Strength of Kimberling X points
Thanks to Edward Brisse for his compilation of the points in barycentrics. Long coordinates are cut off to the right (which hopefully I can correct). The first 422 point are strong. The weak ones are below those. I first plan to use this information in many ways, the first is to search for weak points that collect on strong line; ie., that are colinear. A second is to collect the single strong point that is on each weak line.
| X number | strength | a coordinate in barycentrics |
| 2 | strong | 1 |
| 3 | strong | (a^2 (a^2 - b^2 - c^2)) |
| 4 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 5 | strong | (- a^2) b^2 + b^4 - a^2 c^2 - 2 b^2 c^2 + c^4) |
| 6 | strong | (a^2) |
| 20 | strong | (3 a^4 - 2 a^2 b^2 - b^4 - 2 a^2 c^2 + 2 b^2 c^2 - c^4) |
| 22 | strong | (a^2 (a^4 - b^4 - c^4)) |
| 23 | strong | (a^2 (a^4 - b^4 + b^2 c^2 - c^4)) |
| 24 | strong | (a^2 (a^2 + b^2 - c^2) ( a^2 - b^2 + c^2) (a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 + c^4)) |
| 25 | strong | (a^2 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 26 | strong | (a^2 (a^8 - 2 a^6 b^2 + 2 a^2 b^6 - b^8 - 2 a^6 c^2 + 2 b^6 c^2 - 2 b^4 c^4 + 2 a^2 c^6 + 2 b^2 c^6 - c^8)) |
| 30 | strong | (2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4) |
| 32 | strong | (a^4) |
| 39 | strong | (a^2 (b^2 + c^2)) |
| 49 | strong | (a^4 (a^2 - b^2 - c^2) (a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 - b^2 c^2 + c^4)) |
| 50 | strong | (a^4 (a^2 - b^2 - b c - c^2) (a^2 - b^2 + b c - c^2)) |
| 51 | strong | (a^2 (a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4)) |
| 52 | strong | (a^2 (a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4) (a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 + c^4)) |
| 53 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4)) |
| 54 | strong | (a^2 ( a^4 - 2 a^2 b^2 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - a^2 b^2 - 2 a^2 c^2 - b^2 c^2 + c^4)) |
| 64 | strong | (a^2 (a^4 - 2 a^2 b^2 + b^4 + 2 a^2 c^2 + 2 b^2 c^2 - 3 c^4) (a^4 + 2 a^2 b^2 - 3 b^4 - 2 a^2 c^2 + 2 b^2 c^2 + c^4)) |
| 66 | strong | ((a^4 + b^4 - c^4) (a^4 - b^4 + c^4)) |
| 67 | strong | ((a^4 - a^2 b^2 + b^4 - c^4) (a^4 - b^4 - a^2 c^2 + c^4)) |
| 68 | strong | ((a^2 - b^2 - c^2) (a^4 - 2 a^2 b^2 + b^4 - 2 b^2 c^2 + c^4) (a^4 + b^4 - 2 a^2 c^2 - 2 b^2 c^2 + c^4)) |
| 69 | strong | (a^2 - b^2 - c^2) |
| 70 | strong | ((a^8 - 2 a^6 b^2 + 2 a^4 b^4 - 2 a^2 b^6 + b^8 - 2 a^6 c^2 - 2 b^6 c^2 + 2 a^2 c^6 + 2 b^2 c^6 - c^8) (a^8 - 2 a^6 b^2 + 2 a^2 b^6 - b^8 |
| 74 | strong | (a^2 (a^4 - 2 a^2 b^2 + b^4 + a^2 c^2 + b^2 c^2 - 2 c^4) (a^4 + a^2 b^2 - 2 b^4 - 2 a^2 c^2 + b^2 c^2 + c^4)) |
| 76 | strong | (b^2 c^2) |
| 83 | strong | ((a^2 + b^2) (a^2 + c^2)) |
| 93 | strong | (b^2 c^2 ((-a^2) + b^2 - c^2) ((-a^2) - b^2 + c^2) (a^4 - a^2 b^2 + b^4 - 2 a^2 c^2 - 2 b^2 c^2 + c^4) (a^4 - 2 a^2 b^2 + b^4 - a^2 c^2 - 2 |
| 94 | strong | (b^2 c^2 (a^2 - a b + b^2 - c^2) (a^2 + a b + b^2 - c^2) (a^2 - b^2 - a c + c^2) (a^2 - b^2 + a c + c^2)) |
| 95 | strong | ((a^4 - 2 a^2 b^2 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - a^2 b^2 - 2 a^2 c^2 - b^2 c^2 + c^4)) |
| 96 | strong | (( a^4 - 2 a^2 b^2 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - 2 a^2 b^2 + b^4 - 2 b^2 c^2 + c^4) (a^4 + b^4 - 2 a^2 c^2 - 2 b^2 c^2 + c^4) (a^4 - a^ |
| 97 | strong | (a^2 (a^2 - b^2 - c^2) (a^4 - 2 a^2 b^2 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - a^2 b^2 - 2 a^2 c^2 - b^2 c^2 + c^4)) |
| 98 | strong | ((a^4 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - a^2 b^2 - b^2 c^2 + c^4)) |
| 111 | strong | (a^2 (a^2 + b^2 - 2 c^2) (a^2 - 2 b^2 + c^2)) |
| 113 | strong | ((2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4) (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 + 2 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 |
| 114 | strong | ((a^2 b^2 - b^4 + a^2 c^2 - c^4) (2 a^4 - a^2 b^2 + b^4 - a^2 c^2 - 2 b^2 c^2 + c^4)) |
| 126 | strong | ((2 a^2 - b^2 - c^2) ( a^2 b^2 + b^4 + a^2 c^2 - 4 b^2 c^2 + c^4)) |
| 128 | strong | (( a^2 - b^2 - b c - c^2) (a^2 - b^2 + b c - c^2) ( a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4) (2 a^8 - 4 a^6 b^2 + 3 a^4 b^4 - 2 a^2 b^6 + b |
| 129 | strong | (a^2 (a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4) (a^8 - 2 a^6 b^2 + a^4 b^4 - 2 a^6 c^2 + a^4 b^2 c^2 + b^6 c^2 + a^4 c^4 - 2 b^4 c^4 + |
| 131 | strong | ((a^2 - b^2 - c^2) ( a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 + 2 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 + c^6) (2 a^8 - 3 a^6 b^2 + a^4 b |
| 132 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^2 b^2 - b^4 + a^2 c^2 - c^4) (2 a^6 - a^4 b^2 - b^6 - a^4 c^2 + b^4 c^2 + b^2 c^4 - c^6)) |
| 133 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4) (a^6 b^2 - 3 a^4 b^4 + 3 a^2 b^6 - b^8 + a^6 c^2 |
| 138 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) ( a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4) (2 a^8 - 4 a^6 b^2 + a^4 b^4 + 2 a^2 b^6 - b^8 - 4 a^6 |
| 140 | strong | (2 a^4 - 3 a^2 b^2 + b^4 - 3 a^2 c^2 - 2 b^2 c^2 + c^4) |
| 141 | strong | (b^2 + c^2) |
| 143 | strong | (a^2 (a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4) (a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 - b^2 c^2 + c^4)) |
| 146 | strong | (a^10 + a^8 b^2 - 8 a^6 b^4 + 8 a^4 b^6 - a^2 b^8 - b^10 + a^8 c^2 + 9 a^6 b^2 c^2 - 6 a^4 b^4 c^2 - 7 a^2 b^6 c^2 + 3 b^8 c^2 - 8 a^6 c |
| 147 | strong | (a^8 + a^6 b^2 - 2 a^4 b^4 + a^2 b^6 - b^8 + a^6 c^2 - 3 a^4 b^2 c^2 + a^2 b^4 c^2 + b^6 c^2 - 2 a^4 c^4 + a^2 b^2 c^4 + a^2 c^6 + b^2 |
| 148 | strong | (a^4 - a^2 b^2 - b^4 - a^2 c^2 + 3 b^2 c^2 - c^4) |
| 154 | strong | (a^2 (3 a^4 - 2 a^2 b^2 - b^4 - 2 a^2 c^2 + 2 b^2 c^2 - c^4)) |
| 155 | strong | (a^2 (a^2 - b^2 - c^2) (a^6 - 3 a^4 b^2 + 3 a^2 b^4 - b^6 - 3 a^4 c^2 - 2 a^2 b^2 c^2 + b^4 c^2 + 3 a^2 c^4 + b^2 c^4 - c^6)) |
| 156 | strong | (a^2 (a^8 - 3 a^6 b^2 + 3 a^4 b^4 - a^2 b^6 - 3 a^6 c^2 + 2 a^4 b^2 c^2 + b^6 c^2 + 3 a^4 c^4 - 2 b^4 c^4 - a^2 c^6 + b^2 c^6)) |
| 157 | strong | (a^2 (a^6 - a^4 b^2 + a^2 b^4 - b^6 - a^4 c^2 + b^4 c^2 + a^2 c^4 + b^2 c^4 - c^6)) |
| 159 | strong | (a^2 (a^6 + a^4 b^2 - a^2 b^4 - b^6 + a^4 c^2 - 2 a^2 b^2 c^2 + b^4 c^2 - a^2 c^4 + b^2 c^4 - c^6)) |
| 160 | strong | (a^4 (a^2 b^2 - b^4 + a^2 c^2 - b^2 c^2 - c^4)) |
| 161 | strong | (a^2 (a^10 - a^8 b^2 - 2 a^6 b^4 + 2 a^4 b^6 + a^2 b^8 - b^10 - a^8 c^2 - 2 a^6 b^2 c^2 + 2 a^4 b^4 c^2 - 2 a^2 b^6 c^2 + 3 b^8 c^2 - 2 |
| 182 | strong | (a^2 (a^4 - a^2 b^2 - a^2 c^2 - 2 b^2 c^2)) |
| 183 | strong | (a^4 - a^2 b^2 - a^2 c^2 - 2 b^2 c^2) |
| 184 | strong | (a^4 (a^2 - b^2 - c^2)) |
| 185 | strong | (a^2 (a^2 - b^2 - c^2) (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 + 4 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 + c^6)) |
| 186 | strong | (a^2 (a^2 + b^2 - c^2) (a^2 - b^2 - b c - c^2) (a^2 - b^2 + b c - c^2) (a^2 - b^2 + c^2)) |
| 187 | strong | (a^2 ( 2 a^2 - b^2 - c^2)) |
| 193 | strong | (3 a^2 - b^2 - c^2) |
| 194 | strong | (-a^2) b^2 - a^2 c^2 + b^2 c^2) |
| 195 | strong | (a^2 (a^8 - 4 a^6 b^2 + 6 a^4 b^4 - 4 a^2 b^6 + b^8 - 4 a^6 c^2 + 5 a^4 b^2 c^2 + a^2 b^4 c^2 - 2 b^6 c^2 + 6 a^4 c^4 + a^2 b^2 c^4 + 2 |
| 206 | strong | (a^4 (a^4 - b^4 - c^4)) |
| 211 | strong | (a^4 (b^2 + c^2) (a^2 b^2 - b^4 + a^2 c^2 + b^2 c^2 - c^4)) |
| 216 | strong | (a^2 (a^2 - b^2 - c^2) (a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4)) |
| 217 | strong | (a^4 (a^2 - b^2 - c^2) ( a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4)) |
| 230 | strong | (2 a^4 - a^2 b^2 + b^4 - a^2 c^2 - 2 b^2 c^2 + c^4) |
| 231 | strong | (2 a^8 - 4 a^6 b^2 + 3 a^4 b^4 - 2 a^2 b^6 + b^8 - 4 a^6 c^2 + 2 a^2 b^4 c^2 - 4 b^6 c^2 + 3 a^4 c^4 + 2 a^2 b^2 c^4 + 6 b^4 c^4 - 2 a^2 |
