├── 222flipgraph_rank8 ├── edges.txt └── vertices │ ├── 00bc2f83230b.exp │ ├── 03e559862a37.exp │ ├── 04ba29f8c345.exp │ ├── 04cfe2abcc68.exp │ ├── 077a98c6f42d.exp │ ├── 07c5677256d3.exp │ ├── 089d6b7dd978.exp │ ├── 09f24d2c9fa4.exp │ ├── 0baa2a6a6b21.exp │ ├── 0bea4915cc7f.exp │ ├── 0c1b3588b233.exp │ ├── 0c6da92669c6.exp │ ├── 0cfd8cf632bc.exp │ ├── 0f5c449e889b.exp │ ├── 10312effa91d.exp │ ├── 10b35e3f01f5.exp │ ├── 11031c56d28a.exp │ ├── 11dbbe90cd18.exp │ ├── 1297d43ef91b.exp │ ├── 1300359d84d3.exp │ ├── 145907ae094b.exp │ ├── 1561cef24f80.exp │ ├── 15d00cad4147.exp │ ├── 17028e42c8a7.exp │ ├── 1704ec06d3bf.exp │ ├── 1a3b413d83c5.exp │ ├── 1b248bb39567.exp │ ├── 1baca944df60.exp │ ├── 1c8363f6f787.exp │ ├── 1cc4bb81a020.exp │ ├── 1cf38b94effb.exp │ ├── 1df1283df99b.exp │ ├── 1e311a458044.exp │ ├── 1eaaeb8d08b7.exp │ ├── 1fa190b8001b.exp │ ├── 24dc3c24595b.exp │ ├── 28b4d0be523c.exp │ ├── 28d12bca9ccd.exp │ ├── 294994e98b98.exp │ ├── 2a52f180f866.exp │ ├── 2b67647c7cc3.exp │ ├── 2b8921173ab5.exp │ ├── 2c688cf81f10.exp │ ├── 30ad198c3d6d.exp │ ├── 316a00005f10.exp │ ├── 31e9565aba0a.exp │ ├── 3262f04d8926.exp │ ├── 3293992e6596.exp │ ├── 3445b2f51289.exp │ ├── 349d8b4a1aea.exp │ ├── 363f70e89a53.exp │ ├── 38b741e8e591.exp │ ├── 38f1392c831f.exp │ ├── 3a6321d957b6.exp │ ├── 3ab189e6b28f.exp │ ├── 3ae47a16c388.exp │ ├── 3c505e9c782e.exp │ ├── 3d1739f1a1d4.exp │ ├── 3d206f7e54ce.exp │ ├── 3e755849d387.exp │ ├── 3ed9d19a14fd.exp │ ├── 3f952f32fa0f.exp │ ├── 3fcf94ebac99.exp │ ├── 40797d14a38e.exp │ ├── 41883f50367e.exp │ ├── 41f67daf7343.exp │ ├── 435b0b02dcf6.exp │ ├── 437e948af6fa.exp │ ├── 43fe66a87711.exp │ ├── 444df432f663.exp │ ├── 446cbd116aa3.exp │ ├── 45b1d642db1f.exp │ ├── 45d820933ab8.exp │ ├── 47b76a6c4d83.exp │ ├── 485d4afca366.exp │ ├── 48a58e13e747.exp │ ├── 49de0ee2a726.exp │ ├── 49ed84da18a3.exp │ ├── 4ab8bf04fa37.exp │ ├── 4d5b59649ae8.exp │ ├── 4d6d3848d4c5.exp │ ├── 502640c9e8a0.exp │ ├── 50b32572106a.exp │ ├── 53d7d7ebe129.exp │ ├── 53f879f9f733.exp │ ├── 5689a55d3ab7.exp │ ├── 584435d909e2.exp │ ├── 58d673635bf3.exp │ ├── 5958ced83f95.exp │ ├── 5988bd05931e.exp │ ├── 5a67763d4a8e.exp │ ├── 5a9d8ac8b556.exp │ ├── 5b9794f78feb.exp │ ├── 5bd4c09a3772.exp │ ├── 5c905f25a2eb.exp │ ├── 5cead07809bd.exp │ ├── 5d94317a9caf.exp │ ├── 5f7280660432.exp │ ├── 5fac09281e16.exp │ ├── 6123063912c4.exp │ ├── 62e733171577.exp │ ├── 6337afe649a4.exp │ ├── 63af15a082d3.exp │ ├── 6507cfc81d8a.exp │ ├── 65cdc3573773.exp │ ├── 67c4cdc4197f.exp │ ├── 680ebe4a200a.exp │ ├── 6822672c1e94.exp │ ├── 6a2ace81e12d.exp │ ├── 6a407de74761.exp │ ├── 6a4896c54f10.exp │ ├── 6c519034685c.exp │ ├── 6d3c51775c6d.exp │ ├── 711b92600397.exp │ ├── 71a3e5b1b51a.exp │ ├── 72b469f054ee.exp │ ├── 731c5d837abb.exp │ ├── 745c66c54c3e.exp │ ├── 76caf4f25eb7.exp │ ├── 77224349d139.exp │ ├── 78b278011bb2.exp │ ├── 7988935b77ae.exp │ ├── 7ab0c7ef5a02.exp │ ├── 7c9dd7c19f23.exp │ ├── 7ca765cabf3d.exp │ ├── 7d6e624206e1.exp │ ├── 7dfdf627104b.exp │ ├── 7e1267ee6c29.exp │ ├── 7e475b30fd72.exp │ ├── 809d516e9ce9.exp │ ├── 81aeed624df2.exp │ ├── 81e586a67c55.exp │ ├── 81fc6bbfbbf2.exp │ ├── 834c8155303d.exp │ ├── 844bebd9b0d3.exp │ ├── 84c955313baa.exp │ ├── 859dde324145.exp │ ├── 87b1f6afe9de.exp │ ├── 87b329a70a60.exp │ ├── 87f1541874e0.exp │ ├── 8834e784dfc4.exp │ ├── 884dd995c58a.exp │ ├── 887a65df632a.exp │ ├── 89937d7fb6db.exp │ ├── 89daa09b1cca.exp │ ├── 8a4a456b0b51.exp │ ├── 8af5929f90de.exp │ ├── 8b05b049dc1a.exp │ ├── 8b17fad0a0aa.exp │ ├── 8baed9eb20e0.exp │ ├── 8bcedadf97a4.exp │ ├── 8dbba7d10cbf.exp │ ├── 8e6c2736ea92.exp │ ├── 8e75812809a4.exp │ ├── 8ed4c13da206.exp │ ├── 905c3bc18036.exp │ ├── 90826c1a4a52.exp │ ├── 916b0605a070.exp │ ├── 948ebd6806cb.exp │ ├── 95026b2f9f49.exp │ ├── 954ddf0d8e5d.exp │ ├── 96c278f102c4.exp │ ├── 970efece4a06.exp │ ├── 98bac6679245.exp │ ├── 991d9b3d44d7.exp │ ├── 99d7959c56d8.exp │ ├── 9b2122b02892.exp │ ├── 9bb9f03ee494.exp │ ├── 9be94c1ce714.exp │ ├── 9c09e3e475a7.exp │ ├── 9c7d7d50b6e8.exp │ ├── 9d150efa4361.exp │ ├── 9db0645bde97.exp │ ├── 9efc8ebc649b.exp │ ├── 9f095e51b24c.exp │ ├── 9f54a1cea984.exp │ ├── 9fd07ae62f71.exp │ ├── a0bc40546517.exp │ ├── a0cd8d342548.exp │ ├── a187591d1ed4.exp │ ├── a3267df8a475.exp │ ├── a346e7cef63c.exp │ ├── a3c28361be34.exp │ ├── a5274cdb4b34.exp │ ├── a64ff039661b.exp │ ├── a75b5f95ef1a.exp │ ├── a77174f479c4.exp │ ├── a77b075c699c.exp │ ├── a9538cf70e1b.exp │ ├── aa079219384c.exp │ ├── ab2c2586b47f.exp │ ├── ad94061af9f3.exp │ ├── ade2ab00b27c.exp │ ├── ae6cdcd6c7d0.exp │ ├── ae79b5e146c8.exp │ ├── af479dc82d93.exp │ ├── b015a2c702cc.exp │ ├── b076a29a8064.exp │ ├── b4636c840539.exp │ ├── b4a025591215.exp │ ├── b56c2bdc2246.exp │ ├── b62577b9fa56.exp │ ├── b813dabcbaec.exp │ ├── b93a0bb507dd.exp │ ├── b9580dbf8dc1.exp │ ├── b9f70a3736c0.exp │ ├── ba3aefacd2b2.exp │ ├── bac00c15e220.exp │ ├── bc94c80b32fa.exp │ ├── bdd9e16fec8d.exp │ ├── bf0ed67458f1.exp │ ├── bf906a759a0c.exp │ ├── c08b5db4f1c0.exp │ ├── c177b50746f5.exp │ ├── c1b64ade8662.exp │ ├── c2e37b053996.exp │ ├── c35809afe2e1.exp │ ├── c3916f12d84d.exp │ ├── c3f0bc26a1a1.exp │ ├── c3f6e77f5b6b.exp │ ├── c7067322ec9b.exp │ ├── c845bd3ba402.exp │ ├── c9a3016628a3.exp │ ├── cc17feebb2be.exp │ ├── ccb0ef5a5944.exp │ ├── ccd49782f11d.exp │ ├── cdf3e613564c.exp │ ├── cee459e9f879.exp │ ├── cf0fe0554c88.exp │ ├── d01f6fab675e.exp │ ├── d20618e40723.exp │ ├── d34e3772a1ce.exp │ ├── d41ea67633f5.exp │ ├── d649cc1b7546.exp │ ├── d657ce92f616.exp │ ├── daa41640ab40.exp │ ├── dcfddeb5c183.exp │ ├── de04143d022b.exp │ ├── de24ebef06b2.exp │ ├── e1924e502841.exp │ ├── e2a873b7ab8c.exp │ ├── e315ab15c17a.exp │ ├── e364b0b6b545.exp │ ├── e400ef2ee8f5.exp │ ├── e58ae8a6e757.exp │ ├── e62aecbc3f09.exp │ ├── e67742901c66.exp │ ├── e6a3a0ffdecd.exp │ ├── e77e03ab9f57.exp │ ├── e7e939db4903.exp │ ├── e892f7fa9467.exp │ ├── e8aa2bcb2583.exp │ ├── e93075452cc5.exp │ ├── eb238fd7bdd5.exp │ ├── ee8386d6ecd1.exp │ ├── eff55f8e36af.exp │ ├── f04f557e2962.exp │ ├── f18dfca8694b.exp │ ├── f1c5cee984cd.exp │ ├── f1c90d40443d.exp │ ├── f3d95e1a1488.exp │ ├── f45a2c60b922.exp │ ├── f4b2a1358690.exp │ ├── f4f70fca7ecc.exp │ ├── f6bb70f92080.exp │ ├── f77825d264bd.exp │ ├── f83bbc51310d.exp │ ├── f8802ee6f41d.exp │ ├── fa3abb885d40.exp │ ├── fdcb4362cfe2.exp │ ├── feb19337f639.exp │ ├── ff07a0b0e867.exp │ └── ff82a6c9a1ce.exp ├── LICENSE ├── README.md ├── code ├── 333-27-mod2.exp ├── README.md ├── main.cpp ├── makefile ├── randompath.cpp ├── scheme.cpp └── scheme.hpp └── solutions ├── 223-11-mod0.exp ├── 223-11-mod0.m ├── 224-14-mod0.exp ├── 224-14-mod0.m ├── 225-18-mod0.exp ├── 225-18-mod0.m ├── 226-21-mod2.exp ├── 233-15-mod0.exp ├── 233-15-mod0.m ├── 234-20-mod0.exp ├── 234-20-mod0.m ├── 235-25-mod0.exp ├── 235-25-mod0.m ├── 236-30-mod2.exp ├── 244-26-mod0.exp ├── 244-26-mod0.m ├── 245-33-mod0.exp ├── 246-39-mod2.exp ├── 255-40-mod0.exp ├── 255-40-mod0.m ├── 256-48-mod2.exp ├── 266-56-mod0.m ├── 266-56-mod2.exp ├── 334-29-mod0.exp ├── 334-29-mod0.m ├── 335-36-mod0.exp ├── 335-36-mod0.m ├── 336-42-mod0.m ├── 336-42-mod2.exp ├── 344-38-mod0.exp ├── 344-38-mod0.m ├── 345-47-mod0.exp ├── 345-47-mod0.m ├── 346-56-mod0.m ├── 346-56-mod2.exp ├── 355-58-mod0.exp ├── 355-58-mod0.m ├── 356-71-mod0.m ├── 356-71-mod2.exp ├── 366-85-mod2.exp ├── 444-47-mod2.exp ├── 444-49-mod0.exp ├── 444-49-mod0.m ├── 445-60-mod2.exp ├── 445-60-mod2.m ├── 445-62-mod0.exp ├── 445-62-mod0.m ├── 446-74-mod0.m ├── 446-74-mod2.exp ├── 455-76-mod0.exp ├── 455-76-mod0.m ├── 456-93-mod0.m ├── 456-93-mod2.exp ├── 466-116-mod2.exp ├── 555-95-mod2.exp ├── 555-95-mod2.m ├── 555-97-mod0.exp ├── 555-97-mod0.m ├── 555-97-mod0a.exp ├── 555-97-mod0a.m ├── 556-116-mod0.m ├── 556-116-mod2.exp ├── 566-144-mod2.exp └── 666-164-mod2.exp /222flipgraph_rank8/vertices/00bc2f83230b.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a11)*(b12 + b22)*(c21 + c22) 4 | (a11 + a21)*(b11 + b12)*(c22) 5 | (a12)*(b11 + b21)*(c11) 6 | (a11 + a12)*(b22)*(c11 + c12 + c21 + c22) 7 | (a11 + a12)*(b11 + b22)*(c11 + c12 + c22) 8 | (a11 + a12 + a21 + a22)*(b11)*(c12 + c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/03e559862a37.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12 + b21 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a11 + a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/04ba29f8c345.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12 + c22) 4 | (a11)*(b11 + b12)*(c21) 5 | (a12)*(b21 + b22)*(c21 + c22) 6 | (a12)*(b11 + b21)*(c11 + c21) 7 | (a12 + a22)*(b21 + b22)*(c22) 8 | (a11 + a12)*(b11)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/04cfe2abcc68.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12 + c22) 4 | (a22)*(b21 + b22)*(c21 + c22) 5 | (a11)*(b11 + b12)*(c21) 6 | (a12)*(b11 + b21)*(c11 + c21) 7 | (a12 + a22)*(b21 + b22)*(c21) 8 | (a11 + a12)*(b11)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/077a98c6f42d.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a21 + a22)*(b11)*(c12 + c22) 3 | (a11)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a11)*(b11 + b12 + b21 + b22)*(c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c22) 6 | (a11 + a22)*(b11 + b21)*(c12) 7 | (a11 + a12)*(b21)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/07c5677256d3.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a21 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/089d6b7dd978.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12 + b21 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a11 + a12 + a21 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/09f24d2c9fa4.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c22) 4 | (a22)*(b11 + b21 + b22)*(c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/0baa2a6a6b21.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b11 + b12 + b21 + b22)*(c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c22) 6 | (a11 + a22)*(b11 + b21)*(c11 + c21 + c22) 7 | (a11 + a12)*(b21)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/0bea4915cc7f.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12 + a22)*(b21)*(c11) 7 | (a12 + a22)*(b12 + b22)*(c21) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/0c1b3588b233.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/0c6da92669c6.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c11 + c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c21 + c22) 6 | (a12)*(b11 + b12 + b21 + b22)*(c11) 7 | (a12 + a21)*(b11 + b12)*(c21) 8 | (a11 + a12)*(b11 + b12 + b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/0cfd8cf632bc.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12 + b21 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a21 + a22)*(b11)*(c12 + c21 + c22) 5 | (a11 + a21)*(b12)*(c21) 6 | (a12 + a21)*(b21 + b22)*(c21 + c22) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11 + c21 + c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/0f5c449e889b.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/10312effa91d.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12 + b21 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a21 + a22)*(b21 + b22)*(c11 + c21 + c22) 5 | (a21 + a22)*(b11)*(c12 + c21 + c22) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a21)*(b21 + b22)*(c11) 8 | (a12 + a22)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/10b35e3f01f5.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/11031c56d28a.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12)*(c22) 3 | (a22)*(b21 + b22)*(c22) 4 | (a22)*(b11 + b21)*(c11 + c12 + c22) 5 | (a21 + a22)*(b11)*(c12 + c22) 6 | (a11)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/11dbbe90cd18.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12 + c21 + c22) 5 | (a21 + a22)*(b11 + b12)*(c21 + c22) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/1297d43ef91b.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c12 + c21 + c22) 3 | (a22)*(b22)*(c11 + c22) 4 | (a22)*(b11 + b12 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11 + b12)*(c12) 6 | (a12)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12 + a21)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/1300359d84d3.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a22)*(b12 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c22) 6 | (a11 + a22)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/145907ae094b.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b11 + b21)*(c11 + c21 + c22) 5 | (a11)*(b11 + b12 + b21 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a11 + a12)*(b21)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/1561cef24f80.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a21)*(b22)*(c21) 8 | (a12 + a22)*(b21)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/15d00cad4147.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12)*(c21 + c22) 3 | (a22)*(b21 + b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 5 | (a21 + a22)*(b11)*(c12 + c21 + c22) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/17028e42c8a7.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12)*(c21 + c22) 3 | (a22)*(b21 + b22)*(c11 + c12) 4 | (a22)*(b11 + b22)*(c11 + c12 + c21 + c22) 5 | (a21 + a22)*(b11)*(c12 + c21 + c22) 6 | (a11 + a21)*(b12 + b21 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a11 + a12 + a21 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/1704ec06d3bf.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/1a3b413d83c5.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c12 + c21 + c22) 5 | (a21 + a22)*(b11 + b22)*(c12) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/1b248bb39567.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a22)*(b12 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c22) 6 | (a12 + a22)*(b21)*(c11) 7 | (a12 + a22)*(b12 + b22)*(c21) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/1baca944df60.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a11)*(b11)*(c11 + c12 + c21) 4 | (a11)*(b11 + b12 + b22)*(c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c22) 6 | (a11 + a21 + a22)*(b11)*(c12 + c22) 7 | (a12)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/1c8363f6f787.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12 + b21 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a11 + a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/1cc4bb81a020.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c21 + c22) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/1cf38b94effb.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/1df1283df99b.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b22)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b21 + b22)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12)*(c21 + c22) 6 | (a11 + a21)*(b12)*(c22) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/1e311a458044.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b12)*(c12 + c22) 5 | (a21 + a22)*(b11 + b12)*(c12) 6 | (a12 + a22)*(b21)*(c11) 7 | (a12 + a22)*(b12 + b22)*(c21) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/1eaaeb8d08b7.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b11 + b22)*(c11 + c21 + c22) 5 | (a11)*(b11 + b12)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a12)*(b21 + b22)*(c11) 8 | (a11 + a12)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/1fa190b8001b.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c12 + c22) 3 | (a22)*(b22)*(c11 + c22) 4 | (a22)*(b11 + b12 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11 + b12)*(c12) 6 | (a12)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/24dc3c24595b.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12)*(c21 + c22) 3 | (a22)*(b21 + b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 5 | (a21 + a22)*(b11)*(c12 + c21 + c22) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/28b4d0be523c.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c22) 6 | (a11 + a22)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/28d12bca9ccd.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c12 + c22) 5 | (a21 + a22)*(b11 + b22)*(c12) 6 | (a11 + a21)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/294994e98b98.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12 + b22)*(c21) 6 | (a12 + a22)*(b21)*(c11) 7 | (a11 + a12)*(b22)*(c21 + c22) 8 | (a11 + a12 + a21 + a22)*(b22)*(c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/2a52f180f866.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c11 + c12 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/2b67647c7cc3.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c12 + c21 + c22) 5 | (a21 + a22)*(b11 + b22)*(c12) 6 | (a11)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/2b8921173ab5.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b11 + b21)*(c11) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a11 + a12)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/2c688cf81f10.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12) 4 | (a22)*(b22)*(c22) 5 | (a11)*(b11 + b21)*(c11 + c21) 6 | (a11)*(b11 + b12 + b21 + b22)*(c21) 7 | (a11 + a12)*(b22)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/30ad198c3d6d.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b11 + b21)*(c11) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a11 + a12)*(b22)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/316a00005f10.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c11 + c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c22) 6 | (a12)*(b11 + b12 + b21 + b22)*(c11) 7 | (a11 + a12)*(b22)*(c21) 8 | (a11 + a12)*(b11 + b12 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/31e9565aba0a.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a21 + a22)*(b11 + b22)*(c22) 6 | (a11 + a21)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/3262f04d8926.