 | M = idPrepare(M, iComp); |
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| 206 | |
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| 207 | /* |
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| 208 | try ++; |
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| 209 | |
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| 210 | if( try != 5 ) |
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| 211 | { |
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| 212 | return (0); |
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| 213 | } |
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| 214 | */ |
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| 215 | |
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| 216 | M = simplify(M, 2); |
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| 217 | |
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| 218 | setring Q; |
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| 219 | |
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| 220 | M = imap(P, M); |
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| 221 | |
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| 222 | return (M); |
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| 223 | } |
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| 224 | |
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| 225 | |
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| 226 | |
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| 227 | proc Noro( module M ) |
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| 228 | { |
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| 229 | def save = basering; |
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| 230 | |
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| 231 | |
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| 232 | if( char(save) != 0 ) |
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| 233 | { |
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| 234 | ERROR("Noro: char != 0!"); |
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| 235 | } |
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| 236 | |
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| 237 | int iComp = nrows(M); |
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| 238 | |
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| 239 | |
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| 240 | def Q = MakeSyzCompOrdering(); setring Q; |
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| 241 | // def Q = MakeInducedSchreyerOrdering(); setring Q; |
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| 242 | |
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| 243 | |
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| 244 | SetSyzComp(iComp); |
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| 245 | attrib(Q, "SyzComp", iComp); |
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| 246 | DetailedPrint(basering); |
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| 247 | |
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| 248 | list L = ringlist(basering); |
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| 249 | |
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| 250 | def M = imap(save, M); |
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| 251 | |
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| 252 | M = prepareSyz(M, iComp); |
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| 253 | |
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| 254 | DetailedPrint(basering); |
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| 255 | |
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| 256 | intvec pp = myPrimeList(M, 10); |
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| 257 | |
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| 258 | // intvec pp = 99981793+1; |
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| 259 | |
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| 260 | // intvec pp = 32003 + 1; pp = myPrimeList(M, 10, pp); |
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| 261 | |
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| 262 | int p; |
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| 263 | int i = 1; |
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| 264 | |
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| 265 | int try = 0; |
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| 266 | |
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| 267 | while(1) |
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| 268 | { |
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| 269 | try ++; |
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| 270 | |
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| 271 | // choose p: |
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| 272 | p = pp[i]; |
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| 273 | |
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| 274 | "Current prime: ", p; |
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| 275 | |
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| 276 | if( typeof(L[1]) == "int" || typeof(L[1]) == "bigint" ) |
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| 277 | { |
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| 278 | L[1] = p; |
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| 279 | } |
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| 280 | else |
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| 281 | { |
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| 282 | if( typeof(L[1][1]) == "int" || typeof(L[1][1]) == "bigint" ) |
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| 283 | { |
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| 284 | L[1][1] = p; |
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| 285 | } |
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| 286 | else |
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| 287 | { |
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| 288 | ERROR("NORO: cannot create p-ring list: wrong input ring?"); |
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| 289 | } |
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| 290 | } |
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| 291 | |
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| 292 | // new ring over F_p |
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| 293 | def P = ring(L); setring P; |
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| 294 | |
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| 295 | SetSyzComp(iComp); |
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| 296 | // DetailedPrint(basering); |
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| 297 | |
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| 298 | setring Q; |
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| 299 | |
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| 300 | // M; print(M); |
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| 301 | |
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| 302 | // Compute GB Candidate for M using the ring P / F_p |
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| 303 | "Computing GB Candidate: "; |
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| 304 | def result = GBCandidate(M, P); |
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| 305 | |
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| 306 | if( defined(result) && (size(result) > 0) && (typeof(result) == "list") && (result[1] == "ok") ) |