| 232 | strong | (a^2 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^2 b^2 - b^4 + a^2 c^2 - c^4)) |
| 235 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 + 4 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 + c^6)) |
| 237 | strong | (a^4 ( a^2 b^2 - b^4 + a^2 c^2 - c^4)) |
| 248 | strong | (a^2 (a^2 - b^2 - c^2) (a^4 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - a^2 b^2 - b^2 c^2 + c^4)) |
| 251 | strong | (a^2 (a^2 + b^2) (a^2 + c^2)) |
| 252 | strong | ((a^4 - 2 a^2 b^2 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - a^2 b^2 + b^4 - 2 a^2 c^2 - 2 b^2 c^2 + c^4) ( a^4 - 2 a^2 b^2 + b^4 - a^2 c^2 - 2 b^2 |
| 253 | strong | ((a^4 - 2 a^2 b^2 + b^4 + 2 a^2 c^2 + 2 b^2 c^2 - 3 c^4) (a^4 + 2 a^2 b^2 - 3 b^4 - 2 a^2 c^2 + 2 b^2 c^2 + c^4)) |
| 254 | strong | ((a^2 + b^2 - c^2) ( a^2 - b^2 + c^2) ( a^6 - a^4 b^2 - a^2 b^4 + b^6 - 3 a^4 c^2 + 2 a^2 b^2 c^2 - 3 b^4 c^2 + 3 a^2 c^4 + 3 b^2 c^4 - c^ |
| 262 | strong | ((a^2 b^2 - b^4 + 2 a^2 c^2 + b^2 c^2) (2 a^2 b^2 + a^2 c^2 + b^2 c^2 - c^4)) |
| 263 | strong | (a^2 (a^2 b^2 - b^4 + 2 a^2 c^2 + b^2 c^2) (2 a^2 b^2 + a^2 c^2 + b^2 c^2 - c^4)) |
| 264 | strong | (b^2 c^2 ((-a^2) + b^2 - c^2) ((-a^2) - b^2 + c^2)) |
| 265 | strong | ((a^2 - b^2 - c^2) (a^2 - a b + b^2 - c^2) (a^2 + a b + b^2 - c^2) ( a^2 - b^2 - a c + c^2) (a^2 - b^2 + a c + c^2)) |
| 275 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 - 2 a^2 b^2 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - a^2 b^2 - 2 a^2 c^2 - b^2 c^2 + c^4)) |
| 276 | strong | (b^2 c^2 ((-a^2) + b^2 - c^2) ((-a^2) - b^2 + c^2) (a^4 - 2 a^2 b^2 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - a^2 b^2 - 2 a^2 c^2 - b^2 c^2 + c^4)) |
| 287 | strong | ((a^2 - b^2 - c^2) (a^4 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - a^2 b^2 - b^2 c^2 + c^4)) |
| 288 | strong | (a^2 (a^4 - 2 a^2 b^2 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - 3 a^2 b^2 + 2 b^4 - 2 a^2 c^2 - 3 b^2 c^2 + c^4) (a^4 - a^2 b^2 - 2 a^2 c^2 - b^2 c |
| 290 | strong | (b^2 c^2 (a^4 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - a^2 b^2 - b^2 c^2 + c^4)) |
| 297 | strong | (( a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^2 b^2 - b^4 + a^2 c^2 - c^4)) |
| 305 | strong | (b^2 c^2 ((-a^2) + b^2 + c^2)) |
| 308 | strong | (b^2 (a^2 + b^2) c^2 (a^2 + c^2)) |
| 311 | strong | (b^2 c^2 ((-a^2) b^2 + b^4 - a^2 c^2 - 2 b^2 c^2 + c^4)) |
| 315 | strong | (a^4 - b^4 - c^4) |
| 316 | strong | (a^4 - b^4 + b^2 c^2 - c^4) |
| 317 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 + c^4)) |
| 323 | strong | (a^2 (a^2 - b^2 - b c - c^2) ( a^2 - b^2 + b c - c^2)) |
| 324 | strong | (b^2 c^2 ((-a^2) + b^2 - c^2) ((-a^2) - b^2 + c^2) ((-a^2) b^2 + b^4 - a^2 c^2 - 2 b^2 c^2 + c^4)) |
| 325 | strong | (-a^2) b^2 + b^4 - a^2 c^2 + c^4) |
| 327 | strong | (b^2 c^2 ((- a^2) b^2 + b^4 - 2 a^2 c^2 - b^2 c^2) ((-2) a^2 b^2 - a^2 c^2 - b^2 c^2 + c^4)) |
| 328 | strong | (b^2 c^2 (a^2 - a b + b^2 - c^2) (a^2 + a b + b^2 - c^2) ((-a^2) + b^2 + c^2) (a^2 - b^2 - a c + c^2) (a^2 - b^2 + a c + c^2)) |
| 340 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 - b c - c^2) (a^2 - b^2 + b c - c^2) (a^2 - b^2 + c^2)) |
| 343 | strong | ((a^2 - b^2 - c^2) (a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4)) |
| 352 | strong | (a^2 (a^4 - 4 a^2 b^2 + b^4 - 4 a^2 c^2 + 5 b^2 c^2 + c^4)) |
| 353 | strong | (a^2 (4 a^4 - 4 a^2 b^2 - 2 b^4 - 4 a^2 c^2 - b^2 c^2 - 2 c^4)) 6 |
| 376 | strong | (5 a^4 - 4 a^2 b^2 - b^4 - 4 a^2 c^2 + 2 b^2 c^2 - c^4) |
| 378 | strong | (a^2 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) ( a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 + 4 b^2 c^2 + c^4)) |
| 381 | strong | (a^4 + a^2 b^2 - 2 b^4 + a^2 c^2 + 4 b^2 c^2 - 2 c^4) |
| 382 | strong | (3 a^4 - a^2 b^2 - 2 b^4 - a^2 c^2 + 4 b^2 c^2 - 2 c^4) |
| 384 | strong | (a^4 + b^2 c^2) |
| 385 | strong | ((a^2 - b c) (a^2 + b c)) |
| 389 | strong | (a^2 (a^6 b^2 - 3 a^4 b^4 + 3 a^2 b^6 - b^8 + a^6 c^2 - 3 a^2 b^4 c^2 + 2 b^6 c^2 - 3 a^4 c^4 - 3 a^2 b^2 c^4 - 2 b^4 c^4 + 3 a^2 c^6 + 2 |
| 393 | strong | ((a^2 + b^2 - c^2)^2 (a^2 - b^2 + c^2)^2) |
| 394 | strong | (a^2 (a^2 - b^2 - c^2)^2) |
| 399 | strong | (a^2 (a^8 - 4 a^6 b^2 + 6 a^4 b^4 - 4 a^2 b^6 + b^8 - 4 a^6 c^2 + a^4 b^2 c^2 + a^2 b^4 c^2 + 2 b^6 c^2 + 6 a^4 c^4 + a^2 b^2 c^4 - 6 b |
| 401 | strong | (a^8 - 2 a^6 b^2 + a^4 b^4 - 2 a^6 c^2 + a^4 b^2 c^2 + b^6 c^2 + a^4 c^4 - 2 b^4 c^4 + b^2 c^6) |
| 402 | strong | ((2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4) (a^8 - a^6 b^2 - 2 a^4 b^4 + 3 a^2 b^6 - b^8 - a^6 c^2 + 5 a^4 b^2 c^2 - 3 a^2 b^4 c^ |
| 403 | strong | ((a^2 + b^2 - c^2) ( a^2 - b^2 + c^2) (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 + 2 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 + c^6)) |
| 417 | strong | (a^4 (a^2 - b^2 - c^2)^3 (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 + 4 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 + c^6)) |
| 418 | strong | (a^4 (a^2 - b^2 - c^2)^2 (a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4)) |
| 419 | strong | ((a^2 - b c) (a^2 + b c) (a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 420 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) ( a^4 + a^2 b^2 - b^4 + a^2 c^2 - b^2 c^2 - c^4)) |
| 421 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^8 - 2 a^6 b^2 + a^4 b^4 - 2 a^6 c^2 + a^4 b^2 c^2 - b^6 c^2 + a^4 c^4 + 2 b^4 c^4 - b^2 c^6)) |
| 426 | strong | (a^2 (a^2 - b^2 - c^2)^3 (a^4 + b^4 - 2 b^2 c^2 + c^4)) |
| 427 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (b^2 + c^2)) |
| 428 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (2 a^2 + b^2 + c^2)) |
| 432 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^16 b^2 - 8 a^14 b^4 + 28 a^12 b^6 - 56 a^10 b^8 + 70 a^8 b^10 - 56 a^6 b^12 + 28 a^4 b^14 - 8 a |
| 433 | strong | ((a^2 + b^2 - c^2) (a2 - b^2 + c^2) (a^12 b^2 + 2 a^10 b^4 - a^8 b^6 - 4 a^6 b^8 - a^4 b^10 + 2 a^2 b^12 + b^14 + a^12 c^2 - 4 a^10 b^2 |
| 434 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^16 b^2 - 8 a^14 b^4 + 28 a^12 b^6 - 56 a^10 b^8 + 70 a^8 b^10 - 56 a^6 b^12 + 28 a^4 b^14 - 8 a |
| 435 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^16 b^2 - 8 a^14 b^4 + 28 a^12 b^6 - 56 a^10 b^8 + 70 a^8 b^10 - 56 a^6 b^12 + 28 a^4 b^14 - 8 a |
| 436 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^8 - 2 a^6 b^2 + a^4 b^4 - 2 a^6 c^2 + 3 a^4 b^2 c^2 - b^6 c^2 + a^4 c^4 + 2 b^4 c^4 - b^2 c^6)) |
| 438 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (5 a^12 - 7 a^10 b^2 - 8 a^8 b^4 + 18 a^6 b^6 - 11 a^4 b^8 + 5 a^2 b^10 - 2 b^12 - 7 a^10 c^2 + 26 a |
| 439 | strong | ((3 a^2 - b^2 - c^2)^2) |
| 441 | strong | ((a^2 - b^2 - c^2) (2 a^6 - a^4 b^2 - b^6 - a^4 c^2 + b^4 c^2 + b^2 c^4 - c^6)) |
| 446 | strong | (a^2 (a^2 b^2 - b^4 + a^2 c^2 - c^4) (a^8 b^2 - 2 a^6 b^4 + a^4 b^6 + a^8 c^2 + 2 a^2 b^6 c^2 + b^8 c^2 - 2 a^6 c^4 - 4 a^2 b^4 c^4 - b^ |
| 450 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 - a^2 b^2 + a^2 b c - b^3 c - a^2 c^2 + 2 b^2 c^2 - b c^3) (a^4 - a^2 b^2 - a^2 b c + b^3 c - a^2 c |
| 454 | strong | (a^2 (a^2 - b^2 - c^2) (a^6 - 3 a^4 b^2 + 3 a^2 b^4 - b^6 - 3 a^4 c^2 - 2 a^2 b^2 c^2 + b^4 c^2 + 3 a^2 c^4 + b^2 c^4 - c^6)^2) |
| 455 | strong | (a^2 (a^2 + b^2 - c^2) ( a^2 - b^2 + c^2) (a^6 + a^4 b^2 - a^2 b^4 - b^6 + a^4 c^2 - 2 a^2 b^2 c^2 + b^4 c^2 - a^2 c^4 + b^2 c^4 - c^6)^2 |
| 456 | strong | (a^2 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^8 - 4 a^6 b^2 + 6 a^4 b^4 - 4 a^2 b^6 + b^8 - 4 a^6 c^2 + 5 a^4 b^2 c^2 + a^2 b^4 c^2 - 2 b^ |
| 457 | strong | (a^2 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^8 - 4 a^6 b^2 + 6 a^4 b^4 - 4 a^2 b^6 + b^8 - 4 a^6 c^2 + a^4 b^2 c^2 + a^2 b^4 c^2 + 2 b^6 |
| 458 | strong | (( a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 - a^2 b^2 - a^2 c^2 - 2 b^2 c^2)) |