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b11 + b21 + b22)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12)*(c21) 6 | (a12)*(b22)*(c11 + c12 + c21 + c22) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c11 + c12 + c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/3293992e6596.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11 + a21)*(b12)*(c21) 6 | (a12 + a21)*(b22)*(c21 + c22) 7 | (a12 + a22)*(b22)*(c11 + c22) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/3445b2f51289.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a11)*(b12 + b22)*(c21 + c22) 4 | (a11 + a21)*(b11 + b12)*(c22) 5 | (a12 + a22)*(b11 + b21)*(c11) 6 | (a11 + a12)*(b22)*(c11 + c12 + c21 + c22) 7 | (a11 + a12)*(b11 + b22)*(c11 + c12 + c22) 8 | (a11 + a12 + a21 + a22)*(b11)*(c12 + c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/349d8b4a1aea.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b22)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b21 + b22)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12)*(c21 + c22) 6 | (a11 + a21)*(b12)*(c22) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/363f70e89a53.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a21 + a22)*(b11)*(c12) 4 | (a11)*(b12 + b22)*(c21 + c22) 5 | (a11 + a21)*(b12)*(c22) 6 | (a11 + a22)*(b22)*(c21 + c22) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/38b741e8e591.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b11 + b21)*(c11 + c21 + c22) 5 | (a11)*(b11 + b12 + b21 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a11 + a12)*(b22)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/38f1392c831f.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12 + a22)*(b21)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c21) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/3a6321d957b6.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11)*(c12 + c22) 3 | (a22)*(b21)*(c12 + c22) 4 | (a22)*(b11 + b12 + b21 + b22)*(c11 + c22) 5 | (a21 + a22)*(b11 + b12)*(c22) 6 | (a12)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/3ab189e6b28f.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11 + a21)*(b12)*(c21) 6 | (a12)*(b22)*(c21 + c22) 7 | (a12 + a22)*(b22)*(c11 + c22) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/3ae47a16c388.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12) 4 | (a22)*(b22)*(c22) 5 | (a11)*(b11)*(c11) 6 | (a11)*(b12)*(c21) 7 | (a12)*(b21)*(c11 + c21) 8 | (a12)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/3c505e9c782e.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a12 + a22)*(b21)*(c11) 6 | (a12 + a22)*(b12 + b22)*(c21) 7 | (a11 + a12 + a22)*(b12)*(c21 + c22) 8 | (a11 + a12 + a21 + a22)*(b12)*(c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/3d1739f1a1d4.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12)*(c21) 7 | (a12)*(b22)*(c21) 8 | (a12 + a22)*(b21)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/3d206f7e54ce.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b11 + b21)*(c11) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a11 + a12)*(b21)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/3e755849d387.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c11 + c12 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/3ed9d19a14fd.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12)*(c21 + c22) 3 | (a22)*(b21 + b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 5 | (a21 + a22)*(b11)*(c12 + c21 + c22) 6 | (a12 + a22)*(b21)*(c11) 7 | (a12 + a22)*(b12 + b22)*(c21) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/3f952f32fa0f.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12)*(c21 + c22) 6 | (a11 + a21)*(b12)*(c22) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/3fcf94ebac99.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a21 + a22)*(b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b12 + b22)*(c22) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/40797d14a38e.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12 + a22)*(b21)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c21) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/41883f50367e.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c11 + c22) 2 | (a21)*(b11)*(c12 + c22) 3 | (a22)*(b21)*(c11 + c12) 4 | (a22)*(b11)*(c11 + c22) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a12 + a22)*(b21 + b22)*(c11) 8 | (a11 + a12)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/41f67daf7343.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12 + c21 + c22) 5 | (a21 + a22)*(b11 + b22)*(c21 + c22) 6 | (a12 + a22)*(b21)*(c11) 7 | (a12 + a22)*(b12 + b22)*(c21) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/435b0b02dcf6.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12 + b21 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a21 + a22)*(b21 + b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12 + c21 + c22) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/437e948af6fa.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12)*(c21 + c22) 6 | (a11 + a21)*(b12)*(c22) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/43fe66a87711.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c11 + c21 + c22) 5 | (a11)*(b11 + b12 + b22)*(c11) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a12)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/444df432f663.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a22)*(b12 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a12 + a22)*(b12 + b22)*(c11 + c21) 6 | (a12 + a22)*(b12 + b21 + b22)*(c11) 7 | (a11 + a12)*(b12)*(c21 + c22) 8 | (a11 + a12 + a21 + a22)*(b12)*(c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/446cbd116aa3.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c11 + c22) 2 | (a21)*(b22)*(c11 + c21) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a12 + a22)*(b21 + b22)*(c11) 8 | (a11 + a12 + a21)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/45b1d642db1f.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12 + c22) 4 | (a22)*(b21 + b22)*(c22) 5 | (a11)*(b11 + b21)*(c11 + c21) 6 | (a12)*(b11 + b12 + b21 + b22)*(c21) 7 | (a11 + a12)*(b21)*(c11 + c21) 8 | (a11 + a12)*(b11 + b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/45d820933ab8.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12) 4 | (a22)*(b22)*(c22) 5 | (a11)*(b11)*(c11 + c21) 6 | (a11)*(b11 + b12 + b21 + b22)*(c21) 7 | (a12)*(b21)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/47b76a6c4d83.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12 + c22) 4 | (a22)*(b21 + b22)*(c22) 5 | (a11)*(b12 + b22)*(c11 + c21) 6 | (a11)*(b11 + b12 + b21 + b22)*(c11) 7 | (a11 + a12)*(b21)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/485d4afca366.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a22)*(b12 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c22) 6 | (a11 + a22)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/48a58e13e747.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a22)*(b12 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c21 + c22) 6 | (a12 + a22)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/49de0ee2a726.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b11 + b21 + b22)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11 + a21)*(b12)*(c21) 6 | (a12)*(b22)*(c11 + c12 + c21 + c22) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c11 + c12 + c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/49ed84da18a3.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c11 + c21 + c22) 5 | (a12)*(b11 + b12 + b21 + b22)*(c11) 6 | (a12 + a21)*(b11 + b12)*(c22) 7 | (a11 + a12)*(b22)*(c21 + c22) 8 | (a11 + a12)*(b11 + b12 + b22)*(c11 + c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/4ab8bf04fa37.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a22)*(b11 + b22)*(c22) 5 | (a21 + a22)*(b11)*(c12 + c22) 6 | (a11)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/4d5b59649ae8.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/4d6d3848d4c5.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b11 + b21 + b22)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12)*(c21) 6 | (a12)*(b22)*(c11 + c12 + c21 + c22) 7 | (a12 + a22)*(b21)*(c12 + c22) 8 | (a12 + a22)*(b21 + b22)*(c11 + c12 + c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/502640c9e8a0.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12)*(c21 + c22) 3 | (a22)*(b11 + b22)*(c11 + c12 + c21 + c22) 4 | (a21 + a22)*(b11)*(c12 + c21 + c22) 5 | (a11 + a21)*(b12 + b21 + b22)*(c21) 6 | (a12 + a22)*(b21)*(c11 + c21) 7 | (a11 + a12 + a21)*(b21 + b22)*(c11 + c12) 8 | (a11 + a12 + a21 + a22)*(b21 + b22)*(c11 + c12 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/50b32572106a.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c11 + c22) 2 | (a22)*(b22)*(c11 + c21) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a12 + a22)*(b21 + b22)*(c11) 8 | (a11 + a12 + a22)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/53d7d7ebe129.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c11 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12 + c21 + c22) 5 | (a21 + a22)*(b11 + b22)*(c21 + c22) 6 | (a12 + a22)*(b12 + b21 + b22)*(c11) 7 | (a12 + a21 + a22)*(b12 + b22)*(c11 + c21) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/53f879f9f733.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/5689a55d3ab7.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/584435d909e2.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c11 + c22) 2 | (a22)*(b11 + b21)*(c11 + c21 + c22) 3 | (a22)*(b11 + b21)*(c12 + c21 + c22) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a12 + a22)*(b21 + b22)*(c11) 8 | (a11 + a12)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/58d673635bf3.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c11 + c21 + c22) 5 | (a11)*(b11 + b12 + b21 + b22)*(c11) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a11 + a12)*(b22)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/5958ced83f95.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a22)*(b12 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11 + a21)*(b12)*(c22) 6 | (a11 + a22)*(b12)*(c21 + c22) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/5988bd05931e.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a21)*(b11 + b12)*(c22) 3 | (a22)*(b11 + b21)*(c12) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a11)*(b11 + b22)*(c11 + c21 + c22) 6 | (a11)*(b11 + b12)*(c21) 7 | (a12)*(b21 + b22)*(c11) 8 | (a11 + a12)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/5a67763d4a8e.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c22) 6 | (a12 + a22)*(b21)*(c11) 7 | (a12 + a22)*(b12 + b22)*(c21) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/5a9d8ac8b556.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c11 + c21 + c22) 5 | (a11)*(b11 + b12 + b21 + b22)*(c11) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a11 + a12)*(b21)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/5b9794f78feb.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c22) 6 | (a11 + a22)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/5bd4c09a3772.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12)*(c21 + c22) 6 | (a11 + a21)*(b12)*(c22) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/5c905f25a2eb.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c12 + c21 + c22) 5 | (a21 + a22)*(b11 + b22)*(c12) 6 | (a11)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a21 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/5cead07809bd.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a21 + a22)*(b11)*(c12 + c22) 3 | (a11)*(b11 + b21)*(c11 + c12) 4 | (a11)*(b12 + b22)*(c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c22) 6 | (a11 + a22)*(b11 + b21)*(c12) 7 | (a11 + a12)*(b21)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/5d94317a9caf.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11 + a21)*(b12 + b22)*(c21) 6 | (a12 + a22)*(b21)*(c11) 7 | (a11 + a12 + a21)*(b22)*(c21 + c22) 8 | (a11 + a12 + a21 + a22)*(b22)*(c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/5f7280660432.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a22)*(b12 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a21 + a22)*(b11 + b12)*(c22) 6 | (a11 + a22)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/5fac09281e16.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c11 + c22) 2 | (a21)*(b11)*(c12 + c22) 3 | (a22)*(b21)*(c12 + c22) 4 | (a22)*(b11 + b21)*(c11 + c22) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a12 + a22)*(b21 + b22)*(c11) 8 | (a11 + a12)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/6123063912c4.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12 + a22)*(b21)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c21) 8 | (a11 + a12 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/62e733171577.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a11)*(b12 + b22)*(c21 + c22) 4 | (a11 + a21)*(b11 + b12)*(c22) 5 | (a12 + a22)*(b11 + b21)*(c11) 6 | (a11 + a12)*(b11)*(c11 + c12 + c21 + c22) 7 | (a11 + a12)*(b11 + b22)*(c21) 8 | (a11 + a12 + a21 + a22)*(b11)*(c12 + c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/6337afe649a4.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b21)*(c12 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c11 + c22) 4 | (a21 + a22)*(b11 + b12)*(c12) 5 | (a21 + a22)*(b11 + b12 + b21)*(c12 + c22) 6 | (a12)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/63af15a082d3.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12)*(c21) 6 | (a12)*(b22)*(c21 + c22) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/6507cfc81d8a.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/65cdc3573773.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12) 4 | (a22)*(b22)*(c22) 5 | (a11)*(b11 + b21)*(c11 + c21) 6 | (a11)*(b11 + b12 + b21 + b22)*(c21) 7 | (a11 + a12)*(b21)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/67c4cdc4197f.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a11)*(b12 + b22)*(c21 + c22) 4 | (a11 + a21)*(b11 + b12)*(c22) 5 | (a12)*(b11 + b21)*(c11) 6 | (a11 + a12)*(b11)*(c11 + c12 + c21 + c22) 7 | (a11 + a12)*(b11 + b22)*(c21) 8 | (a11 + a12 + a21 + a22)*(b11)*(c12 + c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/680ebe4a200a.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c22) 6 | (a11 + a22)*(b11 + b21)*(c11) 7 | (a11 + a12)*(b21)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/6822672c1e94.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c21 + c22) 6 | (a11 + a21)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/6a2ace81e12d.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11 + a21)*(b12)*(c22) 6 | (a11 + a22)*(b12)*(c21 + c22) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/6a407de74761.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11 + b22)*(c12) 5 | (a11 + a21)*(b12 + b22)*(c21) 6 | (a12 + a22)*(b21)*(c11) 7 | (a11 + a12)*(b22)*(c12 + c21 + c22) 8 | (a11 + a12 + a21 + a22)*(b22)*(c12 + c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/6a4896c54f10.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11)*(c12 + c22) 3 | (a22)*(b11 + b12 + b22)*(c12 + c22) 4 | (a22)*(b11 + b12 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11 + b12)*(c22) 6 | (a12)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/6c519034685c.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12 + c22) 4 | (a22)*(b21 + b22)*(c22) 5 | (a11)*(b11 + b21)*(c11 + c21) 6 | (a11)*(b11 + b12 + b21 + b22)*(c21) 7 | (a11 + a12)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/6d3c51775c6d.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12 + c22) 4 | (a22)*(b21 + b22)*(c22) 5 | (a11)*(b11)*(c11 + c21) 6 | (a11)*(b11 + b12)*(c21) 7 | (a12)*(b21)*(c11) 8 | (a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/711b92600397.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12) 4 | (a22)*(b22)*(c21 + c22) 5 | (a11)*(b11)*(c11 + c21) 6 | (a11)*(b11 + b12)*(c21) 7 | (a12)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/71a3e5b1b51a.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c11 + c12 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/72b469f054ee.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11 + a21)*(b12 + b22)*(c21) 6 | (a12 + a22)*(b21)*(c11) 7 | (a11 + a12)*(b22)*(c21 + c22) 8 | (a11 + a12 + a21 + a22)*(b22)*(c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/731c5d837abb.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12) 4 | (a22)*(b22)*(c22) 5 | (a11)*(b11 + b21)*(c11) 6 | (a11)*(b12 + b22)*(c21) 7 | (a11 + a12)*(b21)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/745c66c54c3e.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c21 + c22) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/76caf4f25eb7.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12)*(c21) 6 | (a12)*(b22)*(c21 + c22) 7 | (a12 + a22)*(b21)*(c11 + c22) 8 | (a12 + a22)*(b21 + b22)*(c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/77224349d139.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11)*(c12 + c21 + c22) 3 | (a22)*(b21)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b12 + b21 + b22)*(c11 + c21 + c22) 5 | (a21 + a22)*(b11 + b12)*(c21 + c22) 6 | (a12)*(b12 + b21 + b22)*(c11) 7 | (a12 + a22)*(b12 + b22)*(c11 + c21) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/78b278011bb2.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a21)*(b11 + b12)*(c22) 3 | (a22)*(b11 + b21)*(c12) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a11)*(b11 + b22)*(c11 + c22) 6 | (a11)*(b12 + b22)*(c21) 7 | (a12)*(b21 + b22)*(c11) 8 | (a11 + a12)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/7988935b77ae.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b21)*(c12 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c11 + c22) 4 | (a21 + a22)*(b21)*(c12) 5 | (a21 + a22)*(b11 + b12 + b21)*(c22) 6 | (a12)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/7ab0c7ef5a02.