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| 307 | { |
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| 308 | "==================================================================="; |
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| 309 | "It is DONE!"; |
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| 310 | "try: ", try; |
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| 311 | |
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| 312 | result[2]; |
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| 313 | print(result[2]); |
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| 314 | // DetailedPrint(result[2]); |
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| 315 | |
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| 316 | list GB_SYZ = separateSyzGB(result[2], iComp); |
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| 317 | |
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| 318 | module GB = GB_SYZ[1]; //splitSyzGB(, iComp)[1]; |
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| 319 | module SYZ = GB_SYZ[2]; |
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| 320 | |
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| 321 | |
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| 322 | GB; |
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| 323 | SYZ; |
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| 324 | |
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| 325 | |
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| 326 | |
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| 327 | setring save; |
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| 328 | |
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| 329 | |
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| 330 | module GB = imap(Q, GB); |
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| 331 | |
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| 332 | if( size(GB) > 0 ) |
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| 333 | { |
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| 334 | // need the top part! |
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| 335 | GB = transpose(GB); |
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| 336 | GB = GB[1..iComp]; |
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| 337 | GB = transpose(GB); |
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| 338 | } |
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| 339 | |
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| 340 | |
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| 341 | module SYZ = imap(Q, SYZ); |
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| 342 | |
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| 343 | if( size(SYZ) > 0 ) |
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| 344 | { |
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| 345 | int r = nrows(SYZ); |
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| 346 | |
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| 347 | // need the bottom part: |
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| 348 | SYZ = transpose(SYZ); |
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| 349 | SYZ = SYZ[iComp+1 .. r]; |
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| 350 | SYZ = transpose(SYZ); |
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| 351 | } |
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| 352 | |
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| 353 | return (list((GB), (SYZ))); |
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| 354 | } |
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| 355 | |
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| 356 | kill P; |
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| 357 | setring Q; |
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| 358 | |
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| 359 | i ++; |
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| 360 | |
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| 361 | if( i > size(pp) ) |
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| 362 | { |
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| 363 | pp = myPrimeList(M, 10, pp); |
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| 364 | pp; |
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| 365 | } |
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| 366 | |
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| 367 | |
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| 368 | if( !defined(pp) ) |
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| 369 | { |
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| 370 | ERROR("NORO: Sorry no more primes!"); |
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| 371 | return(0); |
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| 372 | } |
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| 373 | } // while(1) |
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| 374 | } |
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| 375 | |
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| 376 | |
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| 377 | // basering is assumed to be Z[x_1, ..., x_n] |
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| 378 | |
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| 379 | // F is a list of vectors of the same length |
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| 380 | proc GBCandidate (module F, def Fp) |
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| 381 | { |
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| 382 | int ss = 1; // symmetric S-polynomial |
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| 383 | |
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| 384 | // TODO: check input for errors |
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| 385 | def br = basering; |
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| 386 | |
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| 387 | int i, j; |
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| 388 | |
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| 389 | int sizeF = size(F); |
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| 390 | |
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| 391 | intvec C; |
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| 392 | list D; // list of intvecs of length 2, as indices of F |
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| 393 | for(i = 1; i <= sizeF; i++) |
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| 394 | { |
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| 395 | for(j = i+1; j <= sizeF; j++) |
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| 396 | { |
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| 397 | D = insert(D, intvec(i, j)); |
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| 398 | } |
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| 399 | } |
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| 400 | |
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| 401 | vector h, s; |
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| 402 | number c; |
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| 403 | |
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| 404 | setring Fp; |
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| 405 | vector h, s; |
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| 406 | module F; |