| 459 | strong | ((3 a^2 - b^2 - c^2) (a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 460 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (2 a^4 - a^2 b^2 + b^4 - a^2 c^2 - 2 b^2 c^2 + c^4)) |
| 467 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4) (a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 + c^4)) |
| 468 | strong | ((2 a^2 - b^2 - c^2) (a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 477 | strong | ((a^8 + a^6 b^2 - 4 a^4 b^4 + a^2 b^6 + b^8 - 3 a^6 c^2 + 2 a^4 b^2 c^2 + 2 a^2 b^4 c^2 - 3 b^6 c^2 + 3 a^4 c^4 - 2 a^2 b^2 c^4 + 3 b^4 |
| 511 | strong | (a^2 (a^2 b^2 - b^4 + a^2 c^2 - c^4)) |
| 524 | strong | (2 a^2 - b^2 - c^2) |
| 538 | strong | (-a^2) b^2 - a^2 c^2 + 2 b^2 c^2) |
| 539 | strong | ((a^2 - b^2 - c^2) ( 2 a^8 - 4 a^6 b^2 + 3 a^4 b^4 - 2 a^2 b^6 + b^8 - 4 a^6 c^2 + 2 a^2 b^4 c^2 - 4 b^6 c^2 + 3 a^4 c^4 + 2 a^2 b^2 c^4 |
| 541 | strong | (2 a^10 - 11 a^6 b^4 + 13 a^4 b^6 - 3 a^2 b^8 - b^10 + 16 a^6 b^2 c^2 - 11 a^4 b^4 c^2 - 8 a^2 b^6 c^2 + 3 b^8 c^2 - 11 a^6 c^4 - 11 a^4 |
| 542 | strong | (2 a^6 - 2 a^4 b^2 + a^2 b^4 - b^6 - 2 a^4 c^2 + b^4 c^2 + a^2 c^4 + b^2 c^4 - c^6) |
| 543 | strong | (2 a^4 - 2 a^2 b^2 - b^4 - 2 a^2 c^2 + 4 b^2 c^2 - c^4) |
| 546 | strong | (2 a^4 + a^2 b^2 - 3 b^4 + a^2 c^2 + 6 b^2 c^2 - 3 c^4) |
| 547 | strong | (2 a^4 - 7 a^2 b^2 + 5 b^4 - 7 a^2 c^2 - 10 b^2 c^2 + 5 c^4) |
| 548 | strong | (6 a^4 - 5 a^2 b^2 - b^4 - 5 a^2 c^2 + 2 b^2 c^2 - c^4) |
| 549 | strong | (4 a^4 - 5 a^2 b^2 + b^4 - 5 a^2 c^2 - 2 b^2 c^2 + c^4) |
| 550 | strong | (4 a^4 - 3 a^2 b^2 - b^4 - 3 a^2 c^2 + 2 b^2 c^2 - c^4) |
| 562 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 - b c - c^2) ( a^2 - b^2 + b c - c^2) (a^2 - b^2 + c^2) ( a^4 - a^2 b^2 + b^4 - 2 a^2 c^2 - 2 b^2 c^2 + c^4) (a^ |
| 565 | strong | (b^2 c^2 ((-a^2) b^2 + b^4 - a^2 c^2 - 2 b^2 c^2 + c^4) (a^4 b^4 - 2 a^2 b^6 + b^8 - a^4 b^2 c^2 + 2 a^2 b^4 c^2 - 4 b^6 c^2 + a^4 c^4 + |
| 566 | strong | (a^2 (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 - a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 + c^6)) |
| 567 | strong | (a^2 (a^8 - 3 a^6 b^2 + 3 a^4 b^4 - a^2 b^6 - 3 a^6 c^2 + 3 a^4 b^2 c^2 + 2 a^2 b^4 c^2 - 2 b^6 c^2 + 3 a^4 c^4 + 2 a^2 b^2 c^4 + 4 b^4 |
| 568 | strong | (a^2 ( a^6 b^2 - 3 a^4 b^4 + 3 a^2 b^6 - b^8 + a^6 c^2 - a^4 b^2 c^2 - 2 a^2 b^4 c^2 + 2 b^6 c^2 - 3 a^4 c^4 - 2 a^2 b^2 c^4 - 2 b^4 c^4 |
| 569 | strong | (a^2 (a^8 - 3 a^6 b^2 + 3 a^4 b^4 - a^2 b^6 - 3 a^6 c^2 + 2 a^4 b^2 c^2 + 3 a^2 b^4 c^2 - 2 b^6 c^2 + 3 a^4 c^4 + 3 a^2 b^2 c^4 + 4 b^4 |
| 570 | strong | (a^2 (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 - 2 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 + c^6)) |
| 571 | strong | (a^4 ( a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 + c^4)) |
| 574 | strong | (a^2 (a^2 - 2 b^2 - 2 c^2)) |
| 575 | strong | (a^2 (2 a^4 - 3 a^2 b^2 + b^4 - 3 a^2 c^2 - 4 b^2 c^2 + c^46 |
| 577 | strong | (a^4 (a^2 - b^2 - c^2)^2) |
| 578 | strong | (a^2 (a^8 - 3 a^6 b^2 + 3 a^4 b^4 - a^2 b^6 - 3 a^6 c^2 + 4 a^4 b^2 c^2 + a^2 b^4 c^2 - 2 b^6 c^2 + 3 a^4 c^4 + a^2 b^2 c^4 + 4 b^4 c^4 |
| 592 | strong | (a^2 (a^6 b^2 - 2 a^4 b^4 + a^2 b^6 + 2 a^6 c^2 - 3 a^4 b^2 c^2 - 3 a^2 b^4 c^2 + 2 b^6 c^2 - 3 a^4 c^4 - 6 a^2 b^2 c^4 - 3 b^4 c^4 + a^ |
| 597 | strong | (4 a^2 + b^2 + c^2) |
| 598 | strong | ((2 a^2 + 2 b^2 - c^2) (2 a^2 - b^2 + 2 c^2)) |
| 599 | strong | (a^2 - 2 b^2 - 2 c^2) |
| 620 | strong | (2 a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 + c^4) |
| 625 | strong | (a^2 b^2 - 2 b^4 + a^2 c^2 + 2 b^2 c^2 - 2 c^4) |
| 626 | strong | (b^4 + c^4) |
| 631 | strong | (3 a^4 - 4 a^2 b^2 + b^4 - 4 a^2 c^2 - 2 b^2 c^2 + c^4) |
| 632 | strong | (4 a^4 - 7 a^2 b^2 + 3 b^4 - 7 a^2 c^2 - 6 b^2 c^2 + 3 c^4) |
| 671 | strong | ((a^2 + b^2 - 2 c^2) ( a^2 - 2 b^2 + c^2)) |
| 682 | strong | (a^4 (a^2 - b^2 - c^2) ( a^2 b^2 + b^4 + a^2 c^2 - 2 b^2 c^2 + c^4)) |
| 683 | strong | (b^2 c^2 ((-a^2) + b^2 - c^2) ((-a^2) - b^2 + c^2) (a^4 - 2 a^2 b^2 + b^4 + a^2 c^2 + b^2 c^2) (a^4 + a^2 b^2 - 2 a^2 c^2 + b^2 c^2 + c^4 |
| 695 | strong | (a^2 ( b^4 + a^2 c^2) (a^2 b^2 + c^4)) |
| 698 | strong | (-a^2) b^4 + b^4 c^2 - a^2 c^4 + b^2 c^4) |
| 699 | strong | (a^2 (a^4 b^2 + a^2 b^4 - a^4 c^2 - b^4 c^2) ((-a^4) b^2 + a^4 c^2 + a^2 c^4 - b^2 c^4)) |
| 702 | strong | (-a^4) b^4 - a^4 c^4 + 2 b^4 c^4) |
| 703 | strong | (a^2 (2 a^4 b^4 - a^4 c^4 - b^4 c^4) ((-a^4) b^4 + 2 a^4 c^4 - b^4 c^4)) |
| 706 | strong | (-a^6) b^4 - a^6 c^4 + b^6 c^4 + b^4 c^6) |
| 707 | strong | (a^2 ((-a^4) b^6 + a^6 c4 - b^6 c^4 + a^4 c^6) (a^6 b^4 + a^4 b^6 - a^4 c^6 - b^4 c^6)) |
| 729 | strong | (a^2 (2 a^2 b^2 - a^2 c^2 - b^2 c^2) ((-a^2) b^2 + 2 a^2 c^2 - b^2 c^2)) 10 |
| 732 | strong | ((a^2 - b c) ( a^2 + b c) (b^2 + c^2)) |
| 736 | strong | (a^6 b^2 + a^6 c^2 - b^6 c^2 - b^2 c^6) |
| 737 | strong | (a^2 ((- a^2) b^6 + a^6 c^2 - b^6 c^2 + a^2 c^6) (a^6 b^2 + a^2 b^6 - a^2 c^6 - b^2 c^6)) |
| 754 | strong | (2 a^4 - b^4 - c^4) |
| 755 | strong | (a^2 (a^4 + b^4 - 2 c^4) (a^4 - 2 b^4 + c^4)) |
| 800 | strong | (a^2 (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 + 4 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 + c^6)) |
| 801 | strong | ((a^6 - a^4 b^2 - a^2 b^4 + b^6 - 2 a^4 c^2 + 4 a^2 b^2 c^2 - 2 b^4 c^2 + a^2 c^4 + b^2 c^4) (a^6 - 2 a^4 b^2 + a^2 b^4 - a^4 c^2 + 4 a^ |
| 841 | strong | (a^2 (a^10 - 3 a^8 b^2 + 2 a^6 b^4 + 2 a^4 b^6 - 3 a^2 b^8 + b^10 + 3 a^8 c^2 + 8 a^6 b^2 c^2 - 22 a^4 b^4 c^2 + 8 a^2 b^6 c^2 + 3 b^8 |
| 842 | strong | (a^2 (a^6 - a^4 b^2 - a^2 b^4 + b^6 - a^4 c^2 - b^4 c^2 + 2 a^2 c^4 + 2 b^2 c^4 - 2 c^6) (a^6 - a^4 b^2 + 2 a^2 b^4 - 2 b^6 - a^4 c^2 + 2 |
| 843 | strong | (a^2 ( a^4 - 4 a^2 b^2 + b^4 + 2 a^2 c^2 + 2 b^2 c^2 - 2 c^4) ( a^4 + 2 a^2 b^2 - 2 b^4 - 4 a^2 c^2 + 2 b^2 c^2 + c^4)) |
| 847 | strong | (b^2 c^2 ((-a^2) + b^2 - c^2) ((-a^2) - b^2 + c^2) (a^4 - 2 a^2 b^2 + b^4 - 2 b^2 c^2 + c^4) (a^4 + b^4 - 2 a^c^2 - 2 b^2 c^2 + c^4)) |
| 852 | strong | (a^2 (a^2 - b^2 - c^2) (a^6 b^2 - 2 a^4 b^4 + a^2 b^6 + a^6 c^2 + 2 a^4 b^2 c^2 - a^2 b^4 c^2 - 2 b^6 c^2 - 2 a^4 c^4 - a^2 b^2 c^4 + 4 b |
| 858 | strong | (a^4 b^2 - b^6 + a^4 c^2 - 2 a^2 b^2 c^2 + b^4 c^2 + b^2 c^4 - c^6) |
| 864 | strong | (a^4 (a^4 b^4 - a^2 b^6 + b^6 c^2 + a^4 c^4 - 2 b^4 c^4 - a^2 c^6 + b^2 c^6)) |
| 895 | strong | (a^2 ( a^2 + b^2 - 2 c^2) (a^2 - b^2 - c^2) (a^2 - 2 b^2 + c^2)) |
| 973 | strong | (a^2 (a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4) ( a^10 - 3 a^8 b^2 + 2 a^6 b^4 + 2 a^4 b^6 - 3 a^2 b^8 + b^10 - 3 a^8 c^2 + 3 a^6 b^2 c |
| 974 | strong | (a^2 (a^2 - b^2 - c^2) ( a^10 b^2 - 3 a^8 b^4 + 2 a^6 b^6 + 2 a^4 b^8 - 3 a^2 b^10 + b^12 + a^10 c^2 + 2 a^8 b^2 c^2 - a^6 b^4 c^2 - 11 |
| 1003 | strong | (3 a^4 - a^2 b^2 - a^2 c^2 + 2 b^2 c^2) |
| 1007 | strong | (a^4 - 4 a^2 b^2 + 3 b^4 - 4 a^2 c^2 - 2 b^2 c^2 + 3 c^4) |
| 1031 | strong | ((a^4 + a^2 b^2 + b^4 + a^2 c^2 + b^2 c^2 - c^4) (a^4 + a^2 b^2 - b^4 + a^2 c^2 + b^2 c^2 + c^4)) |
| 1032 | strong | ((a^2 - b^2 - c^2) (a^8 + 4 a^6 b^2 - 10 a^4 b^4 + 4 a^2 b^6 + b^8 - 4 a^6 c^2 + 4 a^4 b^2 c^2 + 4 a^2 b^4 c^2 - 4 b^6 c^2 + 6 a^4 c^4 - |
| 1033 | strong | (a^2 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^8 - 4 a^6 b^2 + 6 a^4 b^4 - 4 a^2 b^6 + b^8 - 4 a^6 c^2 - 4 a^4 b^2 c^2 + 4 a^2 b^4 c^2 + 4 b |
| 1073 | strong | (a^2 (a^2 - b^2 - c^2) (a^4 - 2 a^2 b^2 + b^4 + 2 a^2 c^2 + 2 b^2 c^2 - 3 c^4) (a^4 + 2 a^2 b^2 - 3 b^4 - 2 a^2 c^2 + 2 b^2 c^2 + c^4)) |
| 1075 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^10 b^2 - 4 a^8 b^4 + 6 a^6 b^6 - 4 a^4 b^8 + a^2 b^10 + a^10 c^2 - a^8 b^2 c^2 - 2 a^6 b^4 c^2 |
| 1078 | strong | (a^4 - a^2 b^2 - a^2 c^2 - b^2 c^2) |
| 1092 | strong | (a^4 ( a^2 - b^2 - c^2)^3) |
| 1093 | strong | (b^2 c^2 ((-a^2) + b^2 - c^2)^3 ((-a^2) - b^2 + c^2)^3) |
| 1105 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^6 - a^4 b^2 - a^2 b^4 + b^6 - 2 a^4 c^2 + 4 a^2 b^2 c^2 - 2 b^4 c^2 + a^2 c^4 + b^2 c^4) (a^6 - 2 |