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c12 + c22) 5 | (a21 + a22)*(b11 + b22)*(c12) 6 | (a11)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/7c9dd7c19f23.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c12 + c22) 5 | (a21 + a22)*(b11 + b22)*(c12) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a21)*(b22)*(c21) 8 | (a12 + a22)*(b21)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/7ca765cabf3d.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/7d6e624206e1.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a12 + a22)*(b12 + b22)*(c11 + c21) 6 | (a12 + a22)*(b12 + b21 + b22)*(c11) 7 | (a11 + a12 + a22)*(b12)*(c21 + c22) 8 | (a11 + a12 + a21 + a22)*(b12)*(c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/7dfdf627104b.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c11 + c22) 2 | (a22)*(b11 + b21)*(c12 + c21) 3 | (a22)*(b11 + b21 + b22)*(c11 + c21) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a12 + a22)*(b21 + b22)*(c11) 8 | (a11 + a12 + a22)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/7e1267ee6c29.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/7e475b30fd72.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/809d516e9ce9.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c22) 6 | (a11 + a22)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/81aeed624df2.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12 + b22)*(c21) 6 | (a12 + a22)*(b21)*(c11) 7 | (a11 + a12)*(b22)*(c21 + c22) 8 | (a11 + a12 + a22)*(b22)*(c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/81e586a67c55.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b11 + b21)*(c11 + c21 + c22) 5 | (a11)*(b11 + b12 + b21 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a11 + a12)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/81fc6bbfbbf2.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/834c8155303d.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12 + c22) 4 | (a22)*(b21 + b22)*(c21 + c22) 5 | (a11)*(b11 + b21)*(c11 + c21) 6 | (a11)*(b11 + b12)*(c21) 7 | (a12 + a22)*(b21 + b22)*(c21) 8 | (a11 + a12)*(b21)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/844bebd9b0d3.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12 + b21 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b11 + b21 + b22)*(c21 + c22) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/84c955313baa.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/859dde324145.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c12 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c12 + c22) 5 | (a21 + a22)*(b11 + b12)*(c12) 6 | (a12)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/87b1f6afe9de.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12 + b21 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a21 + a22)*(b21 + b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12 + c21 + c22) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/87b329a70a60.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c22) 6 | (a12)*(b11 + b21)*(c11) 7 | (a11 + a12)*(b11)*(c11 + c21) 8 | (a11 + a12)*(b11 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/87f1541874e0.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a21 + a22)*(b11)*(c12 + c22) 3 | (a11)*(b12 + b22)*(c11 + c12 + c21 + c22) 4 | (a11)*(b11 + b12 + b21 + b22)*(c11 + c12) 5 | (a11 + a21)*(b11 + b12)*(c22) 6 | (a11 + a22)*(b11 + b21)*(c12) 7 | (a11 + a12)*(b21)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/8834e784dfc4.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12 + c22) 4 | (a22)*(b21 + b22)*(c22) 5 | (a11)*(b11 + b21)*(c11) 6 | (a11)*(b12 + b22)*(c21) 7 | (a11 + a12)*(b21)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/884dd995c58a.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12 + c22) 4 | (a22)*(b21 + b22)*(c22) 5 | (a11)*(b11 + b21)*(c11) 6 | (a11)*(b12 + b22)*(c21) 7 | (a11 + a12)*(b22)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/887a65df632a.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/89937d7fb6db.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12 + c22) 4 | (a22)*(b21 + b22)*(c22) 5 | (a11)*(b11)*(c11 + c21) 6 | (a11)*(b11 + b12)*(c21) 7 | (a12)*(b22)*(c11 + c21) 8 | (a12)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/89daa09b1cca.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c11 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12)*(c21) 7 | (a12)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/8a4a456b0b51.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c12 + c21 + c22) 5 | (a21 + a22)*(b11 + b22)*(c12) 6 | (a12 + a22)*(b21)*(c11) 7 | (a12 + a22)*(b12 + b22)*(c21) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/8af5929f90de.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c21 + c22) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/8b05b049dc1a.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a22)*(b12 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c22) 6 | (a12 + a22)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/8b17fad0a0aa.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a21 + a22)*(b11 + b12)*(c22) 6 | (a11 + a22)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/8baed9eb20e0.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12 + b21 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a21 + a22)*(b21 + b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12 + c21 + c22) 6 | (a11 + a21)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/8bcedadf97a4.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/8dbba7d10cbf.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/8e6c2736ea92.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c11 + c12 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/8e75812809a4.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c12 + c22) 3 | (a22)*(b22)*(c12 + c22) 4 | (a22)*(b11 + b12 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11 + b12)*(c12) 6 | (a12)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/8ed4c13da206.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c12 + c21 + c22) 5 | (a21 + a22)*(b11 + b22)*(c12) 6 | (a11 + a21)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/905c3bc18036.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c11 + c22) 2 | (a22)*(b21 + b22)*(c11 + c12) 3 | (a22)*(b11 + b22)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a12 + a22)*(b21 + b22)*(c11) 8 | (a11 + a12)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/90826c1a4a52.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c11 + c21 + c22) 5 | (a11)*(b11 + b12)*(c11) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a12)*(b21 + b22)*(c11) 8 | (a11 + a12)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/916b0605a070.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/948ebd6806cb.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12 + c21 + c22) 5 | (a21 + a22)*(b11 + b22)*(c21 + c22) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/95026b2f9f49.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c22) 4 | (a22)*(b11 + b21 + b22)*(c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/954ddf0d8e5d.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c11 + c21 + c22) 2 | (a21)*(b11 + b22)*(c11 + c21 + c22) 3 | (a22)*(b11 + b21)*(c12) 4 | (a21 + a22)*(b11)*(c11 + c12 + c21 + c22) 5 | (a11)*(b11 + b12)*(c21 + c22) 6 | (a11 + a21)*(b12 + b22)*(c22) 7 | (a12)*(b21 + b22)*(c11) 8 | (a11 + a12 + a21 + a22)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/96c278f102c4.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b11 + b21 + b22)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11 + a21)*(b12)*(c21) 6 | (a12)*(b22)*(c11 + c12 + c21 + c22) 7 | (a12 + a22)*(b22)*(c12 + c22) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/970efece4a06.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12)*(c21 + c22) 6 | (a11 + a21)*(b12)*(c22) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/98bac6679245.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12) 4 | (a22)*(b22)*(c21 + c22) 5 | (a11)*(b11 + b21)*(c11) 6 | (a11)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c21) 8 | (a11 + a12)*(b21)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/991d9b3d44d7.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12 + a22)*(b21)*(c11) 7 | (a12 + a22)*(b12 + b22)*(c21) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/99d7959c56d8.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b11 + b21 + b22)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11 + a21)*(b12)*(c21) 6 | (a12)*(b22)*(c11 + c12 + c21 + c22) 7 | (a12 + a22)*(b21)*(c12 + c22) 8 | (a12 + a22)*(b21 + b22)*(c11 + c12 + c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/9b2122b02892.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c11 + c12 + c21 + c22) 4 | (a22)*(b21 + b22)*(c22) 5 | (a11)*(b11)*(c11 + c21) 6 | (a11)*(b11 + b12 + b21 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/9bb9f03ee494.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a21 + a22)*(b11 + b22)*(c22) 6 | (a11)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/9be94c1ce714.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b12)*(c12 + c22) 5 | (a21 + a22)*(b11 + b12)*(c12) 6 | (a11 + a22)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/9c09e3e475a7.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b22)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b21 + b22)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12)*(c21 + c22) 6 | (a11 + a21)*(b12)*(c22) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/9c7d7d50b6e8.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c11 + c21 + c22) 5 | (a12)*(b11 + b12 + b21 + b22)*(c11) 6 | (a12 + a21)*(b11 + b12)*(c22) 7 | (a11 + a12)*(b22)*(c11 + c21) 8 | (a11 + a12)*(b11 + b12)*(c11 + c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/9d150efa4361.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a22)*(b12 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c21 + c22) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/9db0645bde97.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a21 + a22)*(b11)*(c12) 4 | (a11)*(b12 + b22)*(c21 + c22) 5 | (a11 + a21)*(b12 + b22)*(c22) 6 | (a12 + a22)*(b21)*(c11) 7 | (a11 + a12)*(b22)*(c21 + c22) 8 | (a11 + a12 + a21 + a22)*(b22)*(c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/9efc8ebc649b.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12) 4 | (a22)*(b22)*(c22) 5 | (a11)*(b11)*(c11 + c21) 6 | (a11)*(b11 + b12)*(c21) 7 | (a12)*(b22)*(c11 + c21) 8 | (a12)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/9f095e51b24c.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c11 + c12 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12)*(c21) 7 | (a12)*(b22)*(c21) 8 | (a12 + a22)*(b21)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/9f54a1cea984.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b11)*(c11 + c21 + c22) 5 | (a11)*(b11 + b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a12)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/9fd07ae62f71.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b11 + b22)*(c11) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a12)*(b21 + b22)*(c11) 8 | (a11 + a12)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/a0bc40546517.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/a0cd8d342548.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c21) 2 | (a22)*(b11 + b21)*(c12 + c21 + c22) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c11) 5 | (a12)*(b11 + b12 + b21 + b22)*(c11 + c21 + c22) 6 | (a12 + a21)*(b11 + b12)*(c22) 7 | (a12 + a22)*(b21 + b22)*(c21 + c22) 8 | (a11 + a12)*(b11 + b12 + b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/a187591d1ed4.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c22) 6 | (a12)*(b11 + b21)*(c11) 7 | (a11 + a12)*(b22)*(c11 + c21) 8 | (a11 + a12)*(b11 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/a3267df8a475.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12 + a22)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/a346e7cef63c.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12 + a22)*(b21)*(c11) 7 | (a12 + a22)*(b12 + b22)*(c21) 8 | (a11 + a12 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/a3c28361be34.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12)*(c21) 6 | (a12)*(b22)*(c21 + c22) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a21 + a22)*(b22)*(c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/a5274cdb4b34.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12) 4 | (a22)*(b22)*(c22) 5 | (a11)*(b11)*(c11) 6 | (a11)*(b12)*(c21) 7 | (a12)*(b21)*(c11) 8 | (a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/a64ff039661b.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a12 + a22)*(b21)*(c11) 6 | (a12 + a22)*(b12 + b22)*(c21) 7 | (a11 + a12)*(b12)*(c21 + c22) 8 | (a11 + a12 + a21 + a22)*(b12)*(c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/a75b5f95ef1a.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11 + a21)*(b12)*(c22) 6 | (a11 + a22)*(b12)*(c21 + c22) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/a77174f479c4.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/a77b075c699c.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c12 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c11 + c12) 4 | (a21 + a22)*(b11 + b12)*(c22) 5 | (a21 + a22)*(b11 + b12 + b22)*(c12 + c22) 6 | (a12)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/a9538cf70e1b.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c11 + c22) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c22) 6 | (a12 + a22)*(b21 + b22)*(c11) 7 | (a11 + a12)*(b22)*(c11 + c21) 8 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/aa079219384c.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c11 + c21 + c22) 5 | (a11)*(b11 + b12 + b21 + b22)*(c11) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a11 + a12)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/ab2c2586b47f.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/ad94061af9f3.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c22) 6 | (a11 + a22)*(b11 + b21)*(c11) 7 | (a11 + a12)*(b22)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/ade2ab00b27c.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c11 + c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c22) 6 | (a12)*(b11 + b12 + b21 + b22)*(c11) 7 | (a11 + a12)*(b11 + b12)*(c21) 8 | (a11 + a12)*(b11 + b12 + b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/ae6cdcd6c7d0.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a21)*(b11 + b12)*(c22) 3 | (a22)*(b11 + b21)*(c12) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a11)*(b12 + b22)*(c11 + c21 + c22) 6 | (a11)*(b11 + b12)*(c11 + c22) 7 | (a12)*(b21 + b22)*(c11) 8 | (a11 + a12)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/ae79b5e146c8.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a21 + a22)*(b11)*(c12 + c21 + c22) 4 | (a21 + a22)*(b11 + b22)*(c21 + c22) 5 | (a12 + a22)*(b12 + b22)*(c11 + c22) 6 | (a12 + a22)*(b12 + b21 + b22)*(c11) 7 | (a12 + a21 + a22)*(b12 + b22)*(c21 + c22) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/af479dc82d93.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/b015a2c702cc.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12)*(c21 + c22) 3 | (a22)*(b21 + b22)*(c11 + c12) 4 | (a22)*(b11 + b22)*(c11 + c12 + c21 + c22) 5 | (a21 + a22)*(b11)*(c12 + c21 + c22) 6 | (a11 + a21)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/b076a29a8064.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12 + a22)*(b21)*(c11) 7 | (a12 + a22)*(b12 + b22)*(c21) 8 | (a11 + a12 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/b4636c840539.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a21)*(b11 + b12 + b21 + b22)*(c11) 3 | (a22)*(b11 + b21)*(c12) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a11)*(b12 + b22)*(c11 + c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c11 + c22) 7 | (a12 + a21)*(b21 + b22)*(c11) 8 | (a11 + a12)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/b4a025591215.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c22) 6 | (a11 + a22)*(b11 + b22)*(c11) 7 | (a12 + a22)*(b21 + b22)*(c11) 8 | (a11 + a12)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/b56c2bdc2246.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c12 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/b62577b9fa56.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/b813dabcbaec.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a21 + a22)*(b22)*(c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b12 + b22)*(c22) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/b93a0bb507dd.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12 + a22)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/b9580dbf8dc1.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11 + a21)*(b12)*(c21) 6 | (a12)*(b22)*(c21 + c22) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/b9f70a3736c0.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a22)*(b12 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c21 + c22) 6 | (a11 + a21)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/ba3aefacd2b2.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b21)*(c12 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c11 + c22) 4 | (a21 + a22)*(b21)*(c12 + c22) 5 | (a21 + a22)*(b11 + b12)*(c22) 6 | (a12)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/bac00c15e220.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c22) 4 | (a22)*(b11 + b21 + b22)*(c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/bc94c80b32fa.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12) 4 | (a22)*(b22)*(c22) 5 | (a11)*(b11)*(c11 + c21) 6 | (a11)*(b11 + b12)*(c21) 7 | (a12)*(b21)*(c11 + c21) 8 | (a12)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/bdd9e16fec8d.