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| 407 | |
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| 408 | int p = char(Fp); |
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| 409 | // TODO: check that characteristic of Fp is permissible for F |
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| 410 | |
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| 411 | |
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| 412 | |
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| 413 | while(size(D) > 0) |
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| 414 | { |
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| 415 | |
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| 416 | if(char(basering) != p ) |
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| 417 | { |
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| 418 | "ERROR: wrong current ring!"; |
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| 419 | $$$ |
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| 420 | } |
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| 421 | |
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| 422 | C = D[size(D)]; |
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| 423 | D = delete(D, size(D)); |
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| 424 | |
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| 425 | // "Pair: (", C[1], ",", C[2], ")"; |
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| 426 | |
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| 427 | F = fetch(br, F); |
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| 428 | s = spoly(F[C[1]], F[C[2]], ss); |
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| 429 | h = MyReduce(s, F); |
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| 430 | |
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| 431 | if(h != 0) |
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| 432 | { |
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| 433 | setring br; |
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| 434 | |
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| 435 | s = spoly(F[C[1]], F[C[2]], ss); |
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| 436 | h = MyReduce(s, F); // h \in Z_<p>[x] ??? |
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| 437 | |
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| 438 | c = leadcoef(h); |
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| 439 | |
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| 440 | if(h != 0) |
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| 441 | { |
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| 442 | if( (denominator(c) mod p) == 0 ) |
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| 443 | { |
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| 444 | "h: ", h; |
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| 445 | "c: ", c; |
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| 446 | "ERROR: GBCandidate: wrong coeff!"; |
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| 447 | $$ |
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| 448 | } |
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| 449 | } |
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| 450 | |
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| 451 | if(h != 0 && (numerator(c) mod p) != 0) |
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| 452 | { |
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| 453 | for(i = 1; i <= sizeF; i++) |
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| 454 | { |
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| 455 | D = insert(D, intvec(i, sizeF+1)); |
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| 456 | } |
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| 457 | sizeF++; |
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| 458 | F[sizeF] = h; |
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| 459 | |
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| 460 | // "new F[",sizeF,"] element: ", h; |
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| 461 | |
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| 462 | setring Fp; |
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| 463 | |
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| 464 | h = fetch(br, h); |
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| 465 | F[sizeF] = h; |
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| 466 | } |
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| 467 | else |
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| 468 | { |
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| 469 | /* |
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| 470 | "&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&"; |
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| 471 | matrix T; // = lift(F, s); |
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| 472 | basering; // /Q |
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| 473 | |
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| 474 | test(23+32); |
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| 475 | option(teach); |
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| 476 | |
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| 477 | "i, j: ", C[1], C[2]; |
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| 478 | |
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| 479 | |
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| 480 | F; |
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| 481 | "f: ", F[C[1]]; |
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| 482 | "g: ", F[C[2]]; |
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| 483 | "s: ", s; |
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| 484 | "ZERO::: h: ", h; // 0!!! |
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| 485 | |
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| 486 | vector m = NFMora(s, F); |
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| 487 | "MORA: ", m; |
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| 488 | |
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| 489 | // matrix(s)-matrix(F)*T; print(T); |
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| 490 | |
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| 491 | MyReduce(s, F); |
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| 492 | "h-test: ", _ == h; |
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| 493 | |
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| 494 | "????"; |
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| 495 | |
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| 496 | setring Fp; |
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| 497 | |
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| 498 | "!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"; |
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| 499 | basering; // /p |
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| 500 | |
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| 501 | |
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| 502 | F; |
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| 503 | "F-proj-test: ", size(module(matrix(F) - matrix(fetch(br, F)))) == 0; |
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| 504 | |
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| 505 | "f: ", F[C[1]]; |
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| 506 | "g: ", F[C[2]]; |