| 1112 | strong | (a^2 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 - 2 a^2 c^4 + c^6)) |
| 1117 | strong | ((a^2 - a b + b^2 - c^2) (a^2 + a b + b^2 - c^2) (a^2 - b^2 - a c + c^2) (a^2 - b^2 + a c + c^2) (a^6 - a^4 b^2 - a^2 b^4 + b^6 - 3 a^4 c^2 + |
| 1138 | strong | ((a^8 + 2 a^6 b^2 - 6 a^4 b^4 + 2 a^2 b^6 + b^8 - 4 a^6 c^2 + a^4 b^2 c^2 + a^2 b^4 c^2 - 4 b^6 c^2 + 6 a^4 c^4 + a^2 b^2 c^4 + 6 b^4 c |
| 1141 | strong | ((a^2 - a b + b^2 - c^2) (a^2 + a b + b^2 - c^2) (a^2 - b^2 - a c + c^2) (a^2 - b^2 + a c + c^2) ( a^4 - 2 a^2 b^2 + b^4 - a^2 c^2 - b^2 c^2) |
| 1147 | strong | (a^4 (a^2 - b^2 - c^2) (a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 + c^4)) |
| 1153 | strong | (10 a^4 - 13 a^2 b^2 + 4 b^4 - 13 a^2 c^2 - 10 b^2 c^2 + 4 c^4) |
| 1154 | strong | (a^2 (a^2 - b^2 - b c - c^2) ( a^2 - b^2 + b c - c^2) (a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4)) 10 |
| 1157 | strong | (a^2 ( a^4 - 2 a^2 b^2 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - a^2 b^2 - 2 a^2 c^2 - b^2 c^2 + c^4) (a^6 - 3 a^4 b^2 + 3 a^2 b^4 - b^6 - 3 a^4 c |
| 1166 | strong | (a^2 (a^4 - 2 a^2 b^2 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - a^2 b^2 - 2 a^2 c^2 - b^2 c^2 + c^4) (a^6 - a^4 b^2 - a^2 b^4 + b^6 - 2 a^4 c^2 - |
| 1173 | strong | (a^2 (a^4 - 3 a^2 b^2 + 2 b^4 - 2 a^2 c^2 - 3 b^2 c^2 + c^4) (a^4 - 2 a^2 b^2 + b^4 - 3 a^2 c^2 - 3 b^2 c^2 + 2 c^4)) |
| 1176 | strong | (a^2 (a^2 + b^2) ( a^2 - b^2 - c^2) (a^2 + c^2)) |
| 1177 | strong | (a^2 (a^6 - a^4 b^2 - a^2 b^4 + b^6 + 2 a^2 b^2 c^2 - a^2 c^4 - b^2 c^4) (a^6 - a^2 b^4 - a^4 c^2 + 2 a^2 b^2 c^2 - b^4 c^2 - a^2 c^4 + c |
| 1179 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) ( a^6 - a^4 b^2 - a^2 b^4 + b^6 - 2 a^4 c^2 - 2 a^2 b^2 c^2 - 2 b^4 c^2 + a^2 c^4 + b^2 c^4) (a^6 - 2 |
| 1180 | strong | (a^2 (a^2 b^2 + b^4 + a^2 c^2 + b^2 c^2 + c^4)) |
| 1181 | strong | (a^2 (a^2 - b^2 - c^2) (a^6 - 3 a^4 b^2 + 3 a^2 b^4 - b^6 - 3 a^4 c^2 - 6 a^2 b^2 c^2 + b^4 c^2 + 3 a^2 c^4 + b^2 c^4 - c^6)) |
| 1184 | strong | (a^2 (a^2 + b^2 - 2 b c + c^2) (a^2 + b^2 + 2 b c + c^2)) |
| 1186 | strong | (a^4 (a^2 b^4 + a^2 b^2 c^2 + b^4 c^2 + a^2 c^4 + b^2 c^4)) |
| 1194 | strong | (a^2 (a^2 b^2 + b^4 + a^2 c^2 + c^4)) |
| 1196 | strong | (a^2 (a^2 b^2 + b^4 + a^2 c^2 - 2 b^2 c^2 + c^4)) |
| 1199 | strong | (a^2 ( a^8 - 4 a^6 b^2 + 6 a^4 b^4 - 4 a^2 b^6 + b^8 - 4 a^6 c^2 + 3 a^4 b^2 c^2 + 4 a^2 b^4 c^2 - 3 b^6 c^2 + 6 a^4 c^4 + 4 a^2 b^2 c^4 |
| 1204 | strong | (a^2 (a^2 - b^2 - c^2) (a^6 - 3 a^2 b^4 + 2 b^6 + 6 a^2 b^2 c^2 - 2 b^4 c^2 - 3 a^2 c^4 - 2 b^2 c^4 + 2 c^6)) |
| 1205 | strong | (a^2 (a^10 b^2 - a^8 b^4 - 2 a^6 b^6 + 2 a^4 b^8 + a^2 b^10 - b^12 + a^10 c^2 - 2 a^8 b^2 c^2 + 3 a^6 b^4 c^2 + 2 a^4 b^6 c^2 - 4 a^2 |
| 1207 | strong | (a^2 (a^2 b^2 - a^2 b c + a^2 c^2 + b^2 c^2) (a^2 b^2 + a^2 b c + a^2 c^2 + b^2 c^2)) |
| 1209 | strong | ((-a^2) b^2 + b^4 - a^2 c^2 - 2 b^2 c^2 + c^4) (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 - 2 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 + c^6) |
| 1216 | strong | (a^2 (a^2 - b^2 - c^2) (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 - 2 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 + c^6)) |
| 1217 | strong | ((a^2 + b^2 - c^2) ( a^2 - b^2 + c^2) (a^6 - a^4 b^2 - a^2 b^4 + b^6 - 3 a^4 c^2 + 6 a^2 b^2 c^2 - 3 b^4 c^2 + 3 a^2 c^4 + 3 b^2 c^4 - c^6 |
| 1225 | strong | (b^2 c^2 ((-a^2) b^2 + b^4 - a^2 c^2 - 2 b^2 c^2 + c^4) (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 - 2 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c |
| 1232 | strong | (b^2 c^2 (2 a^4 - 3 a^2 b^2 + b^4 - 3 a^2 c^2 - 2 b^2 c^2 + c^4)) |
| 1235 | strong | (b^2 c^2 ((- a^2) + b^2 - c^2) ((-a^2) - b^2 + c^2) (b^2 + c^2)) |
| 1236 | strong | (b^2 c^2 ((-a^4) b^2 + b^6 - a^4 c^2 + 2 a^2 b^2 c^2 - b^4 c^2 - b^2 c^4 + c^6)) |
| 1238 | strong | ((a^2 - b^2 - c^2) (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 - 2 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 + c^6)) |
| 1239 | strong | (b^2 c^2 (a^4 + a^2 b^2 + b^4 + a^2 c^2 + b^2 c^2) (a^4 + a^2 b^2 + a^2 c^2 + b^2 c^2 + c^4)) |
| 1241 | strong | (b^2 c^2 ( a^4 + b^4 + a^2 c^2 + b^2 c^2) (a^4 + a^2 b^2 + b^2 c^2 + c^4)) |
| 1249 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (3 a^4 - 2 a^2 b^2 - b^4 - 2 a^2 c^2 + 2 b^2 c^2 - c^4)) |
| 1263 | strong | ((-a^2) b^2 + b^4 - a^2 c^2 - 2 b^2 c^2 + c^4) ((-a^6) + 3 a^4 b^2 - 3 a^2 b^4 + b^6 + a^4 c^2 - a^2 b^2 c^2 - 3 b^4 c^2 + a^2 c^4 + 3 b^ |
| 1272 | strong | (a^8 - 4 a^6 b^2 + 6 a^4 b^4 - 4 a^2 b6 + b^8 - 4 a^6 c^2 + a^4 b^2 c^2 + a^2 b^4 c^2 + 2 b^6 c^2 + 6 a^4 c^4 + a^2 b^2 c^4 - 6 b^4 c^4 |
| 1273 | strong | ((a^2 - b^2 - b c - c^2) (a^2 - b^2 + b c - c^2) (a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4)) |
| 1294 | strong | (( a^8 + 2 a^6 b^2 - 6 a^4 b^4 + 2 a^2 b^6 + b^8 - 3 a^6 c^2 + 3 a^4 b^2 c^2 + 3 a^2 b^4 c^2 - 3 b^6 c^2 + 3 a^4 c^4 - 4 a^2 b^2 c^4 + 3 |
| 1297 | strong | (a^2 (a^6 - a^4 b^2 - a^2 b^4 + b^6 + a^2 c^4 + b^2 c^4 - 2 c^6) (a^6 + a^2 b^4 - 2 b^6 - a^4 c^2 + b^4 c^2 - a^2 c^4 + c^6)) |
| 1298 | strong | (a^2 (a^4 - 2 a^2 b^2 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - a^2 b^2 - 2 a^2 c^2 - b^2 c^2 + c^4) (a^4 b^4 - 2 a^2 b^6 + b^8 + a^6 c^2 + a^2 |
| 1299 | strong | (a^2 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^8 - a^6 b^2 + a^4 b^4 - 3 a^2 b^6 + 2 b^8 - 4 a^6 c^2 + a^4 b^2 c^2 + 2 a^2 b^4 c^2 - 3 b^6 c |
| 1300 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) ( a^6 - a^4 b^2 - a^2 b^4 + b^6 - 2 a^4 c^2 + 2 a^2 b^2 c^2 - 2 b^4 c^2 + a^2 c^4 + b^2 c^4) (a^6 - 2 |
| 1316 | strong | (a^8 - a^6 b^2 - a^6 c^2 + a^4 b^2 c^2 + b^6 c^2 - 2 b^4 c^4 + b^2 c^6) |
| 1350 | strong | (a^2 (a^4 + 2 a^2 b^2 - 3 b^4 + 2 a^2 c^2 - 2 b^2 c^2 - 3 c^4)) |
| 1351 | strong | (a^2 (a^4 - 4 a^2 b^2 + 3 b^4 - 4 a^2 c^2 - 2 b^2 c^2 + 3 c^4)) |
| 1352 | strong | (a^6 - a^4 b^2 + a^2 b^4 - b^6 - a^4 c^2 + 2 a^2 b^2 c^2 + b^4 c^2 + a^2 c^4 + b^2 c^4 - c^6) |
| 1353 | strong | (4 a^6 - 7 a^4 b^2 + 4 a^2 b^4 - b^6 - 7 a^4 c^2 - 4 a^2 b^2 c^2 + b^4 c^2 + 4 a^2 c^4 + b^2 c^4 - c^6) |
| 1368 | strong | ((a^2 - b^2 - c^2) (a^2 b^2 + b^4 + a^2 c^2 - 2 b^2 c^2 + c^4)) |
| 1369 | strong | (a^6 + a^4 b^2 - a^2 b^4 - b^6 + a^4 c^2 - a^2 b^2 c^2 - b^4 c^2 - a^2 c^4 - b^2 c^4 - c^6) |
| 1370 | strong | (a^6 + a^4 b^2 - a^2 b^4 - b^6 + a^4 c^2 - 2 a^2 b^2 c^2 + b^4 c^2 - a^2 c^4 + b^2 c^4 - c^6) |
| 1383 | strong | (a^2 (2 a^2 + 2 b^2 - c^2) (2 a^2 - b^2 + 2 c^2)) |
| 1384 | strong | (a^2 (5 a^2 - b^2 - c^2)) |
| 1485 | strong | (a^2 (a^6 - a^4 b^2 - a^2 b^4 + b^6 - a^4 c^2 - b^4 c^2 + a^2 c^4 + b^2 c^4 - c^6) (a^6 - a^4 b^2 + a^2 b^4 - b^6 - a^4 c^2 + b^4 c^2 - a |
| 1487 | strong | ((a^4 - 3 a^2 b^2 + 2 b^4 - 2 a^2 c^2 - 3 b^2 c^2 + c^4) (a^4 - a^2 b^2 + b^4 - 2 a^2 c^2 - 2 b^2 c^2 + c^4) (a^4 - 2 a^2 b^2 + b^4 - a^2 c |
| 1493 | strong | (a^2 (2 a^4 - 3 a^2 b^2 + b^4 - 3 a^2 c^2 - 2 b^2 c^2 + c^4) ( a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 - b^2 c^2 + c^4)) |
| 1494 | strong | ((a^4 - 2 a^2 b^2 + b^4 + a^2 c^2 + b^2 c^2 - 2 c^4) (a^4 + a^2 b^2 - 2 b^4 - 2 a^2 c^2 + b^2 c^2 + c^4)) |
| 1495 | strong | (a^2 ( 2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4)) |
| 1498 | strong | (a^2 (a^8 - 4 a^6 b^2 + 6 a^4 b^4 - 4 a^2 b^6 + b^8 - 4 a^6 c^2 - 4 a^4 b^2 c^2 + 4 a^2 b^4 c^2 + 4 b^6 c^2 + 6 a^4 c^4 + 4 a^2 b^2 c^4 |
| 1501 | strong | (a^6) |
| 1502 | strong | (b^4 c^4) |
| 1503 | strong | (2 a^6 - a^4 b^2 - b^6 - a^4 c^2 + b^4 c^2 + b^2 c^4 - c^6) |
| 1506 | strong | (-2) a^2 b^2 + b^4 - 2 a^2 c^2 - 2 b^2 c^2 + c^4) |
| 1511 | strong | (a^2 (a^2 - b^2 - b c - c^2) (a^2 - b^2 + b c - c^2) (2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4)) |
| 1513 | strong | ((a^2 b^2 - b^4 + a^2 c^2 - c^4) (3 a^4 + b^4 - 2 b^2 c^2 + c^4)) |