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12 + c22) 4 | (a22)*(b21 + b22)*(c22) 5 | (a11)*(b12 + b22)*(c11 + c21) 6 | (a12)*(b11 + b12 + b21 + b22)*(c11) 7 | (a11 + a12)*(b22)*(c11 + c21) 8 | (a11 + a12)*(b11 + b12)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/bf0ed67458f1.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/bf906a759a0c.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c12 + c22) 3 | (a22)*(b11 + b12 + b21)*(c12 + c22) 4 | (a22)*(b11 + b12 + b21 + b22)*(c11 + c22) 5 | (a21 + a22)*(b11 + b12)*(c12) 6 | (a12)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/c08b5db4f1c0.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c11 + c21 + c22) 5 | (a12)*(b11 + b12 + b21 + b22)*(c11) 6 | (a12 + a21)*(b11 + b12)*(c22) 7 | (a11 + a12)*(b11 + b12)*(c21 + c22) 8 | (a11 + a12)*(b11 + b12 + b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/c177b50746f5.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a21 + a22)*(b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a12 + a22)*(b21)*(c11) 6 | (a12 + a22)*(b12 + b22)*(c22) 7 | (a12 + a21 + a22)*(b12 + b22)*(c21 + c22) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/c1b64ade8662.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12 + b21 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a21 + a22)*(b21 + b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12 + c21 + c22) 6 | (a12 + a22)*(b21)*(c11) 7 | (a12 + a22)*(b12 + b22)*(c21) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/c2e37b053996.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a21 + a22)*(b22)*(c12 + c22) 4 | (a21 + a22)*(b11 + b22)*(c12) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b12 + b22)*(c22) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/c35809afe2e1.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c12 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12)*(c21) 7 | (a12)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/c3916f12d84d.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a12 + a22)*(b12 + b22)*(c11 + c21) 6 | (a12 + a22)*(b12 + b21 + b22)*(c11) 7 | (a11 + a12)*(b12)*(c21 + c22) 8 | (a11 + a12 + a21 + a22)*(b12)*(c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/c3f0bc26a1a1.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c11 + c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c22) 6 | (a12)*(b11 + b12 + b21 + b22)*(c11) 7 | (a11 + a12)*(b22)*(c11 + c21) 8 | (a11 + a12)*(b11 + b12)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/c3f6e77f5b6b.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a21)*(b11 + b12)*(c11) 3 | (a22)*(b11 + b21)*(c12) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a11)*(b12 + b22)*(c11 + c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c11 + c22) 7 | (a12)*(b21 + b22)*(c11) 8 | (a11 + a12)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/c7067322ec9b.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a22)*(b12 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11 + a21)*(b12)*(c22) 6 | (a11 + a22)*(b12)*(c21 + c22) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/c845bd3ba402.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/c9a3016628a3.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a21 + a22)*(b11)*(c12) 4 | (a21 + a22)*(b12)*(c22) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a22)*(b12 + b22)*(c22) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/cc17feebb2be.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12 + a22)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/ccb0ef5a5944.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c11 + c22) 2 | (a22)*(b22)*(c12 + c21) 3 | (a22)*(b11 + b21 + b22)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a12 + a22)*(b21 + b22)*(c11) 8 | (a11 + a12 + a22)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/ccd49782f11d.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c11 + c12 + c21 + c22) 4 | (a11)*(b12 + b22)*(c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c22) 6 | (a12)*(b11 + b21)*(c11) 7 | (a11 + a12)*(b11 + b22)*(c21) 8 | (a11 + a12 + a21 + a22)*(b11)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/cdf3e613564c.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12 + c21 + c22) 5 | (a21 + a22)*(b11 + b22)*(c21 + c22) 6 | (a11)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/cee459e9f879.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12 + c22) 4 | (a22)*(b21 + b22)*(c22) 5 | (a11)*(b11 + b21)*(c11 + c21) 6 | (a11)*(b11 + b12 + b21 + b22)*(c21) 7 | (a11 + a12)*(b22)*(c11 + c21) 8 | (a11 + a12)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/cf0fe0554c88.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a21 + a22)*(b11 + b12)*(c22) 6 | (a11 + a22)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/d01f6fab675e.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/d20618e40723.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a21)*(b11 + b12)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c12) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a11)*(b11 + b22)*(c11 + c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c21) 7 | (a12)*(b21 + b22)*(c11) 8 | (a11 + a12)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/d34e3772a1ce.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12 + c22) 4 | (a22)*(b21 + b22)*(c22) 5 | (a11)*(b11 + b21)*(c11) 6 | (a12)*(b12 + b22)*(c21) 7 | (a11 + a12)*(b21)*(c11) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/d41ea67633f5.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/d649cc1b7546.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/d657ce92f616.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a22)*(b12 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a21 + a22)*(b11 + b12)*(c22) 6 | (a11 + a22)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/daa41640ab40.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a21 + a22)*(b11)*(c11 + c12 + c21 + c22) 4 | (a11)*(b12 + b22)*(c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c22) 6 | (a12 + a22)*(b11 + b21)*(c11) 7 | (a11 + a12)*(b11 + b22)*(c21) 8 | (a11 + a12 + a21 + a22)*(b11)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/dcfddeb5c183.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12 + c21 + c22) 5 | (a21 + a22)*(b11 + b22)*(c21 + c22) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/de04143d022b.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c11 + c22) 2 | (a21)*(b11)*(c12 + c22) 3 | (a22)*(b11)*(c12 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a12 + a22)*(b21 + b22)*(c11) 8 | (a11 + a12)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/de24ebef06b2.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a22)*(b12 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c21 + c22) 6 | (a12 + a22)*(b21)*(c11) 7 | (a12 + a22)*(b12 + b22)*(c21) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/e1924e502841.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a22)*(b12 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c22) 6 | (a11 + a22)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/e2a873b7ab8c.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12 + a22)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/e315ab15c17a.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11 + a21)*(b12)*(c21) 6 | (a12 + a21)*(b22)*(c21 + c22) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/e364b0b6b545.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/e400ef2ee8f5.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/e58ae8a6e757.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c11 + c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c11 + c22) 6 | (a12)*(b11 + b12 + b21 + b22)*(c11) 7 | (a12 + a21)*(b11 + b12)*(c11) 8 | (a11 + a12)*(b22)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/e62aecbc3f09.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/e67742901c66.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b12 + b22)*(c21 + c22) 5 | (a11 + a21)*(b11 + b12)*(c22) 6 | (a12 + a22)*(b11 + b21)*(c11) 7 | (a11 + a12)*(b11)*(c11 + c21) 8 | (a11 + a12)*(b11 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/e6a3a0ffdecd.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a12 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/e77e03ab9f57.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12 + c22) 5 | (a21 + a22)*(b11 + b12)*(c22) 6 | (a12 + a22)*(b21)*(c11) 7 | (a12 + a22)*(b12 + b22)*(c21) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/e7e939db4903.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a21 + a22)*(b11)*(c12) 4 | (a11)*(b12 + b22)*(c21 + c22) 5 | (a11 + a21)*(b12)*(c22) 6 | (a11 + a22)*(b22)*(c21 + c22) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/e892f7fa9467.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12 + b21 + b22)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12 + c22) 4 | (a21 + a22)*(b21 + b22)*(c22) 5 | (a21 + a22)*(b11)*(c12 + c22) 6 | (a11)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/e8aa2bcb2583.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11)*(b12 + b21 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a11 + a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/e93075452cc5.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b22)*(c21 + c22) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12 + a22)*(b21)*(c11) 7 | (a12 + a22)*(b12 + b22)*(c21) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/eb238fd7bdd5.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12 + b22)*(c21 + c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12 + c21 + c22) 5 | (a21 + a22)*(b11 + b22)*(c21 + c22) 6 | (a12 + a22)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/ee8386d6ecd1.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b11 + b21)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12)*(c21) 6 | (a12)*(b22)*(c21 + c22) 7 | (a12 + a22)*(b22)*(c11 + c22) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/eff55f8e36af.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12) 4 | (a22)*(b22)*(c21 + c22) 5 | (a11)*(b12)*(c21) 6 | (a12)*(b11 + b21)*(c11) 7 | (a12 + a22)*(b22)*(c21) 8 | (a11 + a12)*(b11)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/f04f557e2962.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/f18dfca8694b.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a22)*(b12 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c21 + c22) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/f1c5cee984cd.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12 + b21 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11 + c21) 8 | (a11 + a12 + a21 + a22)*(b21 + b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/f1c90d40443d.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11 + b22)*(c22) 2 | (a22)*(b11 + b21)*(c12) 3 | (a21 + a22)*(b11)*(c12 + c22) 4 | (a11)*(b11)*(c11) 5 | (a11)*(b12 + b22)*(c21 + c22) 6 | (a11 + a21)*(b11 + b12)*(c22) 7 | (a12)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/f3d95e1a1488.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12)*(c21 + c22) 3 | (a22)*(b21 + b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 5 | (a21 + a22)*(b11)*(c12 + c21 + c22) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/f45a2c60b922.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b11)*(c12) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b21)*(c12 + c22) 4 | (a22)*(b21 + b22)*(c22) 5 | (a11)*(b11 + b12 + b21 + b22)*(c11) 6 | (a12)*(b12 + b22)*(c11 + c21) 7 | (a11 + a12)*(b21 + b22)*(c11) 8 | (a11 + a12)*(b12)*(c11 + c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/f4b2a1358690.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/f4f70fca7ecc.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b12)*(c12 + c22) 5 | (a21 + a22)*(b11 + b12)*(c12) 6 | (a11 + a22)*(b12)*(c21) 7 | (a12 + a22)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/f6bb70f92080.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b22)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b21 + b22)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a12 + a22)*(b21)*(c11 + c21) 6 | (a12 + a22)*(b12 + b21 + b22)*(c21) 7 | (a11 + a12 + a22)*(b12)*(c21 + c22) 8 | (a11 + a12 + a21 + a22)*(b12)*(c22) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/f77825d264bd.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c22) 6 | (a12 + a22)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/f83bbc51310d.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b11 + b12)*(c21 + c22) 3 | (a22)*(b21 + b22)*(c21 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 5 | (a21 + a22)*(b11)*(c12 + c21 + c22) 6 | (a11 + a21)*(b12 + b22)*(c21) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12 + a21 + a22)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/f8802ee6f41d.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21 + b22)*(c21 + c22) 4 | (a21 + a22)*(b11)*(c12) 5 | (a21 + a22)*(b12)*(c21 + c22) 6 | (a12 + a22)*(b21)*(c11) 7 | (a12 + a22)*(b12 + b22)*(c21) 8 | (a11 + a12 + a21 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/fa3abb885d40.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a22)*(b11 + b21)*(c11 + c12) 3 | (a21 + a22)*(b11)*(c12) 4 | (a11)*(b12 + b22)*(c21 + c22) 5 | (a11 + a21)*(b12)*(c22) 6 | (a11 + a22)*(b22)*(c22) 7 | (a12 + a22)*(b21)*(c11) 8 | (a11 + a12)*(b22)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/fdcb4362cfe2.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c12 + c21 + c22) 3 | (a22)*(b11 + b12 + b21)*(c12 + c22) 4 | (a22)*(b11 + b12 + b21 + b22)*(c11 + c22) 5 | (a21 + a22)*(b11 + b12)*(c12) 6 | (a12)*(b12 + b22)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c11) 8 | (a11 + a12 + a21)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/feb19337f639.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b11 + b21 + b22)*(c11 + c12) 4 | (a21 + a22)*(b11)*(c12) 5 | (a11)*(b12)*(c21) 6 | (a12)*(b22)*(c11 + c12 + c21 + c22) 7 | (a12 + a22)*(b22)*(c12 + c22) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/ff07a0b0e867.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c22) 3 | (a22)*(b22)*(c11 + c12 + c21 + c22) 4 | (a22)*(b11 + b21 + b22)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a12 + a22)*(b21)*(c11 + c21) 7 | (a12 + a22)*(b12 + b21 + b22)*(c21) 8 | (a11 + a12 + a22)*(b12)*(c21) 9 | -------------------------------------------------------------------------------- /222flipgraph_rank8/vertices/ff82a6c9a1ce.exp: -------------------------------------------------------------------------------- 1 | (a11 + a22)*(b11)*(c11) 2 | (a21)*(b12)*(c21 + c22) 3 | (a22)*(b22)*(c11 + c22) 4 | (a22)*(b11 + b21)*(c11 + c12) 5 | (a21 + a22)*(b11)*(c12) 6 | (a11 + a21)*(b12)*(c21) 7 | (a12)*(b22)*(c11 + c21) 8 | (a12 + a22)*(b21 + b22)*(c11) 9 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Flip Graphs for Matrix Multiplication 2 | 3 | This repository contains the code and the data for the publication 4 | [http://arxiv.org/abs/2212.01175](http://arxiv.org/abs/2212.01175). 5 | 6 | 7 | # License 8 | 9 | The included program is free software: you can redistribute it and/or modify it under the 10 | terms of the GNU General Public License as published by the Free Software Foundation, either version 11 | 3 of the License, or (at yor option) any later version. 12 | 13 | The included program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; 14 | without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15 | GNU General Public License for more details. 16 | 17 | You should have received a copy of the GNU General Public License along with this program. If not, 18 | see . 19 | -------------------------------------------------------------------------------- /code/333-27-mod2.exp: -------------------------------------------------------------------------------- 1 | (a11)*(b11)*(c11) 2 | (a12)*(b21)*(c11) 3 | (a13)*(b31)*(c11) 4 | (a11)*(b12)*(c21) 5 | (a12)*(b22)*(c21) 6 | (a13)*(b32)*(c21) 7 | (a11)*(b13)*(c31) 8 | (a12)*(b23)*(c31) 9 | (a13)*(b33)*(c31) 10 | (a21)*(b11)*(c12) 11 | (a22)*(b21)*(c12) 12 | (a23)*(b31)*(c12) 13 | (a21)*(b12)*(c22) 14 | (a22)*(b22)*(c22) 15 | (a23)*(b32)*(c22) 16 | (a21)*(b13)*(c32) 17 | (a22)*(b23)*(c32) 18 | (a23)*(b33)*(c32) 19 | (a31)*(b11)*(c13) 20 | (a32)*(b21)*(c13) 21 | (a33)*(b31)*(c13) 22 | (a31)*(b12)*(c23) 23 | (a32)*(b22)*(c23) 24 | (a33)*(b32)*(c23) 25 | (a31)*(b13)*(c33) 26 | (a32)*(b23)*(c33) 27 | (a33)*(b33)*(c33) -------------------------------------------------------------------------------- /code/README.md: -------------------------------------------------------------------------------- 1 | # Compilation 2 | 3 | The code can be compiled using the included makefile. 4 | 5 | # Input 6 | 7 | Input files must be in exp format, see the file 333-27-mod2.exp or the schemes directory for an 8 | example. 9 | 10 | # Usage 11 | 12 | ./flip filename.exp n m p pathlength restart 13 | 14 | If n=m=p then m and p can be omitted. 15 | 16 | The parameter pathlength sets a limit for the number of flips before aborting. The parameter restart 17 | can be set to 0 or 1, Setting it to 0 will produce a scheme of rank one less than the input scheme, 18 | setting it to 1 will restart the search procedure everytime a reduction is found, with the newly 19 | found scheme as input until no reduction is found within the given limit on the pathlength. 20 | 21 | # Example 22 | 23 | Try: 24 | 25 | ./flip 333-27-mod2.exp 3 1000000 1 26 | -------------------------------------------------------------------------------- /code/main.cpp: -------------------------------------------------------------------------------- 1 | /**************** 2 | Copyright 2022 Jakob Moosbauer 3 | 4 | 5 | This program is free software: you can redistribute it and/or modify 6 | it under the terms of the GNU General Public License as published by 7 | the Free Software Foundation, either version 3 of the License, or 8 | (at your option) any later version. 