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| 507 | "s: ", s; |
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| 508 | |
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| 509 | "s-proj-test: ", s == fetch(br, s); |
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| 510 | |
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| 511 | "NON-ZERO::: h: ", h; |
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| 512 | |
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| 513 | // matrix T = fetch(br, T); def S = (matrix(F)*T); print(S); S; |
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| 514 | |
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| 515 | vector m = NFMora(s, F); |
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| 516 | "MORA: ", m; |
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| 517 | |
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| 518 | "m-proj-test: ", m == fetch(br, m); |
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| 519 | |
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| 520 | |
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| 521 | MyReduce(s, F); |
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| 522 | "h-test: ", _ == h; |
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| 523 | |
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| 524 | "????"; |
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| 525 | $$$ |
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| 526 | */ |
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| 527 | return(list("ng", module())); |
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| 528 | } |
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| 529 | } |
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| 530 | } |
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| 531 | setring br; |
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| 532 | F = interred(F); // ? |
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| 533 | return(list("ok", F)); |
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| 534 | } |
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| 535 | |
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| 536 | |
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| 537 | |
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| 538 | |
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| 539 | echo = 1; |
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| 540 | |
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| 541 | |
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| 542 | ring R = 0, (w, x, y, z), dp; |
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| 543 | module I = w^2 - x*z, w*x - y*z, x^2 - w*y, x*y - z^2, y^2 - w*z; |
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| 544 | |
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| 545 | |
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| 546 | |
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| 547 | /* |
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| 548 | ring r = 0,(x,y,z),(c,dp); |
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| 549 | module I = [x+1, y, 1], [xy, z, z2]; // NO SYZ! |
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| 550 | */ |
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| 551 | |
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| 552 | |
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| 553 | /* |
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| 554 | // Test: kotsireas |
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| 555 | ring R = (0),(B, b, D, d, F, f),dp; |
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| 556 | module I = B*b-b*D-B*d+D*d-2*F+2,B*b+b*D-B*d-D*d-2*b*F+2*d*F-2*B+2*D,b^2-2*b*d+d^2-2*b-2*d+f+1,B^2*b^3-1,D^2*d^3-1,F^2*f^3-1; |
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| 557 | */ |
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| 558 | |
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| 559 | |
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| 560 | |
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| 561 | /* |
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| 562 | // Cohn3 |
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| 563 | ring R = (0),(x1, y, z, t),dp; |
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| 564 | module I = -x1^3*y^2+2*x1^2*y^2*z-x1^2*y*z^2-144*x1^2*y^2-207*x1^2*y*z+288*x1*y^2*z+78*x1*y*z^2+x1*z^3-3456*x1^2*y-5184*x1*y^2-9504*x1*y*z-432*x1*z^2-248832*x1*y+62208*x1*z-2985984*x1,-x1^3*z*t^2+x1^2*z^2*t^2-6*x1^3*z*t+4*x1^2*z^2*t+32*x1^3*t^2-72*x1^2*z*t^2-87*x1*z^2*t^2-z^3*t^2-8*x1^3*z-432*x1^2*z*t-414*x1*z^2*t+2592*x1*z*t^2+864*z^2*t^2-1728*x1^2*z-20736*x1*z*t+3456*z^2*t-186624*z*t^2-124416*x1*z-1492992*z*t-2985984*z,x1^2*y*t^3-2*x1*y^2*t^3+y^3*t^3+8*x1^2*y*t^2-12*x1*y^2*t^2+4*y^3*t^2-24*x1*y*t^3+24*y^2*t^3+20*x1^2*y*t-20*x1*y^2*t-160*x1*y*t^2+96*y^2*t^2+128*x1*t^3+16*x1^2*y+96*x1*y*t+2304*x1*t^2+1152*x1*y+13824*x1*t+27648*x1,y^3*t^3-y^2*z*t^3+4*y^3*t^2-2*y^2*z*t^2+72*y^2*t^3+71*y*z*t^3+288*y^2*t^2+360*y*z*t^2+6*z^2*t^2+1728*y*t^3-464*z*t^3+432*y*z*t+8*z^2*t+6912*y*t^2-4320*z*t^2+13824*t^3+z^2-13824*z*t+55296*t^2-13824*z; |
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| 565 | */ |
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| 566 | |
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| 567 | |
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| 568 | |
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| 569 | /* |
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| 570 | // Cyclic 7: (done) |
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| 571 | ring R = (0),(a, b, c, d, e),dp; |
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| 572 | module I = a+b+c+d+e,a*b+a*e+b*c+c*d+d*e,a*b*c+a*b*e+a*d*e+b*c*d+c*d*e,a*b*c*d+a*b*c*e+a*b*d*e+a*c*d*e+b*c*d*e,a*b*c*d*e-1; |
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| 573 | */ |
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| 574 | |
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| 575 | /* |
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| 576 | // HCyclic 7: (running: 80% of 16GB mem while computing syz!... too slow... ) |
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| 577 | ring R = (0),(x1, x2, x3, x4, x5, x6, x7, w),dp; |
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| 578 | module I = x1+x2+x3+x4+x5+x6+x7,x1*x2+x2*x3+x3*x4+x4*x5+x5*x6+x1*x7+x6*x7,x1*x2*x3+x2*x3*x4+x3*x4*x5+x4*x5*x6+x1*x2*x7+x1*x6*x7+x5*x6*x7,x1*x2*x3*x4+x2*x3*x4*x5+x3*x4*x5*x6+x1*x2*x3*x7+x1*x2*x6*x7+x1*x5*x6*x7+x4*x5*x6*x7,x1*x2*x3*x4*x5+x2*x3*x4*x5*x6+x1*x2*x3*x4*x7+x1*x2*x3*x6*x7+x1*x2*x5*x6*x7+x1*x4*x5*x6*x7+x3*x4*x5*x6*x7,x1*x2*x3*x4*x5*x6+x1*x2*x3*x4*x5*x7+x1*x2*x3*x4*x6*x7+x1*x2*x3*x5*x6*x7+x1*x2*x4*x5*x6*x7+x1*x3*x4*x5*x6*x7+x2*x3*x4*x5*x6*x7,x1*x2*x3*x4*x5*x6*x7-w^7; |
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| 579 | */ |
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| 580 | |
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| 581 | // syz(I); print(_); // |
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| 582 | |
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| 583 | /* |
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| 584 | module M; |
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| 585 | M[5]=abcde*gen(1)-gen(1)+gen(6); |
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| 586 | M[1]=a*gen(1)+b*gen(1)+c*gen(1)+d*gen(1)+e*gen(1)+gen(2); |