| 1514 | strong | ((2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4) (a^6 + a^4 b^2 - 5 a^2 b^4 + 3 b^6 + a^4 c^2 + 10 a^2 b^2 c^2 - 3 b^4 c^2 - 5 a^2 c^ |
| 1515 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (5 a^4 - 4 a^2 b^2 - b^4 - 4 a^2 c^2 + 2 b^2 c^2 - c^4) (a^6 b^2 - 3 a^4 b^4 + 3 a^2 b^6 - b^8 + a^6 |
| 1516 | strong | ((a^2 - b^2 - c^2) (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 + 2 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 + c^6) (4 a^8 - 5 a^6 b^2 - a^4 b^ |
| 1529 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 + 2 a^2 b^2 - 3 b^4 + 2 a^2 c^2 - 2 b^2 c^2 - 3 c^4) (2 a^6 - a^4 b^2 - b^6 - a^4 c^2 + b^4 c^2 + |
| 1531 | strong | ((a^2 - b^2 - c^2) ( a^4 + a^2 b^2 - 2 b^4 + a^2 c^2 + 4 b^2 c^2 - 2 c^4) (2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4)) |
| 1533 | strong | ((2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4) (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 + 8 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 |
| 1539 | strong | ((2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4) (a^6 - 3 a^2 b^4 + 2 b^6 + 5 a^2 b^2 c^2 - 2 b^4 c^2 - 3 a^2 c^4 - 2 b^2 c^4 + 2 c^6)) |
| 1540 | strong | ((2 a^10 - 4 a^8 b^2 + a^6 b^4 + a^4 b^6 + a^2 b^8 - b^10 - 4 a^8 c^2 + 4 a^6 b^2 c^2 - a^4 b^4 c^2 - 2 a^2 b^6 c^2 + 3 b^8 c^2 + a^6 c |
| 1550 | strong | ((2 a^6 - 2 a^4 b^2 + a^2 b^4 - b^6 - 2 a^4 c^2 + b^4 c^2 + a^2 c^4 + b^2 c^4 - c^6) (a^8 - a^6 b^2 + a^4 b^4 - 3 a^2 b^6 + 2 b^8 - a^6 c |
| 1551 | strong | ((2 a^6 - 2 a^4 b^2 + a^2 b^4 - b^6 - 2 a^4 c^2 + b^4 c^2 + a^2 c^4 + b^2 c^4 - c^6) (a^8 + 3 a^6 b^2 - 5 a^4 b^4 - 3 a^2 b^6 + 4 b^8 + 3 |
| 1552 | strong | (( a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 - 2 a^2 b^2 + b^4 + a^2 c^2 + b^2 c^2 - 2 c^4) (a^4 + a^2 b^2 - 2 b^4 - 2 a^2 c^2 + b^2 c^2 + c |
| 1553 | strong | ((2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4)^2 (a^6 b^2 - 3 a^4 b^4 + 3 a^2 b^6 - b^8 + a^6 c^2 + 2 a^4 b^2 c^2 - 2 a^2 b^4 c^2 - |
| 1554 | strong | ((2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4) (2 a^6 - a^4 b^2 - b^6 - a^4 c^2 + b^4 c^2 + b^2 c^4 - c^6) (a^8 b^2 - 2 a^6 b^4 + 2 |
| 1555 | strong | ((2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4) ( a^8 - a^6 b^2 + a^4 b^4 - 3 a^2 b^6 + 2 b^8 - a^6 c^2 + 8 a^4 b^2 c^2 + 3 a^2 b^4 |
| 1556 | strong | ((2 a^6 - a^2 b^4 - b^6 + b^4 c^2 - a^2 c^4 + b^2 c^4 - c^6) (a^8 + a^6 b^2 - 3 a^4 b^4 - a^2 b^6 + 2 b^8 + a^6 c^2 - a^4 b^2 c^2 - 3 a^2 |
| 1557 | strong | ((-3) a^6 b^2 + 2 a^4 b^4 + a^2 b^6 - 3 a^6 c^2 + 2 a^4 b^2 c^2 - a^2 b^4 c^2 + 2 b^6 c^2 + 2 a^4 c^4 - a^2 b^2 c^4 - 4 b^4 c^4 + a^2 c^ |
| 1559 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (3 a^4 - 2 a^2 b^2 - b^4 - 2 a^2 c^2 + 2 b^2 c^2 - c^4) (a^6 b^2 - 3 a^4 b^4 + 3 a^2 b^6 - b^8 + a^6 |
| 1560 | strong | ((2 a^2 - b^2 - c^2) (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 b^2 - b^6 + a^4 c^2 - 2 a^2 b^2 c^2 + b^4 c^2 + b^2 c^4 - c^6)) |
| 1561 | strong | ((2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4) (3 a^6 b^2 - 5 a^4 b^4 + a^2 b^6 + b^8 + 3 a^6 c^2 + 4 a^4 b^2 c^2 - a^2 b^4 c^2 + |
| 1567 | strong | ((- a^6) b^2 + a^4 b^4 - a^6 c^2 + 2 a^4 b^2 c^2 - a^2 b^4 c^2 + b^6 c^2 + a^4 c^4 - a^2 b^2 c^4 - 2 b^4 c^4 + b^2 c^6) ( 2 a^8 b^4 - 3 a |
| 1568 | strong | ((a^2 - b^2 - c^2) (2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4) (a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4)) |
| 1569 | strong | (-2) a^6 b^2 + 2 a^4 b^4 - a^2 b^6 - 2 a^6 c^2 + 4 a^4 b^2 c^2 - a^2 b^4 c^2 + b^6 c^2 + 2 a^4 c^4 - a^2 b^2 c^4 - 2 b^4 c^4 - a^2 c^6 + |
| 1570 | strong | (a^2 (2 a^4 - 3 a^2 b^2 + 3 b^4 - 3 a^2 c^2 - 2 b^2 c^2 + 3 c^4)) |
| 1593 | strong | (a^2 ( a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 + 6 b^2 c^2 + c^4)) |
| 1594 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 - 2 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 + c^6)) |
| 1595 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 - 8 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 + c^6)) |
| 1596 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 b^2 - 2 a^2 b4 + b^6 + a^4 c^2 + 8 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 + c^6)) |
| 1597 | strong | (a^2 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 + 10 b^2 c^2 + c^4)) |
| 1598 | strong | (a^2 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 - 6 b^2 c^2 + c^4)) |
| 1601 | strong | (a^2 (a^20 - 6 a^18 b^2 + 15 a^16 b^4 - 20 a^14 b^6 + 14 a^12 b^8 - 14 a^8 b^12 + 20 a^6 b^14 - 15 a^4 b^16 + 6 a^2 b^18 - b^20 - 6 a |
| 1609 | strong | (a^2 (a^6 - 3 a^4 b^2 + 3 a^2 b^4 - b^6 - 3 a^4 c^2 - 2 a^2 b^2 c^2 + b^4 c^2 + 3 a^2 c^4 + b^2 c^4 - c^6)) |
| 1611 | strong | (a^2 (a^4 + 2 a^2 b^2 + b^4 + 2 a^2 c^2 - 6 b^2 c^2 + c^4)) |
| 1613 | strong | (a^2 (a^2 b^2 + a^2 c^2 - b^2 c^2)) |
| 1614 | strong | (a^2 (a^8 - 3 a^6 b^2 + 3 a^4 b^4 - a^2 b^6 - 3 a^6 c^2 + a^4 b^2 c^2 + a^2 b^4 c^2 + b^6 c^2 + 3 a^4 c^4 + a^2 b^2 c^4 - 2 b^4 c^4 - a |
| 1619 | strong | (a^2 (a^10 - a^8 b^2 - 2 a^6 b^4 + 2 a^4 b^6 + a^2 b^8 - b^10 - a^8 c^2 + 12 a^6 b^2 c^2 - 6 a^4 b^4 c^2 - 4 a^2 b^6 c^2 - b^8 c^2 - 2 a |
| 1620 | strong | (a^2 (7 a^8 - 12 a^6 b^2 - 6 a^4 b^4 + 20 a^2 b^6 - 9 b^8 - 12 a^6 c^2 + 28 a^4 b^2 c^2 - 20 a^2 b^4 c^2 + 4 b^6 c^2 - 6 a^4 c^4 - 20 a^2 |
| 1627 | strong | (a^2 (a^4 + a^2 b^2 + a^2 c^2 - b^2 c^2)) |
| 1628 | strong | (a^2 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^16 - 8 a^14 b^2 + 28 a^12 b^4 - 56 a10 b^6 + 70 a^8 b^8 - 56 a^6 b^10 + 28 a^4 b^12 - 8 a^2 |
| 1629 | strong | ((a^2 + b^2 - c^2)^2 (a^2 - b^2 + c^2)^2 (a^4 - a^2 b^2 - a^2 c^2 - b^2 c^2)) |
| 1641 | strong | ((2 a^2 - b^2 - c^2) (2 a^4 - 2 a^2 b^2 - b^4 - 2 a^2 c^2 + 4 b^2 c^2 - c^4)) |
| 1651 | strong | ((2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4) (2 a^8 - 2 a^6 b^2 - 3 a^4 b^4 + 4 a^2 b^6 - b^8 - 2 a^6 c^2 + 8 a^4 b^2 c^2 - 4 a^2 |
| 1656 | strong | (a^4 - 3 a^2 b^2 + 2 b^4 - 3 a^2 c^2 - 4 b^2 c^2 + 2 c^4) |
| 1657 | strong | (5 a^4 - 3 a^2 b^2 - 2 b^4 - 3 a^2 c^2 + 4 b^2 c^2 - 2 c^4) |
| 1658 | strong | (a^2 (a^8 - 2 a^6 b^2 + 2 a^2 b^6 - b^8 - 2 a^6 c^2 + 2 a^4 b^2 c^2 - a^2 b^4 c^2 + b^6 c^2 - a^2 b^2 c^4 + 2 a^2 c^6 + b^2 c^6 - c^8)) |
| 1660 | strong | (a^4 (a^8 - 2 a^6 b^2 + 2 a^2 b^6 - b^8 - 2 a^6 c^2 + 10 a^4 b^2 c^2 - 6 a^2 b^4 c2 - 2 b^6 c^2 - 6 a^2 b^2 c^4 + 6 b^4 c^4 + 2 a^2 c^6 - |
| 1661 | strong | (a^2 (a^10 + 3 a^8 b^2 - 14 a^6 b^4 + 14 a^4 b^6 - 3 a^2 b^8 - b^10 + 3 a^8 c^2 + 20 a^6 b^2 c^2 - 14 a^4 b^4 c^2 - 12 a^2 b^6 c^2 + 3 |
| 1691 | strong | (a^2 (a^2 - b c) (a^2 + b c)) |
| 1692 | strong | (a^2 (2 a^4 - a^2 b^2 + b^4 - a^2 c^2 - 2 b^2 c^2 + c^4)) |
| 1799 | strong | ((a^2 + b^2) (a^2 - b^2 - c^2) (a^2 + c^2)) |
| 1843 | strong | (a^2 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (b^2 + c^2)) |
| 1853 | strong | (a^6 + a^2 b^4 - 2 b^6 - 2 a^2 b^2 c^2 + 2 b^4 c^2 + a^2 c^4 + 2 b^2 c^4 - 2 c^6) |
| 1879 | strong | (a^4 b^4 - 2 a^2 b^6 + b^8 + 2 a^2 b^4 c^2 - 4 b^6 c^2 + a^4 c^4 + 2 a^2 b^2 c^4 + 6 b^4 c^4 - 2 a^2 c^6 - 4 b^2 c^6 + c^8) |
| 1885 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) ( 2 a^6 - 3 a^4 b^2 + b^6 - 3 a^4 c^2 + 8 a^2 b^2 c^2 - b^4 c^2 - b^2 c^4 + c^6)) |
| 1899 | strong | ((a^2 - b^2 - c^2) (a^4 + b^4 - 2 b^2 c^2 + c^4)) |
| 1907 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 - 12 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 + c^6)) |
| 1915 | strong | (a^2 (a^4 + b^2 c^2)) |
| 1916 | strong | ((b^2 - a c) (b^2 + a c) ((-a) b + c^2) (a b + c^2)) |
| 1941 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) ( a^12 - 4 a^10 b^2 + 6 a^8 b^4 - 4 a^6 b^6 + a^4 b^8 - 4 a^10 c^2 + 13 a^8 b^2 c^2 - 12 a^6 b^4 c^ |
| 1968 | strong | (a^2 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 - a^2 b^2 - a^2 c^2 + 2 b^2 c^2)) |