9 | 10 | This program is distributed in the hope that it will be useful, 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | GNU General Public License for more details. 14 | 15 | You should have received a copy of the GNU General Public License 16 | along with this program. If not, see . 17 | 18 | ******************/ 19 | 20 | # include "scheme.hpp" 21 | 22 | int main(int argc, char* argv[]){ 23 | debug("debugging enabled"); 24 | 25 | int n,m,l; 26 | int pathlength; 27 | int tries; 28 | 29 | if(argc == 5){ 30 | n=m=l=(*argv[2]-'0'); 31 | pathlength = strtol(argv[3],NULL,10); 32 | tries = strtol(argv[4],NULL,10); 33 | } 34 | else if(argc == 7){ 35 | n=*argv[2]-'0'; 36 | m=*argv[3]-'0'; 37 | l=*argv[4]-'0'; 38 | pathlength = strtol(argv[5],NULL,10); 39 | tries = strtol(argv[6],NULL,10); 40 | } 41 | else{ 42 | cerr << "Wrong number of arguments. Usage: " << endl; 43 | cerr << argv[0] << " or" << endl; 44 | cerr << argv[0] << " " << endl; 45 | return 1; 46 | } 47 | 48 | string filename = argv[1]; 49 | 50 | Scheme s = Scheme(filename,n,m,l); 51 | 52 | int oldrank = s.rank; 53 | 54 | if(!s.check()){ 55 | cerr << "Opened incorrect scheme: " << filename << endl; 56 | return 1; 57 | } 58 | 59 | struct timespec ts; 60 | clock_gettime(CLOCK_MONOTONIC, &ts); 61 | long seed = (long)ts.tv_nsec; 62 | 63 | 64 | int steps = -1; 65 | int stepsum = 0; 66 | 67 | if(tries == 0){ 68 | stepsum = s.randompath(pathlength,seed); 69 | } 70 | else{ 71 | do { 72 | for(int i = 0; i < tries; ++i){ 73 | steps = s.randompath(pathlength, seed); 74 | if(steps >= 0){ 75 | stepsum += steps; 76 | break; 77 | } 78 | } 79 | } 80 | while(steps >= 0); 81 | } 82 | 83 | #ifdef DEBUG 84 | if(!s.check()){ 85 | string newfilename = s.newfilename(); 86 | s.write("errors/" + newfilename); 87 | cerr << "Found incorrect scheme. Incorrect scheme name written to errorlog.txt" << endl; 88 | mylog(filename + "," + "errors/" + newfilename + "," + to_string(steps) + ", seed:" + to_string(seed)); 89 | return 1; 90 | } 91 | #endif 92 | 93 | if(steps==-5){ 94 | cerr << "Reduction not possible, scheme was not saved. Information written to errorlog.txt" << endl; 95 | return 1; 96 | } 97 | 98 | #ifdef CONTROL 99 | if(steps==-6){ 100 | mylog("Found undetected reduction."); 101 | } 102 | #endif 103 | 104 | if(stepsum > 0){ 105 | string newfilename = s.newfilename(); 106 | s.write(newfilename); 107 | cout << newfilename << "," << s.rank << endl; 108 | writelog(filename, newfilename, stepsum, oldrank, s.rank); 109 | } 110 | return 0; 111 | } 112 | -------------------------------------------------------------------------------- /code/makefile: -------------------------------------------------------------------------------- 1 | all: scheme.cpp scheme.hpp randompath.cpp main.cpp 2 | g++ -o flip scheme.cpp randompath.cpp main.cpp 3 | -------------------------------------------------------------------------------- /code/scheme.hpp: -------------------------------------------------------------------------------- 1 | /**************** 2 | Copyright 2022 Jakob Moosbauer 3 | 4 | 5 | This program is free software: you can redistribute it and/or modify 6 | it under the terms of the GNU General Public License as published by 7 | the Free Software Foundation, either version 3 of the License, or 8 | (at your option) any later version. 9 | 10 | This program is distributed in the hope that it will be useful, 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | GNU General Public License for more details. 14 | 15 | You should have received a copy of the GNU General Public License 16 | along with this program. If not, see . 17 | 18 | ******************/ 19 | 20 | #ifndef scheme_hpp___ 21 | #define scheme_hpp___ 22 | 23 | #include 24 | #include 25 | #include 26 | #include 27 | #include 28 | #include 29 | #include 30 | #include 31 | #include 32 | #include 33 | #include 34 | #include 35 | #include 36 | 37 | #define get(matrix,m,i,j) matrix&(((mat)1)<<(m*(i-1)+j-1)) 38 | #define set(matrix,m,i,j) matrix = matrix|(((mat)1)<<(m*(i-1)+j-1)) 39 | #define unset(matrix,m,i,j) matrix = matrix&~(((mat)1)<<(m*(i-1)+j-1)) 40 | 41 | #ifdef EXPECT 42 | #define ife(expr) if(__builtin_expect(expr,false)) 43 | #define assume(expr) __builtin_assume(expr) 44 | #else 45 | #define ife(expr) if(expr) 46 | #define assume(expr) do {} while(0) 47 | #endif 48 | 49 | #ifdef DEBUG2 50 | #define DEBUG 51 | #endif 52 | 53 | #ifdef DEBUG3 54 | #define DEBUG 55 | #endif 56 | 57 | #ifdef DEBUG 58 | #define debug(msg) cout << msg << endl 59 | #else 60 | #define debug(msg) do {} while(0) 61 | #endif 62 | 63 | using namespace std; 64 | 65 | typedef unsigned long long mat; 66 | 67 | static const int plus1mod3[] = {1,2,0}; 68 | static const int plus2mod3[] = {2,0,1}; 69 | 70 | class Flip{ 71 | public: 72 | int col; 73 | int row1; 74 | int row2; 75 | 76 | Flip(int, int, int); 77 | }; 78 | 79 | class Scheme{ 80 | public: 81 | int n; 82 | int m; 83 | int l; 84 | int rank; 85 | mat** rows; 86 | 87 | Flip lastFlip; 88 | 89 | Scheme(string filename, int n); 90 | Scheme(string filename, int n, int m, int l); 91 | Scheme(const Scheme &scheme); 92 | 93 | ~Scheme(); 94 | 95 | void write(string filename); 96 | void writetoconsole(); 97 | 98 | string newfilename(); 99 | 100 | vector findFlips(); 101 | 102 | void flip(int col, int row1, int row2); 103 | void flip(Flip f); 104 | 105 | bool check(mat p, mat q, mat t, int b, int c, int a, int i, unordered_multimap cpos); 106 | bool reduce3rows(mat*, mat*, mat*, int, int , int); 107 | bool reduce4rows(mat*, mat*, mat*, mat*, mat, int, int, int, int); 108 | void reduce(mat*, mat*, unordered_multimap::iterator, mat, int, int, int, int, int j); 109 | 110 | bool reduce(); 111 | 112 | int randompath(int steps, long seed); 113 | void randompathwithoutreduction(int steps); 114 | 115 | bool check(); 116 | }; 117 | 118 | void parseMatrix(string s, char x, int m, mat* matrix); 119 | void writeMatrix(ostream &output, char x, int n, int m, mat matrix); 120 | 121 | void writelog(string, string, int, int, int); 122 | 123 | void gauss(mat*, int); 124 | void gauss2(mat*, int); 125 | void gauss(mat*, int*, int); 126 | 127 | void mylog(string); 128 | 129 | bool operator==(const Flip& f1, const Flip& f2); 130 | 131 | #endif 132 | -------------------------------------------------------------------------------- /solutions/223-11-mod0.exp: -------------------------------------------------------------------------------- 1 | (-a21)*(-b11+b13)*c12 2 | a12*b21*(c11+c12) 3 | (-a11+a12+a21-a22)*b12*(c21+2*c22) 4 | (a12-a22)*(-b21+b23)*c12 5 | (-2*a11+2*a12+a21-a22)*(b22+b23)*(c21+c22) 6 | a11*b13*(-c11+2*c12+c31+2*c32) 7 | a12*b23*(-c21-c22+c31+c32) 8 | (a12-a22)*(b12+b22)*(c12-c22+c32) 9 | (-2*a11+a21)*(b12+b13+b22+b23)*(c12+c32) 10 | (2*a11-a12-a21+a22)*(b12+b22+b23)*(c12+c21+c22+c32) 11 | a11*(b11+b13)*c11 12 | -------------------------------------------------------------------------------- /solutions/223-11-mod0.m: -------------------------------------------------------------------------------- 1 | {{{{0, 0}, {-1, 0}}, {{-1, 0, 1}, {0, 0, 0}}, {{0, 1}, {0, 0}, {0, 0}}}, 2 | {{{0, 1}, {0, 0}}, {{0, 0, 0}, {1, 0, 0}}, {{1, 1}, {0, 0}, {0, 0}}}, 3 | {{{-1, 1}, {1, -1}}, {{0, 1, 0}, {0, 0, 0}}, {{0, 0}, {1, 2}, {0, 0}}}, 4 | {{{0, 1}, {0, -1}}, {{0, 0, 0}, {-1, 0, 1}}, {{0, 1}, {0, 0}, {0, 0}}}, 5 | {{{-2, 2}, {1, -1}}, {{0, 0, 0}, {0, 1, 1}}, {{0, 0}, {1, 1}, {0, 0}}}, 6 | {{{1, 0}, {0, 0}}, {{0, 0, 1}, {0, 0, 0}}, {{-1, 2}, {0, 0}, {1, 2}}}, 7 | {{{0, 1}, {0, 0}}, {{0, 0, 0}, {0, 0, 1}}, {{0, 0}, {-1, -1}, {1, 1}}}, 8 | {{{0, 1}, {0, -1}}, {{0, 1, 0}, {0, 1, 0}}, {{0, 1}, {0, -1}, {0, 1}}}, 9 | {{{-2, 0}, {1, 0}}, {{0, 1, 1}, {0, 1, 1}}, {{0, 1}, {0, 0}, {0, 1}}}, 10 | {{{2, -1}, {-1, 1}}, {{0, 1, 0}, {0, 1, 1}}, {{0, 1}, {1, 1}, {0, 1}}}, 11 | {{{1, 0}, {0, 0}}, {{1, 0, 1}, {0, 0, 0}}, {{1, 0}, {0, 0}, {0, 0}}}} 12 | -------------------------------------------------------------------------------- /solutions/224-14-mod0.exp: -------------------------------------------------------------------------------- 1 | (-a11+2*a12+a21-2*a22)*(b12+b13+b14)*(-c11-2*c21+c31) 2 | (a11-a12)*(b12+2*b13)*(-c11-c21+c31) 3 | (a11-a12)*(-b11-b13+b14)*(-c11-2*c21+c31+c41) 4 | (-a12)*(-2*b11+b12+2*b14-2*b21+b22+2*b24)*(-c21-c22+c31+c32) 5 | (a12+a21-2*a22)*(-b12-b21+b24)*(-2*c21-c22+c31+c32+c41) 6 | (a21-a22)*(2*b14+b24)*(-c12-2*c22+c32+c42) 7 | (a11-2*a12-a21+2*a22)*(b11+b13)*(-2*c21+c31+c41) 8 | a12*(-b11+b12+b13+b14-b21+b22+b23+b24)*(c31+c32) 9 | (-a21+a22)*(2*b11+2*b14+b21+b24)*(-c12-c22+c32) 10 | (-a12+a22)*(-4*b11+2*b12-2*b13+2*b14-2*b21+b22-b23+b24)*c22 11 | (-a12+a22)*(2*b11+2*b13+b21+b23)*(c22+c32) 12 | (-a21+2*a22)*(-b11+b14-b21+b24)*(-2*c21-2*c22+c31+c32+c41+c42) 13 | (-a21+2*a22)*(b11+b21)*(c11+c12+c41+c42) 14 | (a12+a21-2*a22)*(b11+b12+b13+b14+b21)*(c11+c32+c41) 15 | -------------------------------------------------------------------------------- /solutions/224-14-mod0.m: -------------------------------------------------------------------------------- 1 | {{{{-1, 2}, {1, -2}}, {{0, 1, 1, 1}, {0, 0, 0, 0}}, 2 | {{-1, 0}, {-2, 0}, {1, 0}, {0, 0}}}, {{{1, -1}, {0, 0}}, 3 | {{0, 1, 2, 0}, {0, 0, 0, 0}}, {{-1, 0}, {-1, 0}, {1, 0}, {0, 0}}}, 4 | {{{1, -1}, {0, 0}}, {{-1, 0, -1, 1}, {0, 0, 0, 0}}, 5 | {{-1, 0}, {-2, 0}, {1, 0}, {1, 0}}}, {{{0, -1}, {0, 0}}, 6 | {{-2, 1, 0, 2}, {-2, 1, 0, 2}}, {{0, 0}, {-1, -1}, {1, 1}, {0, 0}}}, 7 | {{{0, 1}, {1, -2}}, {{0, -1, 0, 0}, {-1, 0, 0, 1}}, 8 | {{0, 0}, {-2, -1}, {1, 1}, {1, 0}}}, {{{0, 0}, {1, -1}}, 9 | {{0, 0, 0, 2}, {0, 0, 0, 1}}, {{0, -1}, {0, -2}, {0, 1}, {0, 1}}}, 10 | {{{1, -2}, {-1, 2}}, {{1, 0, 1, 0}, {0, 0, 0, 0}}, 11 | {{0, 0}, {-2, 0}, {1, 0}, {1, 0}}}, {{{0, 1}, {0, 0}}, 12 | {{-1, 1, 1, 1}, {-1, 1, 1, 1}}, {{0, 0}, {0, 0}, {1, 1}, {0, 0}}}, 13 | {{{0, 0}, {-1, 1}}, {{2, 0, 0, 2}, {1, 0, 0, 1}}, 14 | {{0, -1}, {0, -1}, {0, 1}, {0, 0}}}, {{{0, -1}, {0, 1}}, 15 | {{-4, 2, -2, 2}, {-2, 1, -1, 1}}, {{0, 0}, {0, 1}, {0, 0}, {0, 0}}}, 16 | {{{0, -1}, {0, 1}}, {{2, 0, 2, 0}, {1, 0, 1, 0}}, 17 | {{0, 0}, {0, 1}, {0, 1}, {0, 0}}}, {{{0, 0}, {-1, 2}}, 18 | {{-1, 0, 0, 1}, {-1, 0, 0, 1}}, {{0, 0}, {-2, -2}, {1, 1}, {1, 1}}}, 19 | {{{0, 0}, {-1, 2}}, {{1, 0, 0, 0}, {1, 0, 0, 0}}, 20 | {{1, 1}, {0, 0}, {0, 0}, {1, 1}}}, {{{0, 1}, {1, -2}}, 21 | {{1, 1, 1, 1}, {1, 0, 0, 0}}, {{1, 0}, {0, 0}, {0, 1}, {1, 0}}}} 22 | -------------------------------------------------------------------------------- /solutions/225-18-mod0.exp: -------------------------------------------------------------------------------- 1 | (a11+a12+a21)*(-2*b12+b13-2*b14+b15)*c31 2 | (-a11-a12)*(-b11-b14+b15)*c11 3 | (-a12-a22)*(-b24+b25)*(-c12-c22+c42) 4 | (-a12)*(2*b12-b13+2*b14-b15+b22+b23+b24+b25)*(c21-c22-c31-c51+c52) 5 | a22*(b22+b23+b24+b25)*c32 6 | a12*(b11-b12+b14-b15-b21+b22-b24+b25)*(c11-c12+c21-c22-c41+c42) 7 | (-a12+a21)*(-b11+b12-b14+b15+b21+b24)*(-2*c11+c12+c41-c42-c51+c52) 8 | (-a11-a12)*b12*(-c21-c31+c41+c51) 9 | (a12-a21)*(b12+b22+b24+b25)*(-c11-c22-c31+c41+c52) 10 | (-a11-a21)*(-b14+b15)*(-c11+2*c31+c41) 11 | a12*(-b11+2*b12-b13+b14+b21+b22+b23+2*b24)*(c21-c22-c51+c52) 12 | a21*(b13+b22+b24+b25)*(-2*c11+2*c12-c31+c32+c41-c42-c51+c52) 13 | (-a21)*(-2*b11+b12+2*b13-b14+b15+2*b21+b22+3*b24+b25)*(-c11+c12-c51+c52) 14 | (a21+a22)*(b22+b24+b25)*(-c12-c22-c32+c42+c52) 15 | (-a12-a22)*(b22+b24)*(-c12-2*c22+c42+c52) 16 | a21*(-b11+b12+b13+b15+b21+b24)*(-c41+c42-c51+c52) 17 | (a21+a22)*(b21+b24)*c12 18 | (a11+a21)*(b12+b15)*(c31+c41+c51) 19 | -------------------------------------------------------------------------------- /solutions/225-18-mod0.m: -------------------------------------------------------------------------------- 1 | {{{{1, 1}, {1, 0}}, {{0, -2, 1, -2, 1}, {0, 0, 0, 0, 0}}, 2 | {{0, 0}, {0, 0}, {1, 0}, {0, 0}, {0, 0}}}, 3 | {{{-1, -1}, {0, 0}}, {{-1, 0, 0, -1, 1}, {0, 0, 0, 0, 0}}, 4 | {{1, 0}, {0, 0}, {0, 0}, {0, 0}, {0, 0}}}, 5 | {{{0, -1}, {0, -1}}, {{0, 0, 0, 0, 0}, {0, 0, 0, -1, 1}}, 6 | {{0, -1}, {0, -1}, {0, 0}, {0, 1}, {0, 0}}}, 7 | {{{0, -1}, {0, 0}}, {{0, 2, -1, 2, -1}, {0, 1, 1, 1, 1}}, 8 | {{0, 0}, {1, -1}, {-1, 0}, {0, 0}, {-1, 1}}}, 9 | {{{0, 0}, {0, 1}}, {{0, 0, 0, 0, 0}, {0, 1, 1, 1, 1}}, 10 | {{0, 0}, {0, 0}, {0, 1}, {0, 0}, {0, 0}}}, 11 | {{{0, 1}, {0, 0}}, {{1, -1, 0, 1, -1}, {-1, 1, 0, -1, 1}}, 12 | {{1, -1}, {1, -1}, {0, 0}, {-1, 1}, {0, 0}}}, 13 | {{{0, -1}, {1, 0}}, {{-1, 1, 0, -1, 1}, {1, 0, 0, 1, 0}}, 14 | {{-2, 1}, {0, 0}, {0, 0}, {1, -1}, {-1, 1}}}, 15 | {{{-1, -1}, {0, 0}}, {{0, 1, 0, 0, 0}, {0, 0, 0, 0, 0}}, 16 | {{0, 0}, {-1, 0}, {-1, 0}, {1, 0}, {1, 0}}}, 17 | {{{0, 1}, {-1, 0}}, {{0, 1, 0, 0, 0}, {0, 1, 0, 1, 1}}, 18 | {{-1, 0}, {0, -1}, {-1, 0}, {1, 0}, {0, 1}}}, 19 | {{{-1, 0}, {-1, 0}}, {{0, 0, 0, -1, 1}, {0, 0, 0, 0, 0}}, 20 | {{-1, 0}, {0, 0}, {2, 0}, {1, 0}, {0, 0}}}, 21 | {{{0, 1}, {0, 0}}, {{-1, 2, -1, 1, 0}, {1, 1, 1, 2, 0}}, 22 | {{0, 0}, {1, -1}, {0, 0}, {0, 0}, {-1, 1}}}, 23 | {{{0, 0}, {1, 0}}, {{0, 0, 1, 0, 0}, {0, 1, 0, 1, 1}}, 24 | {{-2, 2}, {0, 0}, {-1, 1}, {1, -1}, {-1, 1}}}, 25 | {{{0, 0}, {-1, 0}}, {{-2, 1, 2, -1, 1}, {2, 1, 0, 3, 1}}, 26 | {{-1, 1}, {0, 0}, {0, 0}, {0, 0}, {-1, 1}}}, 27 | {{{0, 0}, {1, 1}}, {{0, 0, 0, 0, 0}, {0, 1, 0, 1, 1}}, 28 | {{0, -1}, {0, -1}, {0, -1}, {0, 1}, {0, 1}}}, 29 | {{{0, -1}, {0, -1}}, {{0, 0, 0, 0, 0}, {0, 1, 0, 1, 0}}, 30 | {{0, -1}, {0, -2}, {0, 0}, {0, 1}, {0, 1}}}, 31 | {{{0, 0}, {1, 0}}, {{-1, 1, 1, 0, 1}, {1, 0, 0, 1, 0}}, 32 | {{0, 0}, {0, 0}, {0, 0}, {-1, 1}, {-1, 1}}}, 33 | {{{0, 0}, {1, 1}}, {{0, 0, 0, 0, 0}, {1, 0, 0, 1, 0}}, 34 | {{0, 1}, {0, 0}, {0, 0}, {0, 0}, {0, 0}}}, 35 | {{{1, 0}, {1, 0}}, {{0, 1, 0, 0, 1}, {0, 0, 0, 0, 0}}, 36 | {{0, 0}, {0, 0}, {1, 0}, {1, 0}, {1, 0}}}} 37 | -------------------------------------------------------------------------------- /solutions/226-21-mod2.exp: -------------------------------------------------------------------------------- 1 | (a21)*(b15+b16+b25+b26)*(c11+c12+c31+c32+c41+c42+c61+c62) 2 | (a12+a22)*(b22)*(c12+c22+c42+c52+c62) 3 | (a21)*(b11+b13+b14+b15+b16+b21+b23+b24+b25+b26)*(c11+c12+c31+c32+c41+c42+c51+c52+c61+c62) 4 | (a12+a21)*(b11+b12+b14+b21+b24)*(c11+c12+c21+c22+c31+c42+c51+c52+c62) 5 | (a12)*(b11+b13+b14+b16+b21+b23+b24+b26)*(c11+c12+c21+c22+c41+c42+c51+c52+c61+c62) 6 | (a12)*(b14+b16+b24+b26)*(c11+c12+c41+c42) 7 | (a11+a12)*(b14+b16)*(c41) 8 | (a11+a21)*(b11)*(c11+c31+c41+c51+c61) 9 | (a12+a22)*(b21+b25)*(c52+c62) 10 | (a12)*(b12+b13+b16+b22+b23+b26)*(c21+c22) 11 | (a11+a21)*(b11+b12+b15)*(c21+c41+c61) 12 | (a21+a22)*(b21+b24+b25+b26)*(c32+c62) 13 | (a21+a22)*(b21+b24)*(c42+c62) 14 | (a21)*(b11+b14+b21+b24)*(c11+c12+c21+c22+c31+c32) 15 | (a12+a22)*(b21+b22)*(c12+c42+c52+c62) 16 | (a11+a21)*(b11+b15)*(c21+c41+c51+c61) 17 | (a11+a12)*(b11+b13)*(c31+c41+c61) 18 | (a12+a21)*(b14+b16+b21+b24+b25+b26)*(c11+c12+c31+c41+c42+c61) 19 | (a11+a12)*(b12+b13+b16)*(c41+c61) 20 | (a12+a21)*(b12+b13+b16+b23+b25+b26)*(c11+c12+c31+c41+c42+c51+c52+c61+c62) 21 | (a21+a22)*(b21+b23+b24+b25+b26)*(c32) 22 | -------------------------------------------------------------------------------- /solutions/233-15-mod0.exp: -------------------------------------------------------------------------------- 1 | (a11+a12)*b13*(-c11+c31) 2 | (-a11+a13+a21+a22-a23)*(-b11+b12+b21)*(c11+c12+c22) 3 | (a11+a12-a13-a21-a22+a23)*(b13+b21)*c11 4 | (a12-a13-a22+a23)*(-b13+b23)*(-c21+c31) 5 | (a11-a13-a21+a23)*(-b11+b21)*(c12+c22) 6 | a22*(b11-b21+b22+b32)*c22 7 | a12*(-b13+b22+b23)*c21 8 | (a22-a23)*(b12+b32)*(-c21-c22+c31+c32) 9 | (a11-a13)*b12*(c11+c12+c21+c22) 10 | (-a13-a22+a23)*(b12+b13-b23+b32)*(-c21+c31+c32) 11 | (-a13+a23)*(b11+b23+b31+b33)*c32 12 | (-a21-a22)*(b11+b31)*(-c12+c32) 13 | a13*(b12+b32+b33)*(c31+c32) 14 | (-a21-a22+a23)*(b12+b31)*(c11+c12) 15 | (a13+a21+a22-a23)*(b11+b13+b31)*(c11+c32) 16 | -------------------------------------------------------------------------------- /solutions/233-15-mod0.m: -------------------------------------------------------------------------------- 1 | {{{{1, 1, 0}, {0, 0, 0}}, {{0, 0, 1}, {0, 0, 0}, {0, 0, 0}}, 2 | {{-1, 0}, {0, 0}, {1, 0}}}, {{{-1, 0, 1}, {1, 1, -1}}, 3 | {{-1, 1, 0}, {1, 0, 0}, {0, 0, 0}}, {{1, 1}, {0, 1}, {0, 0}}}, 4 | {{{1, 1, -1}, {-1, -1, 1}}, {{0, 0, 1}, {1, 0, 0}, {0, 0, 0}}, 5 | {{1, 0}, {0, 0}, {0, 0}}}, {{{0, 1, -1}, {0, -1, 1}}, 6 | {{0, 0, -1}, {0, 0, 1}, {0, 0, 0}}, {{0, 0}, {-1, 0}, {1, 0}}}, 7 | {{{1, 0, -1}, {-1, 0, 1}}, {{-1, 0, 0}, {1, 0, 0}, {0, 0, 0}}, 8 | {{0, 1}, {0, 1}, {0, 0}}}, {{{0, 0, 0}, {0, 1, 0}}, 9 | {{1, 0, 0}, {-1, 1, 0}, {0, 1, 0}}, {{0, 0}, {0, 1}, {0, 0}}}, 10 | {{{0, 1, 0}, {0, 0, 0}}, {{0, 0, -1}, {0, 1, 1}, {0, 0, 0}}, 11 | {{0, 0}, {1, 0}, {0, 0}}}, {{{0, 0, 0}, {0, 1, -1}}, 12 | {{0, 1, 0}, {0, 0, 0}, {0, 1, 0}}, {{0, 0}, {-1, -1}, {1, 1}}}, 13 | {{{1, 0, -1}, {0, 0, 0}}, {{0, 1, 0}, {0, 0, 0}, {0, 0, 0}}, 14 | {{1, 1}, {1, 1}, {0, 0}}}, {{{0, 0, -1}, {0, -1, 1}}, 15 | {{0, 1, 1}, {0, 0, -1}, {0, 1, 0}}, {{0, 0}, {-1, 0}, {1, 1}}}, 16 | {{{0, 0, -1}, {0, 0, 1}}, {{1, 0, 0}, {0, 0, 1}, {1, 0, 1}}, 17 | {{0, 0}, {0, 0}, {0, 1}}}, {{{0, 0, 0}, {-1, -1, 0}}, 18 | {{1, 0, 0}, {0, 0, 0}, {1, 0, 0}}, {{0, -1}, {0, 0}, {0, 1}}}, 19 | {{{0, 0, 1}, {0, 0, 0}}, {{0, 1, 0}, {0, 0, 0}, {0, 1, 1}}, 20 | {{0, 0}, {0, 0}, {1, 1}}}, {{{0, 0, 0}, {-1, -1, 1}}, 21 | {{0, 1, 0}, {0, 0, 0}, {1, 0, 0}}, {{1, 1}, {0, 0}, {0, 0}}}, 22 | {{{0, 0, 1}, {1, 1, -1}}, {{1, 0, 1}, {0, 0, 0}, {1, 0, 0}}, 23 | {{1, 0}, {0, 0}, {0, 1}}}} 24 | -------------------------------------------------------------------------------- /solutions/234-20-mod0.exp: -------------------------------------------------------------------------------- 