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| 587 | M[2]=ab*gen(1)+bc*gen(1)+cd*gen(1)+ae*gen(1)+de*gen(1)+gen(3); |
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| 588 | M[3]=abc*gen(1)+bcd*gen(1)+abe*gen(1)+ade*gen(1)+cde*gen(1)+gen(4); |
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| 589 | M[4]=abcd*gen(1)+abce*gen(1)+abde*gen(1)+acde*gen(1)+bcde*gen(1)+gen(5); |
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| 590 | |
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| 591 | ring P = (99981794),(a, b, c, d, e),dp; |
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| 592 | setring R; |
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| 593 | |
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| 594 | GBCandidate(M, P);$$ |
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| 595 | */ |
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| 596 | |
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| 597 | int tG = timer; |
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| 598 | def G = groebner(I); |
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| 599 | int ttG = timer; |
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| 600 | |
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| 601 | "Time GB: ", ttG - tG; |
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| 602 | |
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| 603 | |
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| 604 | int tN = timer; |
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| 605 | def L = Noro( I ); |
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| 606 | int ttN = timer; |
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| 607 | |
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| 608 | "Time Noro: ", ttN - tN; |
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| 609 | |
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| 610 | // All syzygies? |
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| 611 | int tS = timer; |
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| 612 | module S = syz(I); |
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| 613 | int ttS = timer; |
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| 614 | |
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| 615 | "Time Syz: ", ttS - tS; |
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| 616 | |
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| 617 | |
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| 618 | module GB = L[1]; |
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| 619 | module SYZ = L[2]; |
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| 620 | |
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| 621 | ":::::::::::::::::::::::::::::::::::::::::::: GB :::::::::::::::::::::::::::::::::::: "; |
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| 622 | print(GB); |
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| 623 | |
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| 624 | // test GB: |
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| 625 | if( size(NF(I, GB)) > 0 ) |
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| 626 | { |
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| 627 | ERROR("NORO was wrong: I is bigger than GB!"); |
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| 628 | } |
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| 629 | |
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| 630 | if( size(NF(GB, G)) > 0 ) |
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| 631 | { |
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| 632 | ERROR("NORO was wrong: GB is bigger than I!"); |
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| 633 | } |
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| 634 | |
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| 635 | ":::::::::::::::::::::::::::::::::::::::::::: SYZ :::::::::::::::::::::::::::::::::::: "; |
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| 636 | print(SYZ); |
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| 637 | |
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| 638 | |
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| 639 | if( size(SYZ) > 0 ) |
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| 640 | { |
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| 641 | // test syzygy |
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| 642 | if( size( module(transpose(SYZ)*transpose(I)) ) > 0 ) |
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| 643 | { |
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| 644 | ERROR("NORO was wrong: SYZ are NOT syzygies of I!"); |
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| 645 | } |
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| 646 | } |
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| 647 | |
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| 648 | |
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| 649 | |
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| 650 | // test SYZ: |
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| 651 | if( size(NF(SYZ, groebner(S))) > 0 ) |
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| 652 | { |
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| 653 | ERROR("NORO was wrong: too much syzygies found!!!"); |
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| 654 | } |
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| 655 | |
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| 656 | if( size(NF(S, groebner(SYZ))) > 0 ) |
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| 657 | { |
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| 658 | ERROR("NORO was wrong: too few syzygies found!!!"); |
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| 659 | } |
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| 660 | |
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| 661 | |
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| 662 | ":::::::::::::::::::::::::::::::::::::::::::: GOOD :::::::::::::::::::::::::::::::::::: "; |
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| 663 | |
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| 664 | |
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| 665 | "Time GB: ", ttG - tG; |
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| 666 | "Time Syz: ", ttS - tS; |
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| 667 | "Time Noro: ", ttN - tN, " vs GB+SYZ: ", (ttS - tS) + (ttG - tG), ""; |
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| 668 | |
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| 669 | "Time NF: ", reduce_time; |
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| 670 | |
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| 671 | |
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| 672 | |
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| 673 | number t = (ttN - tN); |
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| 674 | number tt = ((ttS - tS) + (ttG - tG)); |
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[0917a96] | 675 | "Factor: ", t div tt; |
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| 676 | "Factor: ", (ttN - tN) div ((ttS - tS) + (ttG - tG)); |
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[4f7d76] | 677 | |
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| 678 | |
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[0917a96] | 679 | $$ |
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