| 1970 | strong | (a^2 (a^8 - 2 a^6 b^2 + a^4 b^4 - 2 a^6 c^2 + 3 a^4 b^2 c^2 - b^6 c^2 + a^4 c^4 + 2 b^4 c^4 - b^2 c^6)) |
| 1971 | strong | (a^2 (a^8 - 2 a^6 b^2 + a^4 b^4 - 2 a^6 c^2 + a^4 b^2 c^2 + b^6 c^2 + a^4 c^4 - 2 b^4 c^4 + b^2 c^6)) |
| 1972 | strong | ((a^4 b^4 - 2 a^2 b^6 + b^8 + a^6 c^2 + a^2 b^4 c^2 - 2 b^6 c^2 - 2 a^4 c^4 + b^4 c^4 + a^2 c^6) (a^6 b^2 - 2 a^4 b^4 + a^2 b^6 + a^4 c |
| 1974 | strong | (a^4 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 1975 | strong | (a^4 - a^2 b^2 - a^2 c^2 + 2 b^2 c^2) |
| 1976 | strong | (a^2 (a^4 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - a^2 b^2 - b^2 c^2 + c^4)) |
| 1986 | strong | (a^2 (a^2 + b^2 - c^2) (a^2 - b^2 - b c - c^2) (a^2 - b^2 + b c - c^2) (a^2 - b^2 + c^2) (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 + 2 a^2 b^2 c |
| 1987 | strong | (a^2 (a^4 b^4 - 2 a^2 b^6 + b^8 + a^6 c^2 + a^2 b^4 c^2 - 2 b^6 c^2 - 2 a^4 c^4 + b^4 c^4 + a^2 c^6) (a^6 b^2 - 2 a^4 b^4 + a^2 b^6 + a |
| 1988 | strong | (a^2 (a^6 b^2 - 2 a^4 b^4 + a^2 b^6 - a^6 c^2 + a^4 b^2 c^2 + a^2 b^4 c^2 - b^6 c^2 + 2 a^4 c^4 - a^2 b^2 c^4 + 2 b^4 c^4 - a^2 c^6 - b |
| 1989 | strong | ((a^2 - a b + b^2 - c^2) (a^2 + a b + b^2 - c^2) (a^2 - b^2 - a c + c^2) (a^2 - b^2 + a c + c^2)) |
| 1990 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4)) |
| 1992 | strong | (5 a^2 - b^2 - c^2) |
| 1993 | strong | (a^2 ( a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 + c^4)) |
| 1994 | strong | (a^2 (a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 - b^2 c^2 + c^4)) |
| 1995 | strong | (a^2 (a^4 - b^4 + 4 b^2 c^2 - c^4)) |
| 2001 | strong | (a^2 (a^8 - a^6 b^2 + a^4 b^4 - a^2 b^6 - a^6 c^2 + a^2 b^4 c^2 + a^4 c^4 + a^2 b^2 c^4 + 2 b^4 c^4 - a^2 c^6)) |
| 2021 | strong | (a^2 (3 a^4 b^2 - 2 a^2 b^4 + b^6 + 3 a^4 c^2 - 2 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c4 - b^2 c^4 + c^6)) |
| 2023 | strong | (a^6 b^2 - a^4 b^4 + 2 a^2 b^6 + a^6 c^2 - 2 a^4 b^2 c^2 - a^2 b^4 c^2 + b^6 c^2 - a^4 c^4 - a^2 b^2 c^4 - 2 b^4 c^4 + 2 a^2 c^6 + b^2 c |
| 2024 | strong | (a^2 (3 a^6 b^2 - a^4 b^4 + a^2 b^6 + b^8 + 3 a^6 c^2 - 5 a^2 b^4 c^2 + 2 b^6 c^2 - a^4 c^4 - 5 a^2 b^2 c^4 - 2 b^4 c^4 + a^2 c^6 + 2 b^ |
| 2025 | strong | (a^2 (3 a^6 b^2 - 3 a^4 b^4 + 3 a^2 b^6 + b^8 + 3 a^6 c^2 - 4 a^4 b^2 c^2 - 5 a^2 b^4 c^2 + 4 b^6 c^2 - 3 a^4 c^4 - 5 a^2 b^2 c^4 - 2 b^4 |
| 2030 | strong | (a^2 (4 a^4 - a^2 b^2 + b^4 - a^2 c^2 - 4 b^2 c^2 + c^4)) |
| 2031 | strong | (a^2 (4 a^6 - 5 a^4 b^2 + 4 a^2 b^4 + b^6 - 5 a^4 c^2 - 6 a^2 b^2 c^2 + b^4 c^2 + 4 a^2 c^4 + b2 c^4 + c^6)) |
| 2032 | strong | (a^2 (4 a^8 - a^6 b^2 + 3 a^4 b^4 + a^2 b^6 + b^8 - a^6 c^2 - 8 a^4 b^2 c^2 - a^2 b^4 c^2 - 2 b^6 c^2 + 3 a^4 c^4 - a^2 b^2 c^4 + 2 b^4 |
| 2041 | strong | (-a^2) b^2 + b^4 - a^2 c^2 - 2 b^2 c^2 + c^4 - a^4 f0h1 + a^2 b^2 f0h1 + a^2 c^2 f0h1) |
| 2042 | strong | (-a^2) b^2 + b^4 - a^2 c^2 - 2 b^2 c^2 + c^4 + a^4 f0h1 - a^2 b^2 f0h1 - a^2 c^2 f0h1) |
| 2043 | strong | (a^4 + a^2 b^2 - 2 b^4 + a^2 c^2 + 4 b^2 c^2 - 2 c^4 - a^2 b^2 f0h1 + b^4 f0h1 - a^2 c^2 f0h1 - 2 b^2 c^2 f0h1 + c^4 f0h1) |
| 2044 | strong | (a^4 + a^2 b^2 - 2 b^4 + a^2 c^2 + 4 b^2 c^2 - 2 c^4 + a^2 b^2 f0h1 - b^4 f0h1 + a^2 c^2 f0h1 + 2 b^2 c^2 f0h1 - c^4 f0h1) |
| 2045 | strong | (a^4 - 3 a^2 b^2 + 2 b^4 - 3 a^2 c^2 - 4 b^2 c^2 + 2 c^4 + a^2 b^2 f0h1 - b^4 f0h1 + a^2 c^2 f0h1 + 2 b^2 c^2 f0h1 - c^4 f0h1) |
| 2046 | strong | (a^4 - 3 a^2 b^2 + 2 b^4 - 3 a^2 c^2 - 4 b^2 c^2 + 2 c^4 - a^2 b^2 f0h1 + b^4 f0h1 - a^2 c^2 f0h1 - 2 b^2 c^2 f0h1 + c^4 f0h1) |
| 2052 | strong | (b^2 c^2 ((-a^2) + b^2 - c^2)^2 ((-a^2) - b^2 + c^2)^2) |
| 2055 | strong | (a^2 (a^2 - b^2 - c^2) (a^12 - 4 a^10 b^2 + 6 a^8 b^4 - 4 a^6 b^6 + a^4 b^8 - 4 a^10 c^2 + 9 a^8 b^2 c^2 - 4 a^6 b^4 c^2 - 2 a^4 b^6 c^2 |
| 2056 | strong | (a^2 ( a^4 - 2 a^2 b^2 - 2 a^2 c^2 + b^2 c^2)) |
| 2060 | strong | ((3 a^4 - 2 a^2 b^2 - b^4 - 2 a^2 c^2 + 2 b^2 c^2 - c^4) (5 a^12 - 10 a^10 b^2 - 9 a^8 b^4 + 36 a^6 b^6 - 29 a^4 b^8 + 6 a^2 b^10 + b^12 |
| 2063 | strong | (a^2 (a^2 - b^2 - c^2) (a^8 - 2 a^6 b^2 + 2 a^2 b^6 - b^8 - 2 a^6 c^2 + 10 a^4 b^2 c^2 - 6 a^2 b^4 c^2 - 2 b^6 c^2 - 6 a^2 b^2 c^4 + 6 b^ |
| 2065 | strong | (a^2 (a^4 + b^4 - a^2 c^2 - b^2 c^2) ( a^4 - a^2 b^2 - b^2 c^2 + c^4) (a^4 - a^2 b^2 + 2 b^4 - 2 a^2 c^2 - b^2 c^2 + c^4) (a^4 - 2 a^2 b^2 |
| 2070 | strong | (a^2 ( a^8 - 2 a^6 b^2 + 2 a^2 b^6 - b^8 - 2 a^6 c^2 + a^4 b^2 c^2 - a^2 b^4 c^2 + 2 b^6 c^2 - a^2 b^2 c^4 - 2 b^4 c^4 + 2 a^2 c^6 + 2 b^ |
| 2071 | strong | (a^2 (a^8 - 2 a^6 b^2 + 2 a^2 b^6 - b^8 - 2 a^6 c^2 + 7 a^4 b^2 c^2 - 4 a^2b^4 c^2 - b^6 c^2 - 4 a^2 b^2 c^4 + 4 b^4 c^4 + 2 a^2 c^6 - b^ |
| 2076 | strong | (a^2 (a^4 + a^2 b^2 - b^4 + a^2 c^2 - b^2 c^2 - c^4)) |
| 2079 | strong | (a^2 ( a^8 - 2 a^6 b^2 + 2 a^2 b^6 - b^8 - 2 a^6 c^2 + 5 a^4 b^2 c^2 - 3 a^2 b^4 c^2 + 2 b^6 c^2 - 3 a^2 b^2 c^4 - 2 b^4 c^4 + 2 a^2 c^6 |
| 2080 | strong | (a^2 (a^6 - 3 a^4 b^2 + 2 a^2 b^4 - 3 a^4 c^2 - a^2 b^2 c^2 + b^4 c^2 + 2 a^2 c^4 + b^2 c^4)) |
| 2120 | strong | (a^2 (a^4 - 2 a^2 b^2 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - a^2 b^2 - 2 a^2 c^2 - b^2 c^2 + c^4) (a^18 - 6 a^16 b^2 + 15 a^14 b^4 - 21 a^12 b |
| 2121 | strong | ((-a^2) b^2 + b^4 - a^2 c^2 - 2 b^2 c^2 + c^4) ((-a^18) + 6 a^16 b^2 - 15 a^14 b4 + 21 a^12 b^6 - 21 a^10 b^8 + 21 a^8 b^10 - 21 a^6 b^ |
| 2130 | strong | (a^2 ( a^2 - b^2 - c^2) (a^4 - 2 a^2 b^2 + b^4 + 2 a^2 c^2 + 2 b^2 c^2 - 3 c^4) (a^4 + 2 a^2 b^2 - 3 b^4 - 2 a^2 c^2 + 2 b^2 c^2 + c^4) ( a |
| 2131 | strong | ((a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (3 a^4 - 2 a^2 b^2 - b^4 - 2 a^2 c^2 + 2 b^2 c^2 - c^4) (a^16 + 8 a^14 b^2 - 68 a^12 b^4 + 184 a^10 |
| 2132 | strong | (a^2 (a^4 - 2 a^2 b^2 + b^4 + a^2 c^2 + b^2 c^2 - 2 c^4) (a^4 + a^2 b^2 - 2 b^4 - 2 a^2 c^2 + b^2 c^2 + c^4) (a^18 - 6 a^16 b^2 + 15 a^1 |
| 2138 | strong | (a^2 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^10 - a^8 b^2 - 2 a^6 b^4 + 2 a^4 b^6 + a^2 b^8 - b^10 - a^8 c^2 + 12 a^6 b^2 c^2 - 6 a^4 b^4 |
| 2139 | strong | ((a^2 - b^2 - c^2) (a^10 + a^8 b^2 - 2 a^6 b^4 - 2 a^4 b^6 + a^2 b^8 + b^10 - a^8 c^2 + 4 a^6 b^2 c^2 - 6 a^4 b^4 c^2 + 4 a^2 b^6 c^2 - |
| 2165 | strong | ((a^4 - 2 a^2 b^2 + b^4 - 2 b^2 c^2 + c^4) (a^4 + b^4 - 2 a^2 c^2 - 2 b^2 c^2 + c^4)) |
| 2207 | strong | (a^2 (a^2 + b^2 - c^2)^2 (a^2 - b^2 + c^2)^2) |
| 2211 | strong | (a^4 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^2 b^2 - b^4 + a^2 c^2 - c^4)) 12 |
| 2351 | strong | (a^2 (a^2 - b^2 - c^2) (a^4 - 2 a^2 b^2 + b^4 - 2 b^2 c^2 + c^4) ( a^4 + b^4 - 2 a^2 c^2 - 2 b^2 c^2 + c^4)) |
| 2353 | strong | (a^2 (a^4 + b^4 - c^4) (a^4 - b^4 + c^4)) |
| 2366 | strong | ((a^8 - 2 a^6 b^2 + 2 a^4 b^4 - 2 a^2 b^6 + b^8 + a^6 c^2 - a^4 b^2 c^2 - a^2 b^4 c^2 + b^6 c^2 - a^4 c^4 + 4 a^2 b^2 c^4 - b^4 c^4 - a^ |
| 2367 | strong | (b^2 c^2 ( a^6 + b^6 - a^4 c^2 - b^4 c^2) (a^6 - a^4 b^2 - b^2 c^4 + c^6)) |
| 2373 | strong | ((a^6 - a^4 b^2 - a^2 b^4 + b^6 + 2 a^2 b^2 c^2 - a^2 c^4 - b^2 c^4) (a^6 - a^2 b^4 - a^4 c^2 + 2 a^2 b^2 c^2 - b^4 c^2 - a^2 c^4 + c^6)) |
| 2374 | strong | ((a^2 + b^2 - c^2) ( a^2 - b^2 + c^2) (a^4 - 4 a^2 b^2 + b^4 + a^2 c^2 + b^2 c^2) (a^4 + a^2 b^2 - 4 a^2 c^2 + b^2 c^2 + c^4)) |
| 2383 | strong | (a^2 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^8 - 2 a^6 b^2 + 3 a^4 b^4 - 4 a^2 b^6 + 2 b^8 - 4 a^6 c^2 + 2 a^4 b^2 c^2 - 4 b^6 c^2 + 6 a^4 |
| 2386 | strong | (a^2 ( a^6 b^2 + a^4 b^4 - a^2 b^6 - b^8 + a^6 c^2 - 4 a^4 b^2 c^2 + a^2 b^4 c^2 + 2 b^6 c^2 + a^4 c^4 + a^2 b^2 c^4 - 2 b^4 c^4 - a^2 |
| 2387 | strong | (a^4 (a^2 b^4 - b^6 + a^2 c^4 - c^6)) |
| 2393 | strong | (a^2 ( a^4 b^2 - b^6 + a^4 c^2 - 2 a^2 b^2 c^2 + b^4 c^2 + b^2 c^4 - c^6)) |
| 2450 | strong | ((a^2 b^2 - b^4 + a^2 c^2 - c^4) ( a^4 + b^4 - 2 b^2 c^2 + c^4)) |