1 | (a11-a13)*(-b12+b13)*(c11+c12+c31+c32) 2 | (a11-a21)*(-b11-b12+b13)*c22 3 | (-a12-2*a13)*(-b22+b23)*(-c11-c31+c41) 4 | (-a13-a22-a23)*(b11-b21+b22-b23+b31)*(-c11+c32+c41) 5 | a13*(b13+b22-2*b23+b33)*(-c21-c22+c31+c32) 6 | (-a11+a13-a22-a23)*(b11-b13+b22)*(-c11-c12-c22-c32+c41) 7 | (-a11+a13)*(-b12+b22)*(c11+c12+c21+c22+c31+c32) 8 | (a11-a13-a21+a23)*(-2*b11+b13-b14+b21-b22+b24)*(c12+c32) 9 | (-a13+a23)*(b21+b22-b23-b31-b32+b33)*(c22+2*c32) 10 | (a11+a12+a13-a21-a22-a23)*(b21-b22+b24)*c41 11 | a13*(b12+b13-2*b23+b32+b33)*(c21+c22) 12 | (a13-a21-a22-a23)*(b11+b14-2*b21+b22-2*b24+b31+b34)*(-c22-c32+c41) 13 | (-a22-2*a23)*(2*b11-b13+b14-2*b21+b22-b24+b31)*(-c12-c32+c42) 14 | (a21+a22+a23)*(2*b11-b13+2*b14-2*b21+b22-2*b24+b31+b34)*(c41+c42) 15 | (a12+a13-a22-a23)*(-b21-b22+b23)*(-c11+c41) 16 | (a13-a23)*(2*b11-b13+b14-b21+3*b22-b23-2*b24-2*b32+b33+b34)*(c22+c32) 17 | (-a21-a22)*(2*b11-b13+b14-2*b21+b22-2*b24+b31+b34)*(c22+c32+c42) 18 | (a22+a23)*(2*b11-b13-2*b21+b22+b31)*(-c11-c12+c41+c42) 19 | (-a11+a13+a21+a22+a23)*(-b11+b13-b14+b21-b22+b24)*(c12+c32+c41) 20 | (a11+a12)*b22*(c21+c31+c41) 21 | -------------------------------------------------------------------------------- /solutions/234-20-mod0.m: -------------------------------------------------------------------------------- 1 | {{{{1, 0, -1}, {0, 0, 0}}, {{0, -1, 1, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, 2 | {{1, 1}, {0, 0}, {1, 1}, {0, 0}}}, {{{1, 0, 0}, {-1, 0, 0}}, 3 | {{-1, -1, 1, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, 4 | {{0, 0}, {0, 1}, {0, 0}, {0, 0}}}, {{{0, -1, -2}, {0, 0, 0}}, 5 | {{0, 0, 0, 0}, {0, -1, 1, 0}, {0, 0, 0, 0}}, {{-1, 0}, {0, 0}, {-1, 0}, 6 | {1, 0}}}, {{{0, 0, -1}, {0, -1, -1}}, {{1, 0, 0, 0}, {-1, 1, -1, 0}, 7 | {1, 0, 0, 0}}, {{-1, 0}, {0, 0}, {0, 1}, {1, 0}}}, 8 | {{{0, 0, 1}, {0, 0, 0}}, {{0, 0, 1, 0}, {0, 1, -2, 0}, {0, 0, 1, 0}}, 9 | {{0, 0}, {-1, -1}, {1, 1}, {0, 0}}}, {{{-1, 0, 1}, {0, -1, -1}}, 10 | {{1, 0, -1, 0}, {0, 1, 0, 0}, {0, 0, 0, 0}}, {{-1, -1}, {0, -1}, {0, -1}, 11 | {1, 0}}}, {{{-1, 0, 1}, {0, 0, 0}}, {{0, -1, 0, 0}, {0, 1, 0, 0}, 12 | {0, 0, 0, 0}}, {{1, 1}, {1, 1}, {1, 1}, {0, 0}}}, 13 | {{{1, 0, -1}, {-1, 0, 1}}, {{-2, 0, 1, -1}, {1, -1, 0, 1}, {0, 0, 0, 0}}, 14 | {{0, 1}, {0, 0}, {0, 1}, {0, 0}}}, {{{0, 0, -1}, {0, 0, 1}}, 15 | {{0, 0, 0, 0}, {1, 1, -1, 0}, {-1, -1, 1, 0}}, 16 | {{0, 0}, {0, 1}, {0, 2}, {0, 0}}}, {{{1, 1, 1}, {-1, -1, -1}}, 17 | {{0, 0, 0, 0}, {1, -1, 0, 1}, {0, 0, 0, 0}}, {{0, 0}, {0, 0}, {0, 0}, 18 | {1, 0}}}, {{{0, 0, 1}, {0, 0, 0}}, {{0, 1, 1, 0}, {0, 0, -2, 0}, 19 | {0, 1, 1, 0}}, {{0, 0}, {1, 1}, {0, 0}, {0, 0}}}, 20 | {{{0, 0, 1}, {-1, -1, -1}}, {{1, 0, 0, 1}, {-2, 1, 0, -2}, {1, 0, 0, 1}}, 21 | {{0, 0}, {0, -1}, {0, -1}, {1, 0}}}, {{{0, 0, 0}, {0, -1, -2}}, 22 | {{2, 0, -1, 1}, {-2, 1, 0, -1}, {1, 0, 0, 0}}, 23 | {{0, -1}, {0, 0}, {0, -1}, {0, 1}}}, {{{0, 0, 0}, {1, 1, 1}}, 24 | {{2, 0, -1, 2}, {-2, 1, 0, -2}, {1, 0, 0, 1}}, 25 | {{0, 0}, {0, 0}, {0, 0}, {1, 1}}}, {{{0, 1, 1}, {0, -1, -1}}, 26 | {{0, 0, 0, 0}, {-1, -1, 1, 0}, {0, 0, 0, 0}}, 27 | {{-1, 0}, {0, 0}, {0, 0}, {1, 0}}}, {{{0, 0, 1}, {0, 0, -1}}, 28 | {{2, 0, -1, 1}, {-1, 3, -1, -2}, {0, -2, 1, 1}}, 29 | {{0, 0}, {0, 1}, {0, 1}, {0, 0}}}, {{{0, 0, 0}, {-1, -1, 0}}, 30 | {{2, 0, -1, 1}, {-2, 1, 0, -2}, {1, 0, 0, 1}}, 31 | {{0, 0}, {0, 1}, {0, 1}, {0, 1}}}, {{{0, 0, 0}, {0, 1, 1}}, 32 | {{2, 0, -1, 0}, {-2, 1, 0, 0}, {1, 0, 0, 0}}, 33 | {{-1, -1}, {0, 0}, {0, 0}, {1, 1}}}, {{{-1, 0, 1}, {1, 1, 1}}, 34 | {{-1, 0, 1, -1}, {1, -1, 0, 1}, {0, 0, 0, 0}}, 35 | {{0, 1}, {0, 0}, {0, 1}, {1, 0}}}, {{{1, 1, 0}, {0, 0, 0}}, 36 | {{0, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0, 0}}, {{0, 0}, {1, 0}, {1, 0}, 37 | {1, 0}}}} 38 | -------------------------------------------------------------------------------- /solutions/235-25-mod0.exp: -------------------------------------------------------------------------------- 1 | (-a11-a13)*(-b12+b14-b22+b24)*(c11-c41+c51) 2 | (a11-a12-a13)*(-b12-b21-b22+b24+b25)*c11 3 | (-a11+a13+a22)*(-b11-b13+b15-b21+b25)*(-c12+c31+c32) 4 | (a12-a22)*b23*c31 5 | (-a12-a13)*(b12+b22)*(c11-c21-c41+c51) 6 | (a11-a13)*(-b11+b15-b21+b25)*(-c11-c12+c31+c32) 7 | (-a13)*(-b11+b12-b14+b15-2*b24-b31+b32+b34+b35)*(c11+c12-c21-c22+c31+c32+c51+c52) 8 | (a21+a23)*(-b22-b25+b32+b35)*(c12-c42+c52) 9 | (-a21)*(-b15-b22-b25+b32+b35)*(c11+c12+c51+c52) 10 | (a11-a12-a13-a21+a22+a23)*(b22+b25)*(c22+c42) 11 | a13*(-b11+b12-b14+b15+b22-2*b24-b31+b34+b35)*(c11+c12-c21-c22+c31+c32+c41+c42+c51+c52) 12 | (-a11+a12+a21-a22)*(-b22+b24)*(c11+c41) 13 | (a13-a23)*(-b13-b22-b25-b33+b34+b35)*(c12-c22+c32-c42+c52) 14 | (-a22)*(-b11+b15-b21-b22-b23+b25+b32+b33)*(c31+c32) 15 | (a11-a12-a13)*b12*(c11+c21+c22+c41+c42) 16 | (-a11+a13+a21-a23)*b13*(-c12+c32) 17 | (-a13+a21-a22)*(-b11+b15+b22-b24-b31+b35)*(c11+c41+c42) 18 | (-a21+a22)*(-b11+b15-b31+b35)*(c11+c12+c41+c42) 19 | (-a22-a23)*(b13-b22-b25+b32+b33)*(c12-c22-c42+c52) 20 | (-a13+a23)*(-b22-b25+b34+b35)*(c12-c22+c32+c52) 21 | (a13+a21)*(-b12+b14-2*b22+b24-b25+b32+b35)*(c11+c42+c51) 22 | (a21-a22-a23)*(b13-b31+b35)*c12 23 | (a13+a22)*(b13-b22+b32+b33)*(c12-c22+c31+c32-c42+c52) 24 | (a11-a21)*(b14+b15+b24+b25)*(c11+c51) 25 | (-a11+a12+a13+a21)*(b12+b22+b25)*(c11+c22+c42+c51) 26 | -------------------------------------------------------------------------------- /solutions/235-25-mod0.m: -------------------------------------------------------------------------------- 1 | {{{{-1, 0, -1}, {0, 0, 0}}, {{0, -1, 0, 1, 0}, {0, -1, 0, 1, 0}, 2 | {0, 0, 0, 0, 0}}, {{1, 0}, {0, 0}, {0, 0}, {-1, 0}, {1, 0}}}, 3 | {{{1, -1, -1}, {0, 0, 0}}, {{0, -1, 0, 0, 0}, {-1, -1, 0, 1, 1}, 4 | {0, 0, 0, 0, 0}}, {{1, 0}, {0, 0}, {0, 0}, {0, 0}, {0, 0}}}, 5 | {{{-1, 0, 1}, {0, 1, 0}}, {{-1, 0, -1, 0, 1}, {-1, 0, 0, 0, 1}, 6 | {0, 0, 0, 0, 0}}, {{0, -1}, {0, 0}, {1, 1}, {0, 0}, {0, 0}}}, 7 | {{{0, 1, 0}, {0, -1, 0}}, {{0, 0, 0, 0, 0}, {0, 0, 1, 0, 0}, 8 | {0, 0, 0, 0, 0}}, {{0, 0}, {0, 0}, {1, 0}, {0, 0}, {0, 0}}}, 9 | {{{0, -1, -1}, {0, 0, 0}}, {{0, 1, 0, 0, 0}, {0, 1, 0, 0, 0}, 10 | {0, 0, 0, 0, 0}}, {{1, 0}, {-1, 0}, {0, 0}, {-1, 0}, {1, 0}}}, 11 | {{{1, 0, -1}, {0, 0, 0}}, {{-1, 0, 0, 0, 1}, {-1, 0, 0, 0, 1}, 12 | {0, 0, 0, 0, 0}}, {{-1, -1}, {0, 0}, {1, 1}, {0, 0}, {0, 0}}}, 13 | {{{0, 0, -1}, {0, 0, 0}}, {{-1, 1, 0, -1, 1}, {0, 0, 0, -2, 0}, 14 | {-1, 1, 0, 1, 1}}, {{1, 1}, {-1, -1}, {1, 1}, {0, 0}, {1, 1}}}, 15 | {{{0, 0, 0}, {1, 0, 1}}, {{0, 0, 0, 0, 0}, {0, -1, 0, 0, -1}, 16 | {0, 1, 0, 0, 1}}, {{0, 1}, {0, 0}, {0, 0}, {0, -1}, {0, 1}}}, 17 | {{{0, 0, 0}, {-1, 0, 0}}, {{0, 0, 0, 0, -1}, {0, -1, 0, 0, -1}, 18 | {0, 1, 0, 0, 1}}, {{1, 1}, {0, 0}, {0, 0}, {0, 0}, {1, 1}}}, 19 | {{{1, -1, -1}, {-1, 1, 1}}, {{0, 0, 0, 0, 0}, {0, 1, 0, 0, 1}, 20 | {0, 0, 0, 0, 0}}, {{0, 0}, {0, 1}, {0, 0}, {0, 1}, {0, 0}}}, 21 | {{{0, 0, 1}, {0, 0, 0}}, {{-1, 1, 0, -1, 1}, {0, 1, 0, -2, 0}, 22 | {-1, 0, 0, 1, 1}}, {{1, 1}, {-1, -1}, {1, 1}, {1, 1}, {1, 1}}}, 23 | {{{-1, 1, 0}, {1, -1, 0}}, {{0, 0, 0, 0, 0}, {0, -1, 0, 1, 0}, 24 | {0, 0, 0, 0, 0}}, {{1, 0}, {0, 0}, {0, 0}, {1, 0}, {0, 0}}}, 25 | {{{0, 0, 1}, {0, 0, -1}}, {{0, 0, -1, 0, 0}, {0, -1, 0, 0, -1}, 26 | {0, 0, -1, 1, 1}}, {{0, 1}, {0, -1}, {0, 1}, {0, -1}, {0, 1}}}, 27 | {{{0, 0, 0}, {0, -1, 0}}, {{-1, 0, 0, 0, 1}, {-1, -1, -1, 0, 1}, 28 | {0, 1, 1, 0, 0}}, {{0, 0}, {0, 0}, {1, 1}, {0, 0}, {0, 0}}}, 29 | {{{1, -1, -1}, {0, 0, 0}}, {{0, 1, 0, 0, 0}, {0, 0, 0, 0, 0}, 30 | {0, 0, 0, 0, 0}}, {{1, 0}, {1, 1}, {0, 0}, {1, 1}, {0, 0}}}, 31 | {{{-1, 0, 1}, {1, 0, -1}}, {{0, 0, 1, 0, 0}, {0, 0, 0, 0, 0}, 32 | {0, 0, 0, 0, 0}}, {{0, -1}, {0, 0}, {0, 1}, {0, 0}, {0, 0}}}, 33 | {{{0, 0, -1}, {1, -1, 0}}, {{-1, 0, 0, 0, 1}, {0, 1, 0, -1, 0}, 34 | {-1, 0, 0, 0, 1}}, {{1, 0}, {0, 0}, {0, 0}, {1, 1}, {0, 0}}}, 35 | {{{0, 0, 0}, {-1, 1, 0}}, {{-1, 0, 0, 0, 1}, {0, 0, 0, 0, 0}, 36 | {-1, 0, 0, 0, 1}}, {{1, 1}, {0, 0}, {0, 0}, {1, 1}, {0, 0}}}, 37 | {{{0, 0, 0}, {0, -1, -1}}, {{0, 0, 1, 0, 0}, {0, -1, 0, 0, -1}, 38 | {0, 1, 1, 0, 0}}, {{0, 1}, {0, -1}, {0, 0}, {0, -1}, {0, 1}}}, 39 | {{{0, 0, -1}, {0, 0, 1}}, {{0, 0, 0, 0, 0}, {0, -1, 0, 0, -1}, 40 | {0, 0, 0, 1, 1}}, {{0, 1}, {0, -1}, {0, 1}, {0, 0}, {0, 1}}}, 41 | {{{0, 0, 1}, {1, 0, 0}}, {{0, -1, 0, 1, 0}, {0, -2, 0, 1, -1}, 42 | {0, 1, 0, 0, 1}}, {{1, 0}, {0, 0}, {0, 0}, {0, 1}, {1, 0}}}, 43 | {{{0, 0, 0}, {1, -1, -1}}, {{0, 0, 1, 0, 0}, {0, 0, 0, 0, 0}, 44 | {-1, 0, 0, 0, 1}}, {{0, 1}, {0, 0}, {0, 0}, {0, 0}, {0, 0}}}, 45 | {{{0, 0, 1}, {0, 1, 0}}, {{0, 0, 1, 0, 0}, {0, -1, 0, 0, 0}, 46 | {0, 1, 1, 0, 0}}, {{0, 1}, {0, -1}, {1, 1}, {0, -1}, {0, 1}}}, 47 | {{{1, 0, 0}, {-1, 0, 0}}, {{0, 0, 0, 1, 1}, {0, 0, 0, 1, 1}, 48 | {0, 0, 0, 0, 0}}, {{1, 0}, {0, 0}, {0, 0}, {0, 0}, {1, 0}}}, 49 | {{{-1, 1, 1}, {1, 0, 0}}, {{0, 1, 0, 0, 0}, {0, 1, 0, 0, 1}, 50 | {0, 0, 0, 0, 0}}, {{1, 0}, {0, 1}, {0, 0}, {0, 1}, {1, 0}}}} 51 | -------------------------------------------------------------------------------- /solutions/236-30-mod2.exp: -------------------------------------------------------------------------------- 1 | (a11+a21)*(b15+b25+b35)*(c21+c31+c51) 2 | (a13)*(b21+b22+b23+b24+b25+b26+b31+b32+b33+b34+b35+b36)*(c41+c42) 3 | (a13+a23)*(b11+b12+b14+b15+b16+b21+b22+b24+b25+b26+b31+b32+b34+b35+b36)*(c12+c22+c62) 4 | (a11+a13)*(b25+b35)*(c31+c41+c51+c61) 5 | (a21+a22+a23)*(b13+b15+b16+b23+b25+b26+b31+b32+b35)*(c12+c42) 6 | (a12+a13)*(b11+b21+b22+b23+b26+b32+b33+b36)*(c11+c12+c41+c42+c51+c52+c61+c62) 7 | (a12+a13+a21+a22)*(b11+b12+b14+b15+b16+b21+b22+b24+b26+b35)*(c21+c22+c31+c42+c52+c62) 8 | (a21+a23)*(b11+b12+b13+b14+b21+b22+b23+b24)*(c12+c62) 9 | (a13)*(b21+b22+b23+b26+b31+b32+b33+b36)*(c11+c12+c21+c22+c41+c42+c61+c62) 10 | (a13+a21+a22)*(b11+b12+b14+b15+b16+b23+b33)*(c12+c21+c22+c31+c62) 11 | (a21+a22)*(b13+b15+b16+b21+b22+b23+b26+b31+b32+b35)*(c21+c22+c61+c62) 12 | (a13+a21+a22)*(b11+b12+b13+b14+b21+b22+b23+b25+b31+b32+b33+b35)*(c12+c21+c22+c42+c61+c62) 13 | (a11+a21)*(b12+b13+b16+b22+b23+b26+b32+b33+b36)*(c21+c41) 14 | (a13+a23)*(b11+b12+b13+b14+b21+b22+b23+b24+b31+b32+b33+b34)*(c12+c22+c42+c62) 15 | (a11+a12+a21+a22)*(b13+b15+b16+b22+b23+b25+b26+b32+b33+b35+b36)*(c21+c61) 16 | (a12+a13+a22+a23)*(b13+b15+b16+b23+b25+b26+b32+b33+b35+b36)*(c12+c22) 17 | (a11+a13)*(b22+b23+b26+b32+b33+b36)*(c11+c61) 18 | (a21)*(b11+b12+b13+b16+b21+b22+b23+b26)*(c31+c32+c41+c42+c51+c52) 19 | (a11+a12+a21+a22)*(b11+b12+b14+b15+b16+b25+b35)*(c31+c61) 20 | (a21+a22)*(b11+b12+b14+b15+b16+b21+b22+b23+b24+b25+b26+b33)*(c31+c32+c61+c62) 21 | (a12+a13+a21+a22)*(b11+b12+b13+b14+b21+b24+b26+b32+b33+b36)*(c12+c21+c22+c61) 22 | (a21+a23)*(b11+b12+b14+b15+b16+b21+b22+b24+b25+b26)*(c32+c42+c52+c62) 23 | (a12+a13+a21)*(b12+b13+b14+b16+b22+b23+b24+b26+b32+b33+b35+b36)*(c21+c22+c31+c42+c51+c52+c62) 24 | (a21)*(b14+b15+b24+b25)*(c21+c22+c31+c32+c51+c52) 25 | (a12+a13)*(b12+b13+b14+b16+b24+b25+b32+b33+b35+b36)*(c21+c22+c41+c42+c51+c52+c61+c62) 26 | (a11+a12+a13)*(b12+b13+b14+b16+b22+b23+b25+b26+b32+b33+b35+b36)*(c31+c41+c61) 27 | (a12+a13+a22+a23)*(b11+b12+b14+b15+b16+b21+b22+b24+b25+b26+b35)*(c12+c42+c52+c62) 28 | (a12+a13+a21)*(b11+b21+b32+b33+b36)*(c12+c31+c41+c42+c51+c52+c62) 29 | (a11+a12+a13)*(b11+b22+b23+b26+b32+b33+b36)*(c11+c31+c61) 30 | (a21+a22+a23)*(b11+b12+b14+b15+b16+b21+b22+b24+b25+b26+b33)*(c32+c42+c62) 31 | -------------------------------------------------------------------------------- /solutions/244-26-mod0.exp: -------------------------------------------------------------------------------- 1 | (-a11+a12-a13+a14-a21+a22-a23+a24)*(b21+b22)*c11 2 | (a12-a14+a21+2*a22+2*a23-3*a24)*(-3*b12-b13+3*b14-b22+b24+2*b32+b33-2*b34)*(c11-c21-c31+c32) 3 | (2*a11+3*a13-3*a14+a21-a22+a23-a24)*(b11+3*b12-2*b14-b31-2*b32+b34)*(-c11+c22) 4 | (-a21-2*a22-2*a23+3*a24)*(-3*b12+3*b14-b22+b24+2*b32-2*b34)*(c11-c12-c21+c22-c31+c32) 5 | (-a21-a23+a24)*(3*b11+3*b12+b13-3*b14+b21+b22+b23-b24-2*b31-2*b32+2*b34+b43)*(c11-c12-c21+c22-c31+c32-c41+c42) 6 | (-a11-a13)*(3*b11+3*b12+b21+b22-2*b31-2*b32)*(-c11+c31) 7 | (a11-a12+a13)*(-3*b11-3*b12-2*b13+3*b14-b21-b22+2*b31+2*b32+b33-2*b34)*(-c11+c21+c41) 8 | (a21+a22+2*a23-3*a24)*(-3*b12+2*b14-b22+b24+b32-b42+b44)*(c11-c12-2*c21+2*c22-c41+c42) 9 | (-a12+a14)*(3*b11+3*b13+b21+b23-2*b31-2*b33)*(-c31+c32) 10 | (-a14+a21+a23-a24)*(3*b11+3*b12+b13+b21+b22+b23-2*b31-2*b32+b43)*(c11-c21+c22-c31-c41+c42) 11 | (a12-a14+a21+a23-a24)*(-3*b11-3*b12-2*b13+3*b14-b21-b22+b24+2*b31+2*b32+b33-2*b34)*(-c11+c21+c31-c32+c41) 12 | (2*a11+3*a13-3*a14+a21+a22+2*a23-3*a24)*(-b14+b34)*(-c11+2*c21-c22+c41) 13 | (2*a11+3*a13-3*a14+2*a21+3*a23-3*a24)*(-b11-b12+b31+b32)*c22 14 | (a14-a21-a22-2*a23+3*a24)*(-3*b12+3*b14-b22+b24+b32-b34-b42+b44)*(c11-2*c21+c22-c41+c42) 15 | (-a11-a12-2*a13+2*a14)*(3*b12-b13-3*b14-2*b32+b33+2*b34)*(-c11+c21) 16 | (-a11-a13+a14-a21-a23+a24)*(-3*b11-3*b12-2*b13-b21-b22+2*b31+2*b32+b33)*(-c11+c21+c31+c41) 17 | (a11+2*a12+2*a13-3*a14+a21+2*a22+2*a23-3*a24)*(-b13+b33)*(-c11+c21+c31) 18 | (a21-a22+a23)*(-b13-b14-b23-b31-b32+2*b34-b41-b42-b43+b44)*(-c12+c22+c42) 19 | (a21-a22+a23-a24)*(-b11-3*b12-b13+2*b14-b21-b22-b23+b24+b32-b41-b42-b43+b44)*(-c11+c12) 20 | a14*(3*b11+6*b12+b13-3*b14+b21+2*b22+b23-2*b24-2*b31-3*b32+b42+b43-2*b44)*(-c21+c22-c41+c42) 21 | (a12-a14+a22-a24)*(2*b13+b23-2*b33)*c32 22 | (a14-a21+a22-a23+a24)*(-b13-b23+b24-b31-b32+b34-b41-b42-b43+b44)*(-c11+c22+c42) 23 | (-a21-a22-2*a23+2*a24)*(-b11-b14+b31-b32+2*b34-b42+b44)*(-c12+c22) 24 | (2*a11+3*a13-3*a14)*(-2*b12+b14+b32)*(-c21+c22) 25 | (a21+a23)*(b13+b23+b43)*(-c12+c32) 26 | (a14+a24)*(b13+b23+b31+b32+b41+b42+b43)*(c22+c42) 27 | -------------------------------------------------------------------------------- /solutions/244-26-mod0.m: -------------------------------------------------------------------------------- 1 | {{{{-1, 1, -1, 1}, {-1, 1, -1, 1}}, {{0, 0, 0, 0}, {1, 1, 0, 0}, 2 | {0, 0, 0, 0}, {0, 0, 0, 0}}, {{1, 0}, {0, 0}, {0, 0}, {0, 0}}}, 3 | {{{0, 1, 0, -1}, {1, 2, 2, -3}}, {{0, -3, -1, 3}, {0, -1, 0, 1}, 4 | {0, 2, 1, -2}, {0, 0, 0, 0}}, {{1, 0}, {-1, 0}, {-1, 1}, {0, 0}}}, 5 | {{{2, 0, 3, -3}, {1, -1, 1, -1}}, {{1, 3, 0, -2}, {0, 0, 0, 0}, 6 | {-1, -2, 0, 1}, {0, 0, 0, 0}}, {{-1, 0}, {0, 1}, {0, 0}, {0, 0}}}, 7 | {{{0, 0, 0, 0}, {-1, -2, -2, 3}}, {{0, -3, 0, 3}, {0, -1, 0, 1}, 8 | {0, 2, 0, -2}, {0, 0, 0, 0}}, {{1, -1}, {-1, 1}, {-1, 1}, {0, 0}}}, 9 | {{{0, 0, 0, 0}, {-1, 0, -1, 1}}, {{3, 3, 1, -3}, {1, 1, 1, -1}, 10 | {-2, -2, 0, 2}, {0, 0, 1, 0}}, {{1, -1}, {-1, 1}, {-1, 1}, {-1, 1}}}, 11 | {{{-1, 0, -1, 0}, {0, 0, 0, 0}}, {{3, 3, 0, 0}, {1, 1, 0, 0}, 12 | {-2, -2, 0, 0}, {0, 0, 0, 0}}, {{-1, 0}, {0, 0}, {1, 0}, {0, 0}}}, 13 | {{{1, -1, 1, 0}, {0, 0, 0, 0}}, {{-3, -3, -2, 3}, {-1, -1, 0, 0}, 14 | {2, 2, 1, -2}, {0, 0, 0, 0}}, {{-1, 0}, {1, 0}, {0, 0}, {1, 0}}}, 15 | {{{0, 0, 0, 0}, {1, 1, 2, -3}}, {{0, -3, 0, 2}, {0, -1, 0, 1}, {0, 1, 0, 0}, 16 | {0, -1, 0, 1}}, {{1, -1}, {-2, 2}, {0, 0}, {-1, 1}}}, 17 | {{{0, -1, 0, 1}, {0, 0, 0, 0}}, {{3, 0, 3, 0}, {1, 0, 1, 0}, {-2, 0, -2, 0}, 18 | {0, 0, 0, 0}}, {{0, 0}, {0, 0}, {-1, 1}, {0, 0}}}, 19 | {{{0, 0, 0, -1}, {1, 0, 1, -1}}, {{3, 3, 1, 0}, {1, 1, 1, 0}, 20 | {-2, -2, 0, 0}, {0, 0, 1, 0}}, {{1, 0}, {-1, 1}, {-1, 0}, {-1, 1}}}, 21 | {{{0, 1, 0, -1}, {1, 0, 1, -1}}, {{-3, -3, -2, 3}, {-1, -1, 0, 1}, 22 | {2, 2, 1, -2}, {0, 0, 0, 0}}, {{-1, 0}, {1, 0}, {1, -1}, {1, 0}}}, 23 | {{{2, 0, 3, -3}, {1, 1, 2, -3}}, {{0, 0, 0, -1}, {0, 0, 0, 0}, {0, 0, 0, 1}, 24 | {0, 0, 0, 0}}, {{-1, 0}, {2, -1}, {0, 0}, {1, 0}}}, 25 | {{{2, 0, 3, -3}, {2, 0, 3, -3}}, {{-1, -1, 0, 0}, {0, 0, 0, 0}, 26 | {1, 1, 0, 0}, {0, 0, 0, 0}}, {{0, 0}, {0, 1}, {0, 0}, {0, 0}}}, 27 | {{{0, 0, 0, 1}, {-1, -1, -2, 3}}, {{0, -3, 0, 3}, {0, -1, 0, 1}, 28 | {0, 1, 0, -1}, {0, -1, 0, 1}}, {{1, 0}, {-2, 1}, {0, 0}, {-1, 1}}}, 29 | {{{-1, -1, -2, 2}, {0, 0, 0, 0}}, {{0, 3, -1, -3}, {0, 0, 0, 0}, 30 | {0, -2, 1, 2}, {0, 0, 0, 0}}, {{-1, 0}, {1, 0}, {0, 0}, {0, 0}}}, 31 | {{{-1, 0, -1, 1}, {-1, 0, -1, 1}}, {{-3, -3, -2, 0}, {-1, -1, 0, 0}, 32 | {2, 2, 1, 0}, {0, 0, 0, 0}}, {{-1, 0}, {1, 0}, {1, 0}, {1, 0}}}, 33 | {{{1, 2, 2, -3}, {1, 2, 2, -3}}, {{0, 0, -1, 0}, {0, 0, 0, 0}, {0, 0, 1, 0}, 34 | {0, 0, 0, 0}}, {{-1, 0}, {1, 0}, {1, 0}, {0, 0}}}, 35 | {{{0, 0, 0, 0}, {1, -1, 1, 0}}, {{0, 0, -1, -1}, {0, 0, -1, 0}, 36 | {-1, -1, 0, 2}, {-1, -1, -1, 1}}, {{0, -1}, {0, 1}, {0, 0}, {0, 1}}}, 37 | {{{0, 0, 0, 0}, {1, -1, 1, -1}}, {{-1, -3, -1, 2}, {-1, -1, -1, 1}, 38 | {0, 1, 0, 0}, {-1, -1, -1, 1}}, {{-1, 1}, {0, 0}, {0, 0}, {0, 0}}}, 39 | {{{0, 0, 0, 1}, {0, 0, 0, 0}}, {{3, 6, 1, -3}, {1, 2, 1, -2}, 40 | {-2, -3, 0, 0}, {0, 1, 1, -2}}, {{0, 0}, {-1, 1}, {0, 0}, {-1, 1}}}, 41 | {{{0, 1, 0, -1}, {0, 1, 0, -1}}, {{0, 0, 2, 0}, {0, 0, 1, 0}, {0, 0, -2, 0}, 42 | {0, 0, 0, 0}}, {{0, 0}, {0, 0}, {0, 1}, {0, 0}}}, 43 | {{{0, 0, 0, 1}, {-1, 1, -1, 1}}, {{0, 0, -1, 0}, {0, 0, -1, 1}, 44 | {-1, -1, 0, 1}, {-1, -1, -1, 1}}, {{-1, 0}, {0, 1}, {0, 0}, {0, 1}}}, 45 | {{{0, 0, 0, 0}, {-1, -1, -2, 2}}, {{-1, 0, 0, -1}, {0, 0, 0, 0}, 46 | {1, -1, 0, 2}, {0, -1, 0, 1}}, {{0, -1}, {0, 1}, {0, 0}, {0, 0}}}, 47 | {{{2, 0, 3, -3}, {0, 0, 0, 0}}, {{0, -2, 0, 1}, {0, 0, 0, 0}, {0, 1, 0, 0}, 48 | {0, 0, 0, 0}}, {{0, 0}, {-1, 1}, {0, 0}, {0, 0}}}, 49 | {{{0, 0, 0, 0}, {1, 0, 1, 0}}, {{0, 0, 1, 0}, {0, 0, 1, 0}, {0, 0, 0, 0}, 50 | {0, 0, 1, 0}}, {{0, -1}, {0, 0}, {0, 1}, {0, 0}}}, 51 | {{{0, 0, 0, 1}, {0, 0, 0, 1}}, {{0, 0, 1, 0}, {0, 0, 1, 0}, {1, 1, 0, 0}, 52 | {1, 1, 1, 0}}, {{0, 0}, {0, 1}, {0, 0}, {0, 1}}}} 53 | -------------------------------------------------------------------------------- /solutions/245-33-mod0.exp: -------------------------------------------------------------------------------- 1 | (-a12 + a13)*(-b11 + 2*b13 - 2*b14 + b31 - 2*b33 + 2*b34)*(-c11 - c12 - c22 - c32 + c41) 2 | (-a12 + a14 - a21 + a22 - a23)*(b24 + b25 + b34)*(-2*c11 - 3*c12 - 2*c21 - 2*c22 - 2*c31 - 3*c32 - c41 - c42 + c52) 3 | a22*(-b22 + b23 + b25)*(c11 + c12 + c21 + c22 + c31 + c32 - c41 - c42 + c51 + c52) 4 | (a12 - a13)*(-b11 + 2*b13 - 2*b14 - b21 + b23 + b31 - 2*b33 + 2*b34)*(c21 + c31 + c41) 5 | (a13 - a23)*(b11 - 2*b13 + 2*b14 + b22 + b24 + b32 + b34 - b35 - b41 + b42 + b43 + b44)*c21 6 | (-a11 - a13)*(-b21 + b23 - b31 + b33 + b35)*(2*c11 + c31) 7 | (a11 - a12 + a13 - a21 + a22 - a23)*(-b21 + b23 + b34)*(2*c11 + 2*c21 + 2*c31 + c41) 8 | (-a11 + a21 - a22 + a23)*(-b14 - b21 + b23 + b34)*(2*c11 + 2*c12 + 2*c21 + c22 + 2*c31 + c32 + c41) 9 | (-a12 + a22)*(b24 + b34 + b44)*(c11 + c21 + c31 - c41 + c51) 10 | (-a11 - a14 + a21 + a24)*(b11 - 2*b13 + 2*b14 - b35 - b41 + b43)*(2*c11 + c21 + c31 + c51) 11 | (a11 + a13)*(b11 - 2*b13 + 2*b14)*(c11 + c51) 12 | (-a21 - a23)*(b12 - b13 + b24 + b25 + b34)*(2*c12 + c32) 13 | (-a12 + a14 + a22 - a24)*(b11 - 2*b13 + 2*b14 - b35 - b41 + b42 + b43 + b44)*(-c12 - c32 - c42 + c52) 14 | a11*(b11 - b13 - b15 - b21 + b23 - b31 + b33 + b35)*(2*c11 + 2*c12 + c21 + c22 + c31 + c32) 15 | a24*(b42 - b43 + b44)*(-c12 - c32 + c52) 16 | (a13 - a14 + a21 + a24)*(-b11 + 2*b13 - 2*b14 + b35)*(2*c11 + c12 + c21 + c22 + c31 + c32 + c51) 17 | (-a23)*(b12 - b13 - b32 + b33)*(c21 + c22) 18 | (-a14)*(-b11 + 2*b13 - 2*b14 + b21 - 2*b23 + b25 + b31 - 2*b33 - b43 + b45)*(c11 + c31) 19 | (a12 - a14)*(-b11 + 2*b13 - 2*b14 + b21 - b22 - b23 + 2*b24 + 3*b25 + b31 - 2*b33 + 2*b34)*(-c11 - c12 - c31 - c32 - c41 - c42 + c51 + c52) 20 | (-a21 + a22 - a23)*(-b14 + b24 + b25 + b34)*(2*c11 + 2*c12 + 2*c21 + 2*c22 + 2*c31 + 2*c32 + c41 + c42) 21 | (-a12 + a13 + a22 - a23)*(b11 - 2*b13 + 2*b14 - b21 + b22 + b23 + b24 + 3*b34 - b35 - b41 + b42 + b43 + b44)*(c12 + c22 + c32) 22 | (-a11 - a23)*(-b12 + b13 - b21 + b23 - b31 + b33 + b35)*(2*c12 + c21 + c22 + c32) 23 | (-a11 + a21)*(b11 + b12 - 2*b13 + b14 + b21 - b23 - b34 - b35 - b41 + b43)*(2*c12 + c22 + c32) 24 | a24*(-b15 + b35 - b42 + b43 + b45)*c52 25 | (a11 - a21 - a24)*(b15 - b35 - b41 + b43)*(2*c11 + 2*c12 + c21 + c22 + c31 + c32 + c51) 26 | (a12 - a14 - a22 + a24)*(b11 - 2*b13 + 2*b14 - b35 - b41 + b42 + b43)*(c22 - c42 + c52) 27 | a14*(b24 + b25 + b34 - b41 + b43 + b44 + b45)*(c11 + c31 + c51) 28 | (-a21 - a24)*(-b15 + b35)*(2*c11 + 2*c12 + c21 + c22 + c31 + c32 + c51 + c52) 29 | (-a12 + a14)*(-b11 + 2*b13 - 2*b14 + b21 - 2*b22 + 2*b24 + 3*b25 + b31 - 2*b33 + 2*b34)*(c21 + c22 - c41 - c42 + c51 + c52) 30 | (-a13 + a14 + a23)*(b11 - 2*b13 + 2*b14 - b21 + b22 + b23 + b24 - b31 + 2*b33 + b34 - b41 + b42 + b43 + b44)*(c12 + c21 + c22 + c32) 31 | (a12 - a14 - a22)*(-b22 + b23 + b24 + b25 + b34 + b44)*(c11 + c21 + c22 + c31 - c41 - c42 + c51 + c52) 32 | (-a22 + a23)*(-b14 + b34)*(c22 + c32 + c42) 33 | (a21 + a23)*(b24 + b25 + b34 + b35)*(c12 + c52) 34 | -------------------------------------------------------------------------------- /solutions/246-39-mod2.exp: -------------------------------------------------------------------------------- 1 | (a21+a24)*(b21+b22+b24+b25+b31+b32+b34+b36+b41+b42+b44+b46)*(c11+c12+c21+c22+c41+c42) 2 | (a12+a13+a21)*(b12+b13+b14+b22+b23+b24+b31+b32+b33+b35+b42+b43+b44)*(c31+c41+c42+c52+c62) 3 | (a22+a24)*(b11+b12+b13+b14+b16+b21+b22+b23+b25+b26+b32+b33+b35+b36+b41+b42+b43+b44+b46)*(c21+c22+c31+c32+c41+c42) 4 | (a11+a13+a21+a23)*(b11+b12+b13+b14+b16+b23+b24+b26+b31+b33+b34+b36+b43+b44+b46)*(c12+c22+c42+c62) 5 | (a23+a24)*(b11+b12+b13+b14+b16+b21+b22+b23+b24+b26+b41+b42+b43+b44+b46)*(c42+c52) 6 | (a11+a13+a14+a21+a23+a24)*(b21+b22+b41+b42)*(c22+c32) 7 | (a11+a21)*(b11+b12+b13+b15+b21+b22+b23+b25+b31+b32+b33+b35+b41+b42+b43+b45)*(c21+c31+c51) 8 | (a23)*(b21+b22+b31+b32+b41+b42)*(c12+c52+c62) 9 | (a13)*(b11+b31+b41)*(c11+c51+c61) 10 | (a11+a13+a21)*(b12+b13+b14+b16+b21+b23+b24+b26+b31+b33+b34+b36+b41+b43+b44+b46)*(c12+c21+c22+c41+c42+c51+c62) 11 | (a12+a13+a21+a24)*(b22+b24+b25+b26+b32+b34+b42+b44)*(c31+c42+c52+c61+c62) 12 | (a12+a13+a22+a23)*(b11+b12+b13+b14+b16+b21+b22+b23+b24+b26+b31+b32+b33+b35+b41+b42+b43+b44+b46)*(c42+c52+c62) 13 | (a21+a24)*(b21+b23+b24+b26+b31+b33+b34+b35+b41+b43+b44+b45)*(c11+c12+c21+c22+c31+c32+c41+c42+c61+c62) 14 | (a12+a13+a14+a22+a24)*(b11+b12+b13+b14+b16+b22+b23+b24+b26+b31+b32+b33+b34+b36+b41+b42+b43+b44+b46)*(c12+c21+c22+c31+c32+c41+c42+c52+c62) 15 | (a12+a13+a14)*(b11+b12+b13+b14+b16+b21+b22+b23+b25+b26+b32+b33+b35+b36+b42+b43+b45+b46)*(c11+c12+c21+c22+c31+c32+c41+c42+c51+c52+c61+c62) 16 | (a21+a22+a23)*(b11+b12+b13+b14+b16+b21+b22+b23+b24+b26+b32+b33+b35+b36+b41+b42+b43+b44+b46)*(c32+c52+c62) 17 | (a13+a14)*(b11+b12+b13+b14+b16+b22+b23+b25+b31+b32+b33+b35+b41)*(c31) 18 | (a11+a21)*(b12+b14+b15+b16+b21+b24+b25+b26+b32+b34+b35+b36+b41+b44+b45+b46)*(c21+c41+c51) 19 | (a21)*(b11+b14+b15+b21+b24+b25+b41+b44+b45)*(c31+c32+c41+c42) 20 | (a11+a12+a13)*(b11+b16+b21+b22+b26+b31+b36+b44+b45+b46)*(c31+c51+c61) 21 | (a12+a14+a22+a24)*(b24+b25+b26+b34+b35+b36)*(c21+c31+c41) 22 | (a12+a14+a22+a24)*(b11+b12+b13+b14+b16+b21+b23+b25+b31+b32+b33+b35+b41+b42+b43+b44+b46)*(c21+c51+c61) 23 | (a22+a24)*(b11+b12+b13+b14+b16+b21+b24+b25+b32+b33+b35+b36+b41+b42+b43+b44+b46)*(c31+c32+c41+c42+c51+c52+c61+c62) 24 | (a13+a14)*(b12+b15+b16+b22+b42+b45+b46)*(c31+c41+c51) 25 | (a11+a13+a14)*(b12+b15+b16+b21+b24+b26+b31+b32+b34+b36+b42+b45+b46)*(c21+c22+c31+c32) 26 | (a11+a13+a21+a24)*(b11+b12+b13+b14+b16+b21+b41)*(c11+c12+c21+c22+c31+c41+c42+c61+c62) 27 | (a11+a13+a14+a22+a24)*(b11+b12+b13+b14+b16+b23+b25+b26+b32+b33+b35+b36+b41+b42+b43+b44+b46)*(c21+c22+c32+c51+c61) 28 | (a12+a13+a14+a22+a23+a24)*(b11+b12+b13+b14+b16+b21+b22+b23+b24+b26+b31+b32+b33+b34+b36+b41+b42+b43+b44+b46)*(c12+c22+c32+c42+c52+c62) 29 | (a12+a13)*(b12+b13+b14+b21+b22+b26+b31+b33+b34+b35+b43)*(c41+c42+c51+c52+c61+c62) 30 | (a12+a13+a14+a21+a24)*(b11+b12+b13+b14+b16+b22+b23+b25+b26+b32+b33+b35+b36+b42+b43+b45+b46)*(c11+c12+c21+c22+c32+c41+c42+c52+c62) 31 | (a11+a14+a21+a24)*(b21+b41)*(c11+c21+c41) 32 | (a21+a22)*(b21+b22+b25+b26+b31+b33+b34+b35+b41+b42)*(c32+c42+c52) 33 | (a12+a13+a22+a24)*(b11+b12+b13+b14+b16+b24+b25+b26+b31+b32+b33+b35+b41+b42+b43+b44+b46)*(c31+c41+c42+c51+c52+c61+c62) 34 | (a11+a13+a14+a21)*(b11+b13+b14+b15+b22+b23+b24+b25+b31+b33+b34+b35+b42+b43+b44+b45)*(c21+c22+c32+c41+c51) 35 | (a11+a13)*(b12+b13+b14+b16)*(c11+c12+c21+c22+c41+c42+c61+c62) 36 | (a21+a22+a23+a24)*(b21+b22+b31+b33+b34+b35+b41+b42)*(c32+c42+c52) 37 | (a11+a12+a13+a14)*(b22+b24+b32+b34+b42+b44)*(c31+c41+c51) 38 | (a21)*(b12+b13+b14+b15+b21+b23+b24+b25+b31+b33+b34+b35+b41+b43+b44+b45)*(c21+c22+c41+c42+c51+c52) 39 | (a11+a14+a21+a24)*(b11+b12+b13+b14+b16+b22+b23+b25+b31+b32+b33+b35+b42+b43+b45)*(c31+c61) 40 | -------------------------------------------------------------------------------- /solutions/255-40-mod0.exp: -------------------------------------------------------------------------------- 1 | (-a11+a15+a21-a25)*(-b12+b14-b22+b24-b32+b34)*c42 2 | (-a21+a23+a24)*(-2*b12+2*b15+b21-2*b22-b24+2*b25-2*b32+2*b35-b41+2*b42-b45-b52+b55)*(c11+c12+c21+c22) 3 | (-a11+a13-a21+a23+a25)*(-2*b11+2*b12+2*b13-b21+b22+b23-2*b31+2*b32+2*b33-b51+b52+b53)*(c11+c31+c32+c41) 4 | (-a21+2*a25)*(b11-b12-b14+b15+b21-b22-b24+b25+b41-b42-b44+b45+b51-b52-b54+b55)*(c11+c12) 5 | (-a11+a13+a15+a21-a23-a25)*(-2*b11+2*b12+2*b13+2*b14-b21+b22+b23+2*b24-2*b31+2*b32+2*b33+b34+b44-b51+b52+b53+2*b54)*(c11+c31+c41) 6 | (-2*a11+a13+2*a15)*(2*b11-2*b12-b13-b14+b15+b21-2*b22-b23+b25+2*b31-b32-b33-b34-b41+b43+b45+b51-b52-b54+b55)*(c11+c31) 7 | (2*a21-a22-a23-a25)*(-b12+b14-2*b22+2*b24-b42+b44-b52+b54)*(c22-c32+c52) 8 | (3*a11-a12-2*a13-a14-a15-a21+a23+a24)*(b21-b24-b41+b42)*(-c11-c12-c21-c32+c52) 9 | (-a21+a22+a23+a24-a25)*(b21-b22-b24+b25)*(c51+c52) 10 | (a11-a13)*(-2*b11+b12+3*b13+b15-b21+2*b23+b25-2*b31+2*b32+2*b33-b41+2*b43+b45-b51+2*b53+b55)*(c31+c32) 11 | (-3*a21+a22+2*a23+a25)*(-b12+b14-b22+b24-b42+b44-b52+b54)*(c21+c22+c51+c52) 12 | (a11-a15-a21+a23+a24)*(-2*b12+2*b15+b21-2*b22-b24+2*b25-2*b32+2*b35-b41+b42+b44-b45-b52+b55)*(-c11-c21+c42) 13 | (-a11+a12+a21-a22)*(-b12-b14+2*b15-2*b24+b25-b32+2*b35-b44-b52-b54+b55)*(c12+c22+c42+c52) 14 | (-a11+a15)*(2*b11-2*b12-2*b14+2*b15+2*b21-2*b22-2*b24+2*b25+2*b31-2*b32-2*b34+2*b35-b41+b42+b44-b45+b51-b52-b54+b55)*(c41+c42) 15 | (a13+a14-a15)*(-b12+2*b15+b21-b22-b24+2*b25-b32+2*b35-b41+b42+b44-b45-b52+b55)*(c11+c21+c41) 16 | (a11-a13-a14-a21+a23+a24)*(b21-b24-b41+b44)*(c11+c21) 17 | (a11-a12-2*a21+a22+a23-a24+a25)*(-b12+2*b15+b21-b22-b24+2*b25-b32+2*b35-b41+b42-b45-b52+b55)*(c12+c22+c42+c52) 18 | (-a11+a13+3*a21-a22-2*a23-a25)*(-b12+b14+b21-2*b22-b23+b24-b41+b43+b44-b52+b54)*(c21+c32+c51) 19 | (-3*a11+a12+2*a13+a14+a15+3*a21-a22-2*a23-a24-a25)*(b32-b35-b42+b45)*(-c12-c32+c52) 20 | (-a23-a24+a25)*(-2*b12+2*b15-b22+b25-2*b32+2*b35-b52+b55)*(c12+c22+c42) 21 | (3*a11-a12-2*a13-a14-a15-a21+a22+a23+a24-a25)*(-b21+b24+b32-b35-b42+b45)*(-c12-c32+c51+c52) 22 | (-a11+a13-a21+2*a25)*(2*b11-2*b12-b13-b14+b15+2*b21-2*b22-b23-b24+b25+b31-b32-b33+b43-b44+b45+b51-b52-b54+b55)*(-c11+c32) 23 | (2*a11-2*a13-a15)*(-2*b11+b12+2*b13+b14+2*b15+b23+2*b25-2*b31+b32+2*b33+2*b35-b41+b42+b44-b45-b51+b53+b54+b55)*(c11+c41) 24 | (3*a11-a12-2*a13-a15-3*a21+a22+2*a23+a25)*(-b12+b14+2*b15+2*b21-2*b22-b23+2*b25-b32+2*b35-2*b41+2*b42+b43+b44-b45-b52+b54+b55)*(c21+c51) 25 | (-3*a11+a12+2*a13+a14+a15)*(-b12+b15-b22+b25-b41+b45-b52+b55)*(-c11-c12-c31-c32+c51+c52) 26 | (-a11+a13-a14+a15)*(-b12+2*b15+b21-b22-b24+2*b25-b32+2*b35-b41+b42-b45-b52+b55)*(c11+c21+c41+c51) 27 | (a11-2*a15-a21+2*a25)*(b11-2*b12-b13+b15+b21-2*b22-b23+b25+b31-b32-b33-b41+b43+b45-b52+b55)*c11 28 | (-a11+a12+3*a21-a22-2*a23-a25)*(-b12+b14+2*b15+b21-b22+2*b25-b32+2*b35-b41+b42+b44-b45-b52+b54+b55)*(c12+c21+c22+c42+c51+c52) 29 | (-a11+a12-a21+a23+a25)*(b12+b14+2*b24+b32+b44+b52+b54)*(c11+c12+c22+c31+c41+c42+c52) 30 | (-a11+a13+a21-a23)*(-2*b11+2*b12+2*b13-3*b21+3*b22+3*b23-b31+b32+b33+b41-b42-b43-b51+b52+b53)*c32 31 | (-a11+a12+a13+a14-a15+a21-a22-a23-a24+a25)*(-b12+2*b15-b22+2*b25+b35-b41+b43+b45-b52+b55)*c51 32 | (a21-a23-a25)*(-2*b11+2*b12-b21+b22-2*b31+2*b32-b51+b52)*(c11+c12+c31+c32+c41+c42) 33 | (-2*a21+a23+2*a25)*(-2*b11+b12+b14-b21+b22-b31+b35-b41+b42+b44-b45-b51+b54)*(c12+c32) 34 | (2*a11-a12-2*a13-a14+a15)*(-b12+b15-b22+b25-b41+b43+b45-b52+b55)*(-c31+c51) 35 | (3*a11-a12-2*a13-a14-a15-a21+2*a25)*(-b12+b15-b22+b25-b42+b45-b52+b55)*(-c11-c12-c32+c52) 36 | (-a11+a13-a21+a22+a23+a24-a25)*(-b41+b42+b43)*(c32+c51) 37 | (a11-a12-a21+a22+a23+a24-a25)*(-b12+2*b15+b25-b32+2*b35-b52+b55)*(c12+c22+c42+c51+c52) 38 | (-2*a11+a12+a13+a15)*(b12+b14-b23+2*b24+b32+b43+b44+b52+b54)*(c21-c31+c51) 39 | (-a11+a15-a21+a23+a25)*(-2*b11+b12+b14-b21+b22-2*b31+b32+b34-b51+b54)*(c11+c31+c41+c42) 40 | (a11-a12)*(b12+b14+b24+b32+b44+b52+b54)*(c11+c12+c21+c22+c41+c42+c51+c52) 41 | -------------------------------------------------------------------------------- /solutions/256-48-mod2.exp: -------------------------------------------------------------------------------- 1 | (a11+a12+a15)*(b11+b16+b21+b26+b31+b36+b51+b56)*(c21+c61) 2 | (a21+a24)*(b13+b14+b15+b23+b24+b25+b33+b34+b35+b53+b54+b55)*(c21+c22+c31+c32+c41+c42+c51+c52) 3 | (a11+a13+a15+a21+a24)*(b13+b14+b15+b23+b24+b25+b33+b34+b35+b42+b53+b54+b55)*(c21+c22+c31+c32+c41+c42+c51) 4 | (a11+a14+a21+a24)*(b42)*(c21+c31+c41+c51) 5 | (a11+a13+a15+a21+a23+a25)*(b12+b13+b14+b16+b21+b22+b31+b41+b42+b43+b44+b46+b51+b56)*(c22+c32+c42) 6 | (a21+a22+a24)*(b13+b15+b23+b24+b25+b43+b45+b53+b55)*(c51+c52+c61+c62) 7 | (a11+a21)*(b11+b13+b14+b41+b43+b44)*(c11+c21+c61) 8 | (a12+a15)*(b11+b16+b23+b31+b46+b51+b56)*(c11+c12) 9 | (a11+a13+a15+a23)*(b12+b13+b16+b21+b22+b24+b31+b34+b41+b43+b44+b46+b51+b54+b56)*(c21+c22+c32+c42) 10 | (a11+a12+a13+a15+a22+a23)*(b21+b26+b31+b41+b46+b51+b56)*(c11+c31+c51+c62) 11 | (a15+a25)*(b12+b13+b14+b16+b21+b31+b41+b42+b43+b44+b46+b51+b52+b56)*(c22+c32+c52) 12 | (a12+a15+a21+a22+a24)*(b24+b41+b43+b44)*(c12+c41) 13 | (a11+a12+a13+a14+a15+a21+a22+a23+a24+a25)*(b13+b14+b15+b33+b34+b35+b42+b44+b45)*(c32+c42+c52) 14 | (a12+a13+a22+a23)*(b21+b26+b41+b42+b43+b46+b51+b56)*(c11+c31+c51) 15 | (a22+a23+a24)*(b13+b15+b43+b45+b53+b55)*(c51+c52) 16 | (a11+a12+a13+a14+a15+a21+a22+a24)*(b14+b24+b42+b54)*(c32+c41+c42+c52) 17 | (a11+a12+a13+a14+a15+a22+a23+a24)*(b13+b15+b24+b33+b34+b35+b42+b43+b44+b45+b54)*(c32+c42+c51+c52) 18 | (a23+a25)*(b12+b13+b14+b16+b24+b42+b46+b52+b53+b54+b56)*(c32+c52) 19 | (a12+a13+a14+a22+a23+a24)*(b24+b33+b34+b35+b42+b44+b53+b54+b55)*(c51) 20 | (a21+a25)*(b21+b31+b41+b51)*(c12+c32+c52+c62) 21 | (a21+a24+a25)*(b24+b43+b44)*(c12+c42) 22 | (a21+a22+a25)*(b22)*(c22+c62) 23 | (a13+a14+a15)*(b13+b15+b46+b53+b55)*(c51) 24 | (a15+a21)*(b13+b14+b21+b31+b41+b43+b44+b51)*(c11+c21+c22+c32+c52+c61) 25 | (a21+a22+a24)*(b24)*(c41+c42+c51+c52+c61+c62) 26 | (a11+a12+a13+a15+a23)*(b22+b26+b36+b46)*(c21+c62) 27 | (a13+a23)*(b12+b13+b14+b16+b21+b26+b31+b32+b36+b41+b42+b43+b44+b51+b56)*(c21) 28 | (a23)*(b12+b13+b16+b23+b32+b33+b46+b52+b53+b56)*(c21+c22) 29 | (a12+a15+a21)*(b11+b16+b21+b31+b46+b51+b56)*(c11+c12+c21+c61) 30 | (a11+a12+a14+a21+a22+a24)*(b46)*(c51+c61) 31 | (a13+a15)*(b14+b24+b31+b33+b34+b42+b54)*(c31+c51) 32 | (a11+a12+a13+a14+a15+a22+a23)*(b42+b43)*(c11+c31+c32+c42+c51+c52) 33 | (a11+a12+a13+a15)*(b13+b15+b23+b25+b36+b43+b45+b46+b53+b55)*(c61+c62) 34 | (a11+a12+a14+a21+a22+a24)*(b14+b24+b41+b42+b43+b44+b54)*(c41) 35 | (a22+a23)*(b23)*(c11+c12+c31+c32+c51+c52) 36 | (a11+a12+a13+a15+a21+a22+a24)*(b13+b15+b23+b25+b43+b45+b46+b53+b55)*(c51+c61+c62) 37 | (a11+a15)*(b24+b34+b42+b44+b54)*(c31+c41) 38 | (a12+a15+a22+a25)*(b21+b24+b31+b41+b43+b44)*(c12) 39 | (a15)*(b13+b14+b23+b24+b33+b34+b53+b54)*(c21+c22+c31+c32+c51+c52) 40 | (a21)*(b16+b46+b56)*(c11+c12+c21+c22+c61+c62) 41 | (a11+a12+a13+a15+a21+a22+a23+a25)*(b21+b22+b31+b41+b51+b56)*(c62) 42 | (a11+a15)*(b13+b14+b21+b26+b31+b41+b43+b44+b46+b51+b56)*(c11+c31+c51+c61) 43 | (a12+a15+a22+a23)*(b23+b31)*(c11+c12+c31+c51) 44 | (a15+a23)*(b12+b13+b14+b16+b23+b24+b33+b34+b42+b46+b52+b53+b54+b56)*(c21+c22+c32+c52) 45 | (a23+a24+a25)*(b13+b14+b15+b24+b33+b34+b35+b42+b43+b45+b53+b54+b55)*(c52) 46 | (a21+a25)*(b12+b15+b16+b21+b22+b24+b31+b33+b34+b35+b41+b44+b45+b46+b51+b54+b56)*(c32+c42) 47 | (a11+a13+a15)*(b13+b15+b23+b25+b33+b35+b53+b55)*(c21+c22+c31+c32+c41+c42) 48 | (a11+a14+a15)*(b41+b42+b43)*(c11+c41) 49 | -------------------------------------------------------------------------------- /solutions/266-56-mod2.exp: -------------------------------------------------------------------------------- 1 | (a23+a26)*(b12+b14+b16+b22+b24+b26+b62+b64+b66)*(c31+c32+c61+c62) 2 | (a22+a23)*(b14+b24+b31+b34+b35+b41+b44+b45+b51+b54+b55+b64)*(c11+c12+c31+c32) 3 | (a12+a14+a15+a16)*(b13+b16+b24+b26+b31+b32+b33+b35+b41+b42+b44+b45+b51+b53+b55+b62+b64+b66)*(c31+c32) 4 | (a11+a12)*(b12+b16+b42+b46)*(c11+c12+c51+c52+c61+c62) 5 | (a11+a16+a21)*(b15+b25+b32+b42+b62+b65)*(c21+c31+c52+c61) 6 | (a23+a25)*(b11+b21+b31+b41)*(c12) 7 | (a11+a13+a14+a16)*(b21+b24+b25+b31+b34+b35+b51+b54+b55)*(c31+c41) 8 | (a11+a21)*(b11+b13+b15+b21+b23+b25+b31+b33+b35+b41+b43+b45+b51+b53+b55+b61+b63+b65)*(c21+c31+c61) 9 | (a12+a13+a15+a16)*(b14+b23+b33+b44+b53+b54+b62+b64+b66)*(c61) 10 | (a21+a23+a24+a26)*(b32+b34+b36+b42+b44+b46+b62+b64+b66)*(c32+c42) 11 | (a12+a13+a16+a21+a24+a26)*(b14+b22+b24+b32+b34+b42+b44+b52+b64)*(c12+c21+c22+c31+c41+c51+c52+c62) 12 | (a23+a24)*(b14+b22+b32+b44+b52+b54)*(c31+c32+c41+c42+c51+c52) 13 | (a21+a22+a23+a24)*(b14+b21+b24+b25+b31+b34+b35+b41+b44+b45+b51+b55+b64)*(c12+c32+c42+c62) 14 | (a11+a14+a23+a26)*(b14+b24+b32+b36+b42+b46+b62+b64+b66)*(c31+c42+c61+c62) 15 | (a21+a22+a23+a24)*(b12+b16+b21+b24+b25+b26+b31+b32+b35+b45+b46+b51+b54+b55+b56)*(c12+c32+c52) 16 | (a11+a16+a23+a24)*(b14+b21+b25+b31+b35+b44+b51+b54+b55)*(c31+c41+c51+c52) 17 | (a21+a23+a25+a26)*(b11+b12+b16+b32+b35+b41+b45+b46+b54+b55)*(c11+c12+c51+c52) 18 | (a11+a16)*(b11+b14+b15+b41+b44+b45)*(c51+c52) 19 | (a12+a13+a16+a22+a23)*(b11+b14+b21+b24+b31+b34+b35+b41+b44+b45+b51+b54+b55+b61+b64)*(c11+c12+c22+c31+c52+c62) 20 | (a11+a14+a22+a23)*(b14+b21+b25+b31+b34+b35+b41+b44+b45+b51+b54+b55+b64)*(c11+c31+c42+c62) 21 | (a11+a12+a15)*(b11+b12+b13+b21+b23+b31+b32+b33+b35+b41+b43+b45+b51+b53+b55+b61+b62+b63)*(c21+c61) 22 | (a11+a12+a13+a14+a15+a21+a24+a26)*(b12+b14+b16+b22+b24+b26+b32+b34+b36+b42+b44+b46+b52+b56+b62+b64+b66)*(c21+c22+c31+c32+c41+c42+c51+c52+c62) 23 | (a12+a13+a16)*(b14+b24+b32+b34+b42+b44+b64)*(c11+c12+c21+c22+c51+c52+c61+c62) 24 | (a11+a12+a21+a23+a25+a26)*(b12+b16+b21+b31+b42+b46+b51)*(c11+c12+c51+c52+c62) 25 | (a12+a15+a22+a23)*(b11+b21+b33+b34+b36+b43+b44+b46+b61+b63+b64+b66)*(c11+c31+c32) 26 | (a21+a24+a26)*(b12+b16+b22+b26+b32+b36+b42+b46+b52+b56+b62+b66)*(c21+c22+c31+c32+c41+c42+c51+c52) 27 | (a14+a16)*(b11+b13+b14+b16+b21+b23+b24+b26+b61+b63+b64+b66)*(c31+c32) 28 | (a11+a14+a21+a24)*(b14+b21+b25+b31+b32+b34+b35+b36+b41+b42+b44+b45+b46+b51+b54+b55+b62+b64+b66)*(c42+c62) 29 | (a12+a15+a23+a26)*(b12+b16+b22+b23+b24+b26+b32+b33+b34+b36+b42+b46+b53+b54)*(c31+c32+c61) 30 | (a12+a14+a15+a16+a21+a23+a25+a26)*(b11+b12+b16+b21+b23+b24+b26+b31+b32+b33+b34+b35+b36+b43+b44+b45+b51+b53+b55+b56+b61+b63+b64+b66)*(c11+c32+c51) 31 | (a12+a14+a15+a16+a22+a24+a25+a26)*(b11+b12+b16+b21+b23+b24+b26+b31+b32+b33+b34+b35+b36+b43+b44+b45+b51+b54+b55+b56+b61+b63+b64+b66)*(c32) 32 | (a21+a22+a25)*(b32+b35+b42+b45+b52+b55)*(c22+c62) 33 | (a21)*(b12+b22+b32+b42)*(c21+c22+c31+c32+c61+c62) 34 | (a16)*(b15+b25+b65)*(c21+c31+c51+c61) 35 | (a11+a12+a13+a14+a15+a21+a22+a23+a24+a25)*(b54)*(c22+c32+c42+c52+c62) 36 | (a26)*(b11+b14+b21+b24+b31+b32+b34+b35+b41+b42+b44+b45+b51+b54+b55+b61+b62+b64)*(c22+c32+c52+c62) 37 | (a12+a15+a21)*(b11+b12+b13+b21+b22+b23+b31+b33+b35+b41+b43+b45+b51+b53+b55+b61+b62+b63)*(c21+c31+c32+c61) 38 | (a11+a16+a21+a23+a25+a26)*(b11+b21+b31+b41+b51+b54+b55)*(c11+c51+c52) 39 | (a13+a14+a23+a24)*(b12+b16+b21+b22+b24+b25+b26+b31+b35+b42+b46+b51+b52+b55+b56)*(c31+c41+c51) 40 | (a13+a16+a23+a26)*(b23+b24+b33+b34+b53+b54)*(c31+c61) 41 | (a11+a12+a13+a14)*(b11+b23+b25+b33+b34+b36+b43+b44+b46+b53+b54+b61+b63+b64+b66)*(c11+c31+c51) 