| 2452 | strong | (a^8 - a^6 b^2 - 2 a^4 b^4 + 2 a^2 b^6 - a^6 c^2 + 5 a^4 b^2 c^2 - 2 a^2 b^4 c^2 - b^6 c^2 - 2 a^4 c^4 - 2 a^2 b^2 c^4 + 2 b^4 c^4 + 2 a^ |
| 2453 | strong | (a^8 - a^6 b^2 + a^4 b^4 - a^2 b^6 - a^6 c^2 - a^4 b^2 c^2 + a^2 b^4 c^2 + 2 b^6 c^2 + a^4 c^4 + a^2 b^2 c^4 - 4 b^4 c^4 - a^2 c^6 + 2 |
| 2456 | strong | (a^2 (a^8 - 2 a^6 b^2 + 3 a^4 b^4 - 2 a^2 b^6 - 2 a^6 c^2 + a^4 b^2 c^2 + 2 a^2 b^4 c^2 - 3 b^6 c^2 + 3 a^4 c^4 + 2 a^2 b^2 c^4 + 2 b^4 |
| 2458 | strong | (a^2 (a^8 + 2 a^4 b^4 - a^2 b^6 + a^4 b^2 c^2 - 2 b^6 c^2 + 2 a^4 c^4 - a^2 c^6 - 2 b^2 c^6)) |
| 2482 | strong | ((2 a^2 - b^2 - c^2)^2) |
| 2493 | strong | (a^2 (a^6 b^2 - a^4 b^4 - a^2 b^6 + b^8 + a^6 c^2 - 2 a^4 b^2 c^2 + 2 a^2 b^4 c^2 - 3 b^6 c^2 - a^4 c^4 + 2 a^2 b^2 c^4 + 4 b^4 c^4 - a^ |
| 2502 | strong | (a^2 (2 a^4 - 2 a^2 b^2 - b^4 - 2 a^2 c^2 + 4 b^2 c^2 - c^4)) |
| 2548 | strong | (a^4 + 2 a^2 b^2 - b^4 + 2 a^2 c^2 + 2 b^2 c^2 - c^4) |
| 2549 | strong | (a^4 - 2 a^2 b^2 - b^4 - 2 a^2 c^2 + 2 b^2 c^2 - c^4) |
| 2675 | strong | (-17) a^4 + 2 a^2 b^2 + 15 b^4 + 2 a^2 c^2 - 30 b^2 c^2 + 15 c^4 + 3 a^4 f0h2 - 6 a^2 b^2 f0h2 + 3 b^4 f0h2 - 6 a^2 c^2 f0h2 - 6 b^2 c^2 f |
| 2676 | strong | (-a^4) - 14 a^2 b^2 + 15 b^4 - 14 a^2 c^2 - 30 b^2 c^2 + 15 c^4 + 3 a^4 f0h2 - 6 a^2 b^2 f0h2 + 3 b^4 f0h2 - 6 a^2 c^2 f0h2 - 6 b^2 c^2 f0h |
| 2133 | strong1 | |
| 1 | weak | a |
| 7 | weak | ((a + b - c) (a - b + c)) |
| 8 | weak | (a - b - c) |
| 9 | weak | (a (a - b - c)) |
| 10 | weak | (b + c) |
| 11 | weak | (b + c - a)(b - c)^2 |
| 12 | weak | (( a + b - c) (a - b + c) (b + c)^2) |
| 19 | weak | (a (a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 21 | weak | (a (a + b) (a - b - c) (a + c)) |
| 27 | weak | ((a + b) (a + c) (a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 28 | weak | (a (a + b) (a + c) (a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 29 | weak | ((a + b) (a - b - c) (a + c) (a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 31 | weak | (a^3) |
| 33 | weak | (a (a - b - c) ( a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 34 | weak | (a (a + b - c) (a - b + c) (a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 35 | weak | (a^2 (a^2 - b^2 - b c - c^2)) |
| 36 | weak | (a^2 (a^2 - b^2 + b c - c^2)) |
| 37 | weak | (a (b + c)) |
| 38 | weak | (a (b^2 + c^2)) |
| 40 | weak | (a (a^3 + a^2 b - a b^2 - b^3 + a^2 c - 2 a b c + b^2 c - a c^2 + b c^2 - c^3)) |
| 41 | weak | (a^3 (a - b - c)) |
| 42 | weak | (a^2 (b + c)) |
| 43 | weak | (a (a b + a c - b c)) |
| 44 | weak | (a (2 a - b - c)) |
| 45 | weak | (a (a - 2 b - 2 c)) |
| 46 | weak | (a (a^3 + a^2 b - a b^2 - b^3 + a^2 c + b^2 c - a c^2 + b c^2 - c^3)) |
| 47 | weak | (a^3 ( a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 + c^4)) |
| 48 | weak | (a^3 (a^2 - b^2 - c^2)) |
| 55 | weak | (a^2 (a - b - c)) |
| 56 | weak | (a^2 (a + b - c) (a - b + c)) |
| 57 | weak | (a (a + b - c) (a - b + c)) |
| 58 | weak | (a^2 (a + b) (a + c)) |
| 59 | weak | (a^2 (a - b)^2 (a + b - c) ((-a) + c)^2 (a - b + c)) |
| 60 | weak | (a^2 (a + b)^2 (a - b - c) (a + c)^2) |
| 63 | weak | (a (a^2 - b^2 - c^2)) |
| 65 | weak | (a (a + b - c) (a - b + c) (b + c)) |
| 71 | weak | (a^2 (b + c) (a^2 - b^2 - c^2)) |
| 72 | weak | (a (b + c) ( a^2 - b^2 - c^2)) |
| 73 | weak | (a^2 (a + b - c) (a - b + c) (b + c) (a^2 - b^2 - c^2)) |
| 75 | weak | (b c) |
| 77 | weak | (a (a + b - c) (a - b + c) (a^2 - b^2 - c^2)) |
| 78 | weak | (a (a - b - c) (a^2 - b^2 - c^2)) |
| 79 | weak | ((a^2 + a b + b^2 - c^2) (a^2 - b^2 + a c + c^2)) |
| 80 | weak | (( a^2 - a b + b^2 - c^2) (a^2 - b^2 - a c + c^2)) |
| 81 | weak | (a (a + b) (a + c)) |
| 82 | weak | (a (a^2 + b^2) ( a^2 + c^2)) |
| 84 | weak | (a (a^3 - a^2 b - a b^2 + b^3 + a^2 c + 2 a b c + b^2 c - a c^2 - b c^2 - c^3) (a^3 + a^2 b - a b^2 - b^3 - a^2 c + 2 a b c - b^2 c - a c^2 + b c |
| 85 | weak | (b ((-a) + b - c) c ((- a) - b + c)) |
| 86 | weak | ((a + b) (a + c)) |
| 87 | weak | (a (a b - a c - b c) ((-a) b + a c - b c)) |
| 88 | weak | (a (a + b - 2 c) (a - 2 b + c)) |
| 89 | weak | (a (2 a + 2 b - c) (2 a - b + 2 c)) |
| 90 | weak | (a (a^3 - a^2 b - a b^2 + b^3 + a^2 c + b^2 c - a c^2 - b c^2 - c^3) (a3 + a^2 b - a b^2 - b^3 - a^2 c - b^2 c - a c^2 + b c^2 + c^3)) |
| 91 | weak | (b c (a^4 - 2 a^2 b^2 + b^4 - 2 b^2 c^2 + c^4) ( a^4 + b^4 - 2 a^2 c^2 - 2 b^2 c^2 + c^4)) |
| 92 | weak | (b c ((-a^2) + b^2 - c^2) ((-a^2) - b^2 + c^2)) |
| 99 | weak | ((a - b) (a + b) ((-a) + c) (a + c)) |
| 100 | weak | (a (a - b) ((-a) + c)) |
| 101 | weak | (a^2 (a - b) ((-a) + c)) |
| 102 | weak | (a^2 (a^4 - 2 a^2 b^2 + b^4 - a^3 c + a^2 b c + a b^2 c - b^3 c + a^2 c^2 - 2 a b c^2 + b^2 c^2 + a c^3 + b c^3 - 2 c^4) (a^4 - a^3 b + a^2 |
| 103 | weak | (a^2 (a^3 - a^2 b - a b^2 + b^3 + a c^2 + b c^2 - 2 c^3) (a^3 + a b^2 - 2 b^3 - a^2 c + b^2 c - a c^2 + c^3)) |
| 104 | weak | (a (a^3 - a^2 b - a b^2 + b^3 + 2 a b c - a c^2 - b c^2) ( a^3 - a b^2 - a^2 c + 2 a b c - b^2 c - a c^2 + c^3)) |
| 105 | weak | (a (a^2 + b^2 - a c - b c) (a^2 - a b - b c + c^2)) |
| 106 | weak | (a^2 (a + b - 2 c) (a - 2 b + c)) |
| 107 | weak | ((a - b) ( a + b) ((-a) + c) (a + c) (a^2 + b^2 - c^2)^2 (a^2 - b^2 + c^2)^2) |
| 108 | weak | (a (a - b) ( a + b - c) ((- a) + c) (a - b + c) (a^2 + b^2 - c^2) ( a^2 - b^2 + c^2)) |
| 109 | weak | (a^2 (a - b) (a + b - c) ((-a) + c) (a - b + c)) |
| 110 | weak | (a^2 (a - b) (a + b) ((-a) + c) (a + c)) |
| 112 | weak | (a^2 (a - b) (a + b) ((-a) + c) (a + c) (a^2 + b^2 - c^2) ( a^2 - b^2 + c^2)) |
| 115 | weak | ((b - c)^2 (b + c)^2) |
| 116 | weak | ((b - c)^2 ((-a) b + b^2 - a c + b c + c^2)) |
| 117 | weak | ((2 a^4 - a^3 b - a^2 b^2 + a b^3 - b^4 - a^3 c + 2 a^2 b c - a b^2 c - a^2 c^2 - a b c^2 + 2 b^2 c^2 + a c^3 - c^4) (a^4 b^2 - 2 a^2 b^4 + b |
| 118 | weak | ((2 a^3 - a^2 b - b^3 - a^2 c + b^2 c + b c^2 - c^3) (a^3 b^2 - a^2 b^3 - a b^4 + b^5 + a^3 c^2 + 2 a b^2 c^2 - b^3 c^2 - a^2 c^3 - b^2 c^3 |
| 119 | weak | ((a^2 b - b^3 + a^2 c - 2 a b c + b^2 c + b c^2 - c^3) (a^3 b - a^2 b^2 - a b^3 + b^4 + a^3 c + a b^2 c - a^2 c^2 + a b c^2 - 2 b^2 c^2 - a c^ |
| 120 | weak | ((- a) b + b^2 - a c + c^2) (a^2 b + b^3 + a^2 c - 2 a b c - b^2 c - b c^2 + c^3)) |
| 121 | weak | ((2 a - b - c) (a b^2 + b^3 - 2 b^2 c + a c^2 - 2 b c^2 + c^3)) |
| 122 | weak | ((b - c)^2 ( b + c)^2 ((-a^2) + b^2 + c^2)^2 ((-3) a^4 + 2 a^2 b^2 + b^4 + 2 a^2 c^2 - 2 b^2 c^2 + c^4)) |
| 123 | weak | ((a - b - c) ( b - c)^2 (a^2 - b^2 - c^2) (a^4 - b^4 + 2 a^2 b c - 2 a b^2 c - 2 a b c^2 + 2 b^2 c^2 - c^4)) |
| 124 | weak | ((a - b - c) (b - c)^2 (a^2 b - b^3 + a^2 c - a b c - c^3)) |
| 125 | weak | ((b - c)^2 (b + c)^2 ((-a^2) + b^2 + c^2)) |
| 127 | weak | ((b - c)^2 (b + c)^2 ((-a^2) + b^2 + c^2) ((-a^4) + b^4 + c^4)) |
| 130 | weak | (a^2 (b - c)^2 (b + c)^2(a^2 - b^2 - c^2)^2 (a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4) (a^8 - 2 a^6 b^2 + a^4 b^4 - 2 a^6 c^2 + 3 a^4 b^2 |
| 134 | weak | (a^2 (b - c)^2 (b + c)^2 (a^2 b^2 - b^4 + a^2 c^2 + 2 b^2 c^2 - c^4) (a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 + c^4)^2 (a^12 - 4 a^10 b^2 + 6 a^ |
| 135 | weak | ((b - c)^2 (b + c)^2 ((-a^2) + b^2 - c^2) ((-a^2) - b^2 + c^2) (a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 + c^4) ((- a^6) + 3 a^4 b^2 - 3 a^2 b^4 + b |
| 136 | weak | ((b - c)^2 (b + c)^2 ((-a^2) + b^2 - c^2) ((-a^2) - b^2 + c^2) (a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 + c^4)) |
| 137 | weak | ((b - c)^2 (b + c)^2 ((-a^2) b^2 + b^4 - a^2 c^2 - 2 b^2 c^2 + c^4) (a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 - b^2 c^2 + c^4)) |
| 139 | weak | ((b - c)^2 (b + c)^2 ((- a^2) + b^2 - c^2) ((-a^2) - b^2 + c^2) (a^4 - 2 a^2 b^2 + b^4 - 2 a^2 c^2 + c^4) ((-a^2) b^2 + b^4 - a^2 c2 - 2 b^2 c |
| 142 | weak | (- a) b + b^2 - a c - 2 b c + c^2) |
| 144 | weak | (3 a^2 - 2 a b - b^2 - 2 a c + 2 b c - c^2) |
| 145 | weak | (3 a - b - c) |
| 149 | weak | (a^3 - a^2 b + a b^2 - b^3 - a^2 c - a b c + b^2 c + a c^2 + b c^2 - c^3) |
| 150 | weak | (a^4 - a^3 b + a b^3 - b^4 - a^3 c + a^2 b c - a b^2 c + b^3 c - a b c^2 + a c^3 + b c^3 - c^4) |
| 151 | weak | (a^10 - a^9 b + a^8 b^2 + 2 a^7 b^3 - 8 a^6 b^4 + 8 a^4 b^6 - 2 a^3 b^7 - a2 b^8 + a b^9 - b^10 - a^9 c + 3 a^8 b c - 6 a^7 b^2 c + 2 a^6 |
| 152 | weak | (a^8 - a^7 b + 2 a^6 b^2 - 5 a^5 b^3 + 5 a^3 b^5 - 2 a^2 b^6 + a b^7 - b^8 - a^7 c + a^6 b c + a^5 b^2 c - a^4 b^3 c + a^3 b^4 c - a^2 b^5 |
| 153 | weak | (a^7 - a^6 b - a^5 b^2 + a^4 b^3 - a^3 b^4 + a^2 b^5 + a b^6 - b^7 - a^6 c + 7 a^5 b c - 5 a^4 b^2 c - 2 a^3 b^3 c + 5 a^2 b^4 c - 5 a b^5 |
| 158 | weak | (b c ((- a^2) + b^2 - c^2)^2 ((-a^2) - b^2 + c^2)^2) |
| 162 | weak | (a (a - b) (a + b) ((-a) + c) ( a + c) (a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 163 | weak | (a^3 (a - b) (a + b) ((- a) + c) (a + c)) |
| 165 | weak | (a (3 a^2 - 2 a b - b^2 - 2 a c + 2 b c - c^2)) |
| 169 | weak | (a (a^3 - a^2 b + a b^2 - b^3 - a^2 c + b^2 c + a c^2 + b c^2 - c^3)) |
| 170 | weak | (a (a^5 b - 4 a^4 b^2 + 6 a^3 b^3 - 4 a^2 b^4 + a b^5 + a^5 c - a^4 b c - 2 a^3 b^2 c + 2 a^2 b^3 c + a b^4 c - b^5 c - 4 a^4 c^2 - 2 a^3 b c |
| 171 | weak | (a (a^2 + b c)) |
| 172 | weak | (a^2 (a^2 + b c)) |
| 181 | weak | (a^2 ( a + b - c) (a - b + c) (b + c)^2) |
| 189 | weak | ((a^3 - a^2 b - a b^2 + b^3 + a^2 c + 2 a b c + b^2 c - a c^2 - b c^2 - c^3) (a^3 + a^2 b - a b^2 - b^3 - a^2 c + 2 a b c - b^2 c - a c^2 + b c^2 |
| 190 | weak | ((a - b) ((-a) + c)) |
| 191 | weak | (a (a^3 + a^2 b - a b^2 - b^3 + a^2 c - a b c - b^2 c - a c^2 - b c^2 - c^3)) |
| 192 | weak | (-a) b - a c + b c) |
| 196 | weak | ((a + b - c) (a - b + c) (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^3 + a^2 b - a b^2 - b^3 + a^2 c - 2 a b c + b^2 c - a c^2 + b c^2 - c^3)) |
| 197 | weak | (a^2 (a^4 - b^4 + 2 a^2 b c - 2 a b^2 c - 2 a b c^2 + 2 b^2 c^2 - c^4)) |
| 198 | weak | (a^2 (a^3 + a^2 b - a b^2 - b^3 + a^2 c - 2 a b c + b^2 c - a c^2 + b c^2 - c^3)) |
| 199 | weak | (a^2 (a^4 + a^3 b - a b^3 - b^4 + a^3 c + a^2 b c - a b^2 c - b^3 c - a b c^2 - a c^3 - b c^3 - c^4)) |
| 200 | weak | (a (a - b - c)^2) |
| 201 | weak | (a (a + b - c) (a - b + c) (b + c)^2 (a^2 - b^2 - c^2)) |
| 204 | weak | (a (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (3 a^4 - 2 a^2 b^2 - b^4 - 2 a^2 c^2 + 2 b^2 c^2 - c^4)) |
| 205 | weak | (a^3 (a^4 - b^4 + 2 a^2 b c - 2 a b^2 c - 2 a b c^2 + 2 b^2 c^2 - c^4)) |
| 207 | weak | (a (a + b - c) (a - b + c) (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^6 - 2 a^5 b - a^4 b^2 + 4 a^3 b^3 - a^2 b^4 - 2 a b^5 + b^6 - 2 a^5 c - 2 a^ |
| 208 | weak | (a (a + b - c) (a - b + c) (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^3 + a^2 b - a b^2 - b^3 + a^2 c - 2 a b c + b^2 c - a c^2 + b c^2 - c^3)) |
| 209 | weak | (a^2 (b + c) (a^2 b - b^3 + a^2 c + a b c - c^3)) |
| 210 | weak | (a (a - b - c) (b + c)) |
| 212 | weak | (a^3 (a - b - c) (a^2 - b^2 - c^2)) |
| 213 | weak | (a^3 (b + c)) |
| 214 | weak | (a (2 a - b - c) (a^2 - b^2 + b c - c^2)) |
| 215 | weak | (a^4 ( a - b - c) (a^2 - b^2 + b c - c^2)^2) |
| 218 | weak | (a^2 (a^2 - 2 a b + b^2 - 2 a c + c^2)) |
| 219 | weak | (a^2 (a - b - c) (a^2 - b^2 - c^2)) |
| 220 | weak | (a^2 (a - b - c)^2) |
| 221 | weak | (a^2 ( a + b - c) (a - b + c) (a^3 + a^2 b - a b^2 - b^3 + a^2 c - 2 a b c + b^2 c - a c^2 + b c^2 - c^3)) |
| 222 | weak | (a^2 ( a + b - c) (a - b + c) (a^2 - b^2 - c^2)) |
| 223 | weak | (a (a + b - c) (a - b + c) (a^3 + a^2 b - a b^2 - b^3 + a^2 c - 2 a b c + b^2 c - a c^2 + b c^2 - c^3)) |
| 224 | weak | (a (a^2 - b^2 - c^2) (a^4 - 2 a^3 b + 2 a b^3 - b^4 - 2 a^3 c - 2 a^2 b c + 2 b^2 c^2 + 2 a c^3 - c^4)) |
| 225 | weak | (( a + b - c) (a - b + c) (b + c) (a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 226 | weak | ((a + b - c) (a - b + c) ( b + c)) |
| 227 | weak | (a (a + b - c) (a - b + c) (b + c) (a^3 + a^2 b - a b^2 - b^3 + a^2 c - 2 a b c + b^2 c - a c^2 + b c^2 - c^3)) |
| 228 | weak | (a^3 (b + c) (a^2 - b^2 - c^2)) |
| 229 | weak | (a (a + b) ( a + c) (a^4 - b^4 + a^2 b c + a b^2 c + a b c^2 + 2 b^2 c^2 - c^4)) |
| 238 | weak | (a (a^2 - b c)) |
| 239 | weak | (a^2 - b c) |
| 240 | weak | (a (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^2 b^2 - b^4 + a^2 c^2 - c^4)) |
| 241 | weak | (a (a + b - c) (a - b + c) (a b - b^2 + a c - c^2)) |
| 242 | weak | ((a^2 - b c) (a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 243 | weak | ((a - b - c) (a^2 + b^2 - c^2) ( a^2 - b^2 + c^2) (a^4 - a^2 b^2 + a^2 b c - b^3 c - a^2 c^2 + 2 b^2 c^2 - b c^3)) |
| 244 | weak | (a (b - c)^2) |
| 245 | weak | (a (b - c)^2 (b + c) (a^7 - 2 a^5 b^2 + a^4 b^3 + a^3 b^4 - 2 a^2 b^5 + b^7 - a^5 b c + a^4 b^2 c + a^3 b^3 c - 2 a^2 b^4 c + b^6 c - 2 a^5 |
| 246 | weak | (a^2 (b - c)^2 (b + c)^2 (a^8 - 4 a^6 b^2 + 6 a^4 b^4 - 4 a^2 b^6 + b^8 - 4 a^6 c^2 + 7 a^4 b^2 c^2 - 5 a^2 b^4 c^2 + 2 b^6 c^2 + 6 a^4 c^ |
| 247 | weak | ((b - c)^2 (b + c)^2 (a^10 - 4 a^8 b^2 + 5 a^6 b^4 - a^4 b^6 - 2 a^2 b^8 + b^10 - 4 a^8 c^2 + 7 a^6 b^2 c^2 - 6 a^4 b^4 c^2 + 5 a^2 b^6 c |
| 249 | weak | (a^2 ( a - b)^2 (a + b)^2 ((-a) + c)^2 (a + c)^2) |
| 250 | weak | (a^2 (a - b)^2 (a + b)^2((-a) + c)^2 (a + c)^2 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) 14 |
| 255 | weak | (a^3 (a^2 - b^2 - c^2)^2) |
| 256 | weak | (a (b^2 + a c) ( a b + c^2)) |
| 257 | weak | ((b^2 + a c) ( a b + c^2)) |
| 261 | weak | ((a + b)^2 (a - b - c) ( a + c)^2) |
| 267 | weak | (a (a^3 + a^2 b + a b^2 + b^3 + a^2 c + a b c + b^2 c - a c^2 - b c^2 - c^3) (a^3 + a^2 b - a b^2 - b^3 + a^2 c + a b c - b^2 c + a c^2 + b c^ |
| 268 | weak | (a^2 (a - b - c) (a^2 - b^2 - c^2) (a^3 - a^2 b - a b^2 + b^3 + a^2 c + 2 a b c + b^2 c - a c^2 - b c^2 - c^3) (a^3 + a^2 b - a b^2 - b^3 - a^2 c |
| 269 | weak | (a (a + b - c)^2 (a - b + c)^2) |
| 270 | weak | (a ( a + b)^2 (a - b - c) (a + c)^2 (a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 271 | weak | (a (a - b - c) (a^2 - b^2 - c^2) ( a^3 - a^2 b - a b^2 + b^3 + a^2 c + 2 a b c + b^2 c - a c^2 - b c^2 - c^3) (a^3 + a^2 b - a b^2 - b^3 - a^2 c |
| 272 | weak | ((a + b) (a + c) (a^3 + b^3 - a b c - a c^2 - b c^2) (a^3 - a b^2 - a b c - b^2 c + c^3)) 8 |
| 274 | weak | (b (a + b) c (a + c)) |
| 277 | weak | ((a^2 - 2 a b + b^2 - 2 b c + c^2) (a^2 + b^2 - 2 a c - 2 b c + c^2)) |
| 278 | weak | (( a + b - c) (a - b + c) (a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 279 | weak | ((a + b - c)^2 (a - b + c)^2) |
| 280 | weak | ((a - b - c) (a^3 - a^2 b - a b^2 + b^3 + a^2 c + 2 a b c + b^2 c - a c^2 - b c^2 - c^3) (a^3 + a^2 b - a b^2 - b^3 - a^2 c + 2 a b c - b^2 c - a c |
| 281 | weak | ((a - b - c) (a^2 + b^2 - c^2) (a^2 - b^2 + c^2)) |
| 282 | weak | (a ( a - b - c) (a^3 - a^2 b - a b^2 + b^3 + a^2 c + 2 a b c + b^2 c - a c^2 - b c^2 - c^3) (a^3 + a^2 b - a b^2 - b^3 - a^2 c + 2 a b c - b^2 c - |
| 283 | weak | (a^2 (a + b) (a - b - c) (a + c) ( a^2 - b^2 - c^2)) |
| 284 | weak | (a^2 (a + b) (a - b - c) (a + c)) |
| 285 | weak | (a (a + b) (a - b - c) (a + c) (a^3 - a^2 b - a b^2 + b^3 + a^2 c + 2 a b c + b^2 c - a c^2 - b c^2 - c^3) (a^3 + a^2 b - a b^2 - b^3 - a^2 c + 2 |
| 286 | weak | (b (a + b) c (a + c) ((- a^2) + b^2 - c^2) ((-a^2) - b^2 + c^2)) |
| 291 | weak | (a ((-b^2) + a c) (a b - c^2)) |
| 292 | weak | (a^2 ((-b^2) + a c) (a b - c^2)) |
| 293 | weak | (a (a^2 - b^2 - c^2) (a^4 + b^4 - a^2 c^2 - b^2 c^2) (a^4 - a^2 b^2 - b^2 c^2 + c^4)) |
| 294 | weak | (a ( a - b - c) (a^2 + b^2 - a c - b c) (a^2 - a b - b c + c^2)) |
| 295 | weak | (a^2 ((-b^2) + a c) (a b - c^2) (a^2 - b^2 - c^2)) |
| 304 | weak | (b c ((-a^2) + b^2 + c^2)) |
| 306 | weak | ((b + c) ((-a^2) + b^2 + c^2)) |
| 307 | weak | ((a + b - c) ( a - b + c) (b + c) (a^2 - b^2 - c^2)) |