42 | (a11+a12+a21+a22)*(b12+b16+b21+b22+b24+b26+b31+b42+b46+b51+b52+b54+b56)*(c12+c52+c62) 43 | (a11+a13+a15+a16+a21+a23+a25+a26)*(b11+b12+b16+b21+b23+b24+b26+b31+b32+b33+b34+b35+b36+b43+b44+b45+b51+b53+b54+b56+b61+b63+b64+b66)*(c11+c51) 44 | (a11+a14+a16+a21+a24+a26)*(b22+b32+b42+b52)*(c21+c31+c41+c51) 45 | (a14+a16+a24+a26)*(b11+b14+b21+b23+b31+b32+b33+b35+b41+b42+b44+b45+b51+b54+b55+b61+b62+b63)*(c32) 46 | (a12+a13+a16+a21+a23+a25+a26)*(b32+b35+b42+b45+b54+b55)*(c11+c12+c22+c51+c52+c62) 47 | (a11+a12+a13+a14+a15+a23+a24)*(b22+b32+b52+b54)*(c22+c31+c32+c41+c42+c51+c52+c62) 48 | (a13+a15)*(b11+b21+b33+b34+b36+b43+b44+b46+b51+b54+b55+b61+b63+b64+b66)*(c11) 49 | (a11+a12+a13+a14+a15)*(b12+b14+b16+b24+b26+b34+b36+b42+b44+b46+b56+b62+b64+b66)*(c21+c22+c31+c32+c41+c42+c51+c52+c61+c62) 50 | (a22+a23+a25+a26)*(b12+b16+b21+b31+b42+b46+b51+b52+b56)*(c62) 51 | (a11+a12+a13+a14)*(b12+b14+b16+b24+b26+b32+b34+b44+b46+b56+b64)*(c11+c31+c41+c61) 52 | (a12+a13+a16+a22+a23+a26)*(b11+b14+b21+b22+b24+b31+b32+b34+b41+b42+b44+b51+b52+b61+b64)*(c12+c22+c52+c62) 53 | (a11+a16+a21+a26)*(b32+b35+b42+b45+b62+b65)*(c52) 54 | (a11+a12+a23+a24)*(b12+b16+b22+b24+b26+b42+b46+b52+b54+b56)*(c12+c31+c41+c51+c52+c62) 55 | (a12+a13+a22+a23)*(b14+b21+b25+b31+b33+b35+b36+b41+b43+b45+b46+b51+b54+b55+b63+b66)*(c11+c31) 56 | (a11+a14)*(b14+b24+b64)*(c41+c42+c61+c62) 57 | -------------------------------------------------------------------------------- /solutions/334-29-mod0.exp: -------------------------------------------------------------------------------- 1 | (-a11+a22-a31)*(-b13+b22+b23)*(c12+c22-c23+c33) 2 | (-a12-a22-a32)*(-b14+b22+b24)*(-c23+c33) 3 | (a11+a31)*(-b12-b13+b22+b23)*(-c11+c12-c21+c22) 4 | (-a13-a23)*(b13-b21+b22-b31+2*b32+b33)*c12 5 | (-a12)*(b11-b12-b13-b21+b22+b23)*(c11+c21-c23-c31+c33) 6 | (a11+a12+a31+a32)*(-b14+b22+b23)*c33 7 | (-a13+a32-a33)*(-b14+b24+b31+b34)*(-c13-c41+c43) 8 | (a21+a22-a23)*(b32+b33)*(-c13+c31-c32-c42+c43) 9 | a31*(b11+b14)*(-c11+c13-c21+c23) 10 | a22*(b13-b23+b32)*(c12+c22-c23-c32+c33) 11 | (a12-a13+a32-a33)*(-b14+b24)*(-c23+c33+c41) 12 | (-a11-a12)*b14*(c11-c13+c21-c23-c41+c43) 13 | (-a11-a12-a31)*(b11-b12-b13+b14+b22+b23)*(-c11-c21+c23) 14 | (a13+a23+a33)*(b14+b32+b34)*c42 15 | (a13+a33)*(-b14+b24-b32-b33+b34)*(-c13-c42+c43) 16 | (a13-a21-a22+a23+a33)*(b14+b32+b33)*(-c13+c33-c42+c43) 17 | (-a11-a13+a22-a23)*(b11-b12-b21+b22)*(c21-c23-c31+c33) 18 | a13*b31*(c11-c12-c13-c41+c43) 19 | (a11+a12-a13+a21+a22-a23+a31+a32-a33)*b14*(-c13+c33+c43) 20 | (-a11-a12+a13-a21-a22+a23)*(-b11+b12+b13)*(-c31+c33) 21 | (-a13+a21+a22-a23)*(-b11+b12+b13+b32+b33)*(-c12-c31+c33) 22 | (a22-a23)*b32*(c21-c22-c23-c31+c32+c33+c42) 23 | (-a32+a33)*(b31+b34)*(-c41+c43) 24 | (-a13-a22-a33)*(b14-b24+b32)*(-c23+c33+c42) 25 | (a13-a22+a23)*(b11-b12-b21+b22+b32)*(c12+c21-c23-c31+c33) 26 | (a11+a12)*(-b21+b22)*(c21-c23-c31+c33) 27 | a32*(b21+b24+b31+b34)*c13 28 | (a11+a21+a31)*b12*(c12+c22) 29 | (a21+a22)*(b13+b32+b33)*(c12+c32) 30 | -------------------------------------------------------------------------------- /solutions/334-29-mod0.m: -------------------------------------------------------------------------------- 1 | {{{{-1, 0, 0}, {0, 1, 0}, {-1, 0, 0}}, {{0, 0, -1, 0}, {0, 1, 1, 0}, 2 | {0, 0, 0, 0}}, {{0, 1, 0}, {0, 1, -1}, {0, 0, 1}, {0, 0, 0}}}, 3 | {{{0, -1, 0}, {0, -1, 0}, {0, -1, 0}}, {{0, 0, 0, -1}, {0, 1, 0, 1}, 4 | {0, 0, 0, 0}}, {{0, 0, 0}, {0, 0, -1}, {0, 0, 1}, {0, 0, 0}}}, 5 | {{{1, 0, 0}, {0, 0, 0}, {1, 0, 0}}, {{0, -1, -1, 0}, {0, 1, 1, 0}, 6 | {0, 0, 0, 0}}, {{-1, 1, 0}, {-1, 1, 0}, {0, 0, 0}, {0, 0, 0}}}, 7 | {{{0, 0, -1}, {0, 0, -1}, {0, 0, 0}}, {{0, 0, 1, 0}, {-1, 1, 0, 0}, 8 | {-1, 2, 1, 0}}, {{0, 1, 0}, {0, 0, 0}, {0, 0, 0}, {0, 0, 0}}}, 9 | {{{0, -1, 0}, {0, 0, 0}, {0, 0, 0}}, {{1, -1, -1, 0}, {-1, 1, 1, 0}, 10 | {0, 0, 0, 0}}, {{1, 0, 0}, {1, 0, -1}, {-1, 0, 1}, {0, 0, 0}}}, 11 | {{{1, 1, 0}, {0, 0, 0}, {1, 1, 0}}, {{0, 0, 0, -1}, {0, 1, 1, 0}, 12 | {0, 0, 0, 0}}, {{0, 0, 0}, {0, 0, 0}, {0, 0, 1}, {0, 0, 0}}}, 13 | {{{0, 0, -1}, {0, 0, 0}, {0, 1, -1}}, {{0, 0, 0, -1}, {0, 0, 0, 1}, 14 | {1, 0, 0, 1}}, {{0, 0, -1}, {0, 0, 0}, {0, 0, 0}, {-1, 0, 1}}}, 15 | {{{0, 0, 0}, {1, 1, -1}, {0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, 16 | {0, 1, 1, 0}}, {{0, 0, -1}, {0, 0, 0}, {1, -1, 0}, {0, -1, 1}}}, 17 | {{{0, 0, 0}, {0, 0, 0}, {1, 0, 0}}, {{1, 0, 0, 1}, {0, 0, 0, 0}, 18 | {0, 0, 0, 0}}, {{-1, 0, 1}, {-1, 0, 1}, {0, 0, 0}, {0, 0, 0}}}, 19 | {{{0, 0, 0}, {0, 1, 0}, {0, 0, 0}}, {{0, 0, 1, 0}, {0, 0, -1, 0}, 20 | {0, 1, 0, 0}}, {{0, 1, 0}, {0, 1, -1}, {0, -1, 1}, {0, 0, 0}}}, 21 | {{{0, 1, -1}, {0, 0, 0}, {0, 1, -1}}, {{0, 0, 0, -1}, {0, 0, 0, 1}, 22 | {0, 0, 0, 0}}, {{0, 0, 0}, {0, 0, -1}, {0, 0, 1}, {1, 0, 0}}}, 23 | {{{-1, -1, 0}, {0, 0, 0}, {0, 0, 0}}, {{0, 0, 0, 1}, {0, 0, 0, 0}, 24 | {0, 0, 0, 0}}, {{1, 0, -1}, {1, 0, -1}, {0, 0, 0}, {-1, 0, 1}}}, 25 | {{{-1, -1, 0}, {0, 0, 0}, {-1, 0, 0}}, {{1, -1, -1, 1}, {0, 1, 1, 0}, 26 | {0, 0, 0, 0}}, {{-1, 0, 0}, {-1, 0, 1}, {0, 0, 0}, {0, 0, 0}}}, 27 | {{{0, 0, 1}, {0, 0, 1}, {0, 0, 1}}, {{0, 0, 0, 1}, {0, 0, 0, 0}, 28 | {0, 1, 0, 1}}, {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}, {0, 1, 0}}}, 29 | {{{0, 0, 1}, {0, 0, 0}, {0, 0, 1}}, {{0, 0, 0, -1}, {0, 0, 0, 1}, 30 | {0, -1, -1, 1}}, {{0, 0, -1}, {0, 0, 0}, {0, 0, 0}, {0, -1, 1}}}, 31 | {{{0, 0, 1}, {-1, -1, 1}, {0, 0, 1}}, {{0, 0, 0, 1}, {0, 0, 0, 0}, 32 | {0, 1, 1, 0}}, {{0, 0, -1}, {0, 0, 0}, {0, 0, 1}, {0, -1, 1}}}, 33 | {{{-1, 0, -1}, {0, 1, -1}, {0, 0, 0}}, {{1, -1, 0, 0}, {-1, 1, 0, 0}, 34 | {0, 0, 0, 0}}, {{0, 0, 0}, {1, 0, -1}, {-1, 0, 1}, {0, 0, 0}}}, 35 | {{{0, 0, 1}, {0, 0, 0}, {0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, 36 | {1, 0, 0, 0}}, {{1, -1, -1}, {0, 0, 0}, {0, 0, 0}, {-1, 0, 1}}}, 37 | {{{1, 1, -1}, {1, 1, -1}, {1, 1, -1}}, {{0, 0, 0, 1}, {0, 0, 0, 0}, 38 | {0, 0, 0, 0}}, {{0, 0, -1}, {0, 0, 0}, {0, 0, 1}, {0, 0, 1}}}, 39 | {{{-1, -1, 1}, {-1, -1, 1}, {0, 0, 0}}, {{-1, 1, 1, 0}, {0, 0, 0, 0}, 40 | {0, 0, 0, 0}}, {{0, 0, 0}, {0, 0, 0}, {-1, 0, 1}, {0, 0, 0}}}, 41 | {{{0, 0, -1}, {1, 1, -1}, {0, 0, 0}}, {{-1, 1, 1, 0}, {0, 0, 0, 0}, 42 | {0, 1, 1, 0}}, {{0, -1, 0}, {0, 0, 0}, {-1, 0, 1}, {0, 0, 0}}}, 43 | {{{0, 0, 0}, {0, 1, -1}, {0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, 44 | {0, 1, 0, 0}}, {{0, 0, 0}, {1, -1, -1}, {-1, 1, 1}, {0, 1, 0}}}, 45 | {{{0, 0, 0}, {0, 0, 0}, {0, -1, 1}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, 46 | {1, 0, 0, 1}}, {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}, {-1, 0, 1}}}, 47 | {{{0, 0, -1}, {0, -1, 0}, {0, 0, -1}}, {{0, 0, 0, 1}, {0, 0, 0, -1}, 48 | {0, 1, 0, 0}}, {{0, 0, 0}, {0, 0, -1}, {0, 0, 1}, {0, 1, 0}}}, 49 | {{{0, 0, 1}, {0, -1, 1}, {0, 0, 0}}, {{1, -1, 0, 0}, {-1, 1, 0, 0}, 50 | {0, 1, 0, 0}}, {{0, 1, 0}, {1, 0, -1}, {-1, 0, 1}, {0, 0, 0}}}, 51 | {{{1, 1, 0}, {0, 0, 0}, {0, 0, 0}}, {{0, 0, 0, 0}, {-1, 1, 0, 0}, 52 | {0, 0, 0, 0}}, {{0, 0, 0}, {1, 0, -1}, {-1, 0, 1}, {0, 0, 0}}}, 53 | {{{0, 0, 0}, {0, 0, 0}, {0, 1, 0}}, {{0, 0, 0, 0}, {1, 0, 0, 1}, 54 | {1, 0, 0, 1}}, {{0, 0, 1}, {0, 0, 0}, {0, 0, 0}, {0, 0, 0}}}, 55 | {{{1, 0, 0}, {1, 0, 0}, {1, 0, 0}}, {{0, 1, 0, 0}, {0, 0, 0, 0}, 56 | {0, 0, 0, 0}}, {{0, 1, 0}, {0, 1, 0}, {0, 0, 0}, {0, 0, 0}}}, 57 | {{{0, 0, 0}, {1, 1, 0}, {0, 0, 0}}, {{0, 0, 1, 0}, {0, 0, 0, 0}, 58 | {0, 1, 1, 0}}, {{0, 1, 0}, {0, 0, 0}, {0, 1, 0}, {0, 0, 0}}}} 59 | -------------------------------------------------------------------------------- /solutions/335-36-mod0.exp: -------------------------------------------------------------------------------- 1 | (a11+a12+a31+a32)*(b24+b25)*(2*c11-2*c21-c31+c41) 2 | (-a22+a23+a32-a33)*(b21+b22+b23+b24)*c33 3 | (-a21-a22+a31+a32)*(b22+b24+b25)*(2*c12-2*c22-c32+c42) 4 | (-a11+a12-a13-a31+a32-a33)*(b21+b22)*(c13-c43+c53) 5 | (-a12+a13-a22+a23)*(b22-b23+b24+b25)*c31 6 | (-a13)*(b34+b35)*(c12+c21-c22+c31-c32-c41+c42) 7 | (-a33)*(-b11-b12-b13-b14+b31+2*b32+b34)*(-c12-c23-c33+c43) 8 | (-a11+2*a12-2*a13-a31)*(-b13-b14+b32+b34)*(c11-2*c13+2*c23+2*c33-c41-2*c43+c51) 9 | (a21-a31)*(-b11-2*b12-b13-2*b14-b15+b22+b24+b25)*(-c13+c23+c33-c43+c53) 10 | (-a11-a31)*(-b11-b12+b13-b15+b24+b25+b31+b35)*(c13-c23-c33+c43) 11 | (-a11+a12-a13-a31-a33)*(-b21-b22+b32+b34)*(-c11+c13-c43+c53) 12 | (-a13-a23)*(b12-2*b13-b22+b23-b24-b25+b33)*(c12-c22-c32+c42) 13 | a11*(b12-b13+b14+b15)*(-c13+c23+c33-c43+c51) 14 | (a11-a12+a13)*(b13+b14)*(-c11+c12+c13+c41-c42-c43-c51+c52+c53) 15 | (a22-a23+a33)*(b21+b22+b23+b24-b32+b33)*(c12+c33) 16 | (a11+a31+a32)*(b12-b13+b24+b25)*(-2*c11+c13+2*c21-c23+c31-c33-c41+c43) 17 | (a31+a32)*(-b12+b13)*(-2*c11+2*c12+2*c13+2*c21-2*c22-2*c23+c31-c32-c33-c41+c42+c43) 18 | (-a21+a31+a32)*(-b12+b13+b22+b24+b25)*(-2*c12-c13+2*c22+c23+c32+c33-c42-c43+c53) 19 | (a13+a21+a23)*(b12-2*b13+b32+b34+b35)*(-c11+c12+c21-c22+c31-c32-c41+c42+c51) 20 | a22*(b23+b24+b25-b32+b33)*(-c22+c42) 21 | (-a32)*(-b12+b13+b21+2*b22+b24)*(c33-c43+c53) 22 | (-a11+a12-a13-a21-a23)*(-b25+b32+b34)*(c11+c12-c21-c31+c41-c42-c51+c52) 23 | (a21+a23)*(b32+b34+b35)*(c11-2*c12-c21+c22-c31+c32+c41-c42-c51+c52) 24 | (-a22+a23)*(-b32+b33)*(c12-c31+c32+c33-c42+c52) 25 | (a13-a22+a23)*(-b22+b23-b24-b25-b32+b33)*(c12-c22+c31-c32+c42) 26 | (-a11-a13-a21-a23)*(b12-2*b13-b25+b32+b34)*(-c11+c21+c31-c41+c51) 27 | (a11-a12+a13+a21)*(-b13-b14-2*b25+2*b32-b33+b34)*(c12-c42+c52) 28 | (a11-a12+a13+a31)*(-b13-b14+b32+b34)*(c11-3*c13+4*c23+4*c33-c41-5*c43+c51+c53) 29 | (a11-a12+a13+a21+a22-a23)*(b25-b32+b33)*(c12-c42+c52) 30 | (a23-a33)*(b21+b22+b23+b24+b31+2*b32+b33+2*b34+b35)*c12 31 | (a11+a31+a33)*(-b11-b12-b13-b14+b31+2*b32+2*b34+b35)*(-c11+c13-c23-c33+c43) 32 | (-a21)*(-b13-b14-b15+b32+b34+b35)*(-c13+c23+c33-c43+c52+c53) 33 | (-a31-a33)*(b11+b12+b13+b14)*(c11-2*c13+c23+c33-c43+c53) 34 | (a21+a33)*(b11+b12+b13+b14+b32+b34+b35)*(c12-c13+c23+c33-c43+c53) 35 | a12*(b22+2*b24+b25+b32+b34)*(-c11+c21+c31) 36 | (a11+a13+a31+a33)*(b21+b22+b31+b32+b34+b35)*c11 37 | -------------------------------------------------------------------------------- /solutions/336-42-mod2.exp: -------------------------------------------------------------------------------- 1 | (a31+a32)*(b13+b14+b16+b21+b25+b26+b31+b35)*(c11+c13+c22+c31+c33+c41+c43) 2 | (a33)*(b13+b14+b16+b21+b24+b31+b34+b36)*(c11+c12+c13+c21+c22+c23+c32+c42+c51+c52+c53) 3 | (a11+a13+a21+a23)*(b15+b16+b31+b32+b33+b34)*(c11+c12+c13+c22+c23+c32+c33+c41+c42+c43+c51+c52+c53+c61) 4 | (a22+a32)*(b13+b14+b16+b23+b24+b33+b34+b36)*(c11+c12+c21+c22+c23+c32+c33+c42+c51+c52) 5 | (a13+a23)*(b15+b16+b35+b36)*(c12+c22+c32+c42+c52) 6 | (a12+a13+a32+a33)*(b21+b23+b26+b31+b35)*(c11+c41+c51+c52+c53+c61+c62+c63) 7 | (a22)*(b11+b15+b23+b25+b26+b31+b35)*(c11+c22+c23+c32+c33+c41+c51+c52+c53+c61+c62+c63) 8 | (a21+a22)*(b11+b15+b31+b35)*(c12+c22+c32+c42) 9 | (a11+a31)*(b11+b12+b13+b14+b15+b21+b22+b23+b24+b26+b31+b32+b33+b34)*(c11+c41+c51+c61) 10 | (a11+a12+a21+a23+a32+a33)*(b13+b14+b16+b31+b32+b33+b34)*(c22+c41) 11 | (a21+a31)*(b16+b36)*(c12+c42+c52+c62) 12 | (a12+a22+a31)*(b11+b12+b16+b21+b25+b26+b31+b35)*(c21+c22+c23) 13 | (a11+a13+a21+a23+a32+a33)*(b31+b32+b33+b34)*(c11+c12+c13+c22+c23+c32+c33+c42+c43+c51+c52+c53+c61) 14 | (a32+a33)*(b13+b14+b16+b21+b24+b25+b26+b32+b33+b34+b35)*(c22+c23+c42+c43) 15 | (a22+a23+a32+a33)*(b13+b14+b16+b33+b34+b36)*(c22+c42) 16 | (a12+a22)*(b11+b12+b13+b14+b21+b22+b23+b24+b25+b26+b31+b32+b33+b34)*(c11+c22+c23+c41+c51+c61) 17 | (a22+a31)*(b11+b15+b21+b25+b26+b31+b35)*(c12+c21+c23+c31+c33+c42+c51+c52+c53+c61+c62+c63) 18 | (a21+a23+a31+a33)*(b13+b14+b16+b36)*(c11+c12+c13+c21+c22+c32+c33+c42+c51+c52+c53+c63) 19 | (a11+a22+a31)*(b11+b13+b14+b15+b16+b21+b22+b23+b24+b26+b31+b32+b33+b34)*(c11+c21+c31+c41) 20 | (a12+a13+a21+a23+a32+a33)*(b31+b35)*(c31+c41+c51+c52+c53+c61+c62+c63) 21 | (a11+a12+a31+a32)*(b13+b14+b16+b21+b22+b23+b24+b26+b31+b32+b33+b34)*(c11+c22+c31+c41) 22 | (a13+a21+a23+a31)*(b15+b16+b36)*(c12+c21+c22+c31+c32+c42+c52+c61) 23 | (a21+a23+a32+a33)*(b13+b14+b16+b31+b35)*(c11+c13+c22+c31+c33+c42) 24 | (a13+a33)*(b13+b14+b16+b23+b24+b25+b33+b34+b35+b36)*(c11+c12+c21+c22+c32+c42+c51+c52) 25 | (a21+a23+a31)*(b11+b13+b16+b36)*(c11+c12+c13+c31+c33+c42+c51+c52+c53+c61+c62+c63) 26 | (a12+a13+a22+a32+a33)*(b21+b23+b26)*(c11+c21+c31+c41+c51+c52+c53+c61+c62+c63) 27 | (a11+a13+a21+a23+a31+a33)*(b13+b14+b16+b21+b24+b25+b26+b31+b34+b35)*(c11+c12+c13+c21+c22+c23+c32+c33+c42+c43+c51+c52+c53) 28 | (a11+a13+a21+a23+a31)*(b13+b14+b15+b21+b24+b25+b26+b31+b34+b35)*(c11+c12+c13+c21+c22+c23+c31+c32+c33+c41+c42+c43+c51+c52+c53) 29 | (a21+a22+a23+a31+a32+a33)*(b26)*(c12+c21+c31+c32+c41+c42+c51+c52+c53+c63) 30 | (a32+a33)*(b25+b26+b31+b32+b33+b34)*(c11+c12+c13+c22+c23+c32+c33+c41+c51+c52+c53+c61) 31 | (a12+a13)*(b13+b14+b16+b21+b24+b25+b26+b32+b33+b34+b35)*(c21+c41) 32 | (a13+a22+a32+a33)*(b13+b14+b16+b23+b24+b25+b33+b34+b36)*(c11+c12+c22+c31+c32+c42+c51+c52) 33 | (a21+a23)*(b11+b13+b16+b31+b35)*(c11+c12+c13+c32+c33+c41+c51+c52+c53+c61+c62+c63) 34 | (a12+a22+a32)*(b13+b14+b16+b22+b23+b24+b25+b26+b32+b33+b34+b35)*(c11+c22+c23+c31+c41) 35 | (a11+a12+a22+a31)*(b11+b12+b13+b14+b21+b22+b23+b24+b26+b31+b32+b33+b34)*(c11+c21+c22+c41+c51+c61) 36 | (a11+a21+a23+a31)*(b11+b14+b21+b24+b25+b26+b31+b34+b35)*(c31+c41) 37 | (a23)*(b11+b13+b16+b31+b33+b36)*(c32+c42) 38 | (a22+a32+a33)*(b13+b14+b16+b21+b24+b33+b34+b36)*(c21+c22+c23+c31+c33+c42) 39 | (a12+a22+a32+a33)*(b25+b26)*(c22+c23+c31+c41+c61) 40 | (a21+a23+a31+a33)*(b13+b14+b16+b26)*(c12+c21+c31+c32+c41+c42+c51+c52+c53+c63) 41 | (a31)*(b13+b15+b21+b25+b26+b31+b35)*(c11+c12+c13+c41+c42+c43+c51+c52+c53+c61+c62+c63) 42 | (a11+a12+a21+a22)*(b11+b12+b13+b14+b31+b32+b33+b34)*(c22) 43 | -------------------------------------------------------------------------------- /solutions/344-38-mod0.exp: -------------------------------------------------------------------------------- 1 | (a11+a21-a31)*(b11-b12-b13-b14+b22+b23+b31-b32-b33-b34+b42)*c43 2 | (a13+a21)*(-b21+b22+b24+b32+b34)*(c11+c41) 3 | (-a21-a22+a23+a31-a34)*(b22+b23+b42)*(-c23+c31-c32+c33+c43) 4 | (a31-a34)*(-b13+b22+b23-b33+b42)*(-c31+c32-c33+c43) 5 | (2*a11+a12-a13-a14+2*a21+a22-a23-a24)*(b21-b22-b24+b32)*(-c21+c41) 6 | (a11-a13+a14+a21-a23+a24-a31+a33-a34)*(-3*b21+5*b22+2*b23+3*b24-b31+b32+b33+b34-2*b41+4*b42+2*b43+2*b44)*c31 7 | (2*a21+a22-a23-a24)*(b21+b42)*(c21-c22-c41+c42) 8 | (a11+a12-a14+a21+a22-a24+a31-a33)*(b22+b23+b32)*(-c23+c31+c33+c43) 9 | (a11-a14+2*a21+a22-a23-a24)*(-b21+2*b22+b24+b42)*(-c21+c41+c42) 10 | (a11-a14)*(b11-b12+b14+b31-b32+b34+2*b44)*(-c41+c42) 11 | (-a11-a12+a14-2*a21-a22+a23+a24)*(-b21+b22+b32)*(c12-c21+c22+c41) 12 | (-a11-a21+a31-a33)*(b11+b21-b22-b24+b31-b32-b34+b41)*(-c11+c43) 13 | (-a11-a12+a14-a23+a24+a32)*b23*(-c23+c33+c43) 14 | (-a11+a14+a21)*(b11-b12+b14-b21+b31-b32+b34-b42+b44)*(-c41+c42) 15 | (-a11+a14-a21+a24)*(b22+b31-b32-b34-b41+2*b42+b44)*(-c31+c42) 16 | (-a11-a12+a14-a21+a31+a32-a33-a34)*b21*(-c11+c12-c21+c22) 17 | (-a31+a33)*(-b11+b13-b22-b23-b32-b41+b43)*(c11+c13) 18 | (-a21+a23)*(b21+b22+b23-b31+b32+b33+2*b41)*(-c31+c32) 19 | (-2*a31-a32+a33+a34)*(b12+b22+b23+b32+b42)*(-c23+c43) 20 | (a31-a33-a34)*(b13+b33+b43)*(c13-c31-c33+c43) 21 | (-2*a11+2*a13-a14-2*a21+2*a23-a24+2*a31-2*a33+a34)*(-2*b21+3*b22+b23+2*b24-b31+b32+b33+b34-b41+2*b42+b43+b44)*c31 22 | (a21+a22-a23)*(b22+b42)*(c22-c23+c31-c32+c33-2*c42+c43) 23 | (-a11-a21+a34)*(-b13-b21+2*b22+b23+b24-b33-b41+2*b42+b44)*(c31+c43) 24 | (a31-a33)*(b13-b22-b23-b32+b43)*(c11+c13+c31+c33) 25 | a21*(-b11+b12+b21-b31+b32+b42)*(c11-c12+c13-c41+c42+c43) 26 | (a11+a21)*(2*b12+b14+b21-b22-b24+b32+2*b42+b44)*(c41+c43) 27 | (a31+a32-a33-a34)*(b12+b32+b42)*(-c11+c12-c13-2*c21+c22-c23+2*c41+c43) 28 | (-a21+a31+a32-a33-a34)*(b12+b21+b32+b42)*(c11-c12+c13+c21-c22+c43) 29 | (-a21+a24-a31+a34)*(b21+b41+b43)*(-c31+c32) 30 | (-a11-a21-a31-a32+a33+a34)*(b12+b21-b22-b24+b32+b42)*(-c21+2*c41+c43) 31 | (-a12+a13+a21+a31+a32-a33-a34)*(-b21+b22+b24)*(c21-2*c41) 32 | (a21-a23)*(b22-b31+b32+b41)*(c12-c31+c32+c42) 33 | (-a21-a31+a34)*(b13+b21+b33+b41+b43)*(c13+c31-c32+c43) 34 | (a21-a23-a24)*(b21+b41)*(c11-c12-c31+c32) 35 | (-a11-a12+a14-a21-a22+a24)*(b22+b32)*(-c12-c22-c23+c31+c33+c43) 36 | (2*a11-a13-a14+2*a21-a23-a24-a31+a33)*(-b21+b22+b24-b31+b32+b34)*(c11+c31) 37 | (-a11+a14-2*a21+a23+a24)*(b22+b24-b31+b32+b34+b41)*(c11+c42) 38 | (a21+a33)*(b11+b13+b21+b31+b33+b41+b43)*(c13+c43) 39 | -------------------------------------------------------------------------------- /solutions/345-47-mod0.exp: -------------------------------------------------------------------------------- 1 | (a14-a24-a32+a33)*(b21-b22-b23-b24-b25+b42+b43)*(2*c11-c13+2*c21-c31-c43+c51+c53) 2 | (-a31-a33+a34)*(-b21+b22+b23+b24+b44+b45)*(c13+c23-c33+c43) 3 | (a24-a31-a33)*(-b11+b12+b13+2*b14+b15-b21+b22+b23+b24+b44+b45)*(c12+c22-c32-c43+c52+c53) 4 | (a23-a33)*(b11-b12-b13-2*b14-b15-b31+b32+b33+2*b34+b35)*(c11+c12+c41+c42) 5 | (-a11+a12-a23+a24-a32)*(b23+b24+b25+b33+b34+b35)*(c11+c41) 6 | a31*(-b11+b12+b13+2*b14+2*b15-b25+b31-b32-b34-b35+b43+b44+b45)*(c12+c13+c22-c32+c52+c53) 7 | (a11-a22+a23-a24)*(b11-b12-b13-b14-b15+b23+b25-b31+b32+b33+b34+b35)*(c11+c22-c31-c32+c41) 8 | (-a11+a12-2*a13+a24+a32-a33)*(b11-b14-b15-b31+b34+b35)*(c11+c21) 9 | (a24-a34)*(b21-b22-b23-b24-b41+b42+b43+b44)*(-c11-c21+c31-c43-c51+c53) 10 | (a11-a21)*(b11-b12-2*b13-2*b14-2*b15-b24-b31+b32+b33+b34+b35)*(-c22+c32) 11 | (-a21+a22-a23+a24-a32)*(-b21+b22+b23+2*b24+b25)*(c12+c42) 12 | (a11+a13)*(-b11+b14+b15-b22-b23-b31+b32+b34-2*b41+2*b42+b43+2*b44+b45)*(-2*c11-c12-c21+c31-c41-c42+c52) 13 | (a21-a31)*(b11-b12-b13-b14-b22-b23-b31+b34)*(c12+c22-c32+c52) 14 | (-a24+a33)*(-b11+b12+b13+2*b14+b15+b31-b32-b34+b43+b44+b45)*(-c11+c22-c32-c41-c42-c43+c52+c53) 15 | (-a11+a12-a13+a14-a32+a33-a34)*(b11-b12-b14-b15+b25-b31+b32+b34+b35)*(c11+c21+c23-c31-c33+c51) 16 | (-a11+a12-a13+a24+a32-a33)*(b11-b14-b15-b21+b24+b25-b31+b34+b35)*(-c21-c22-c23+c41+c42+c43) 17 | (a14-a24-a31-a33+a34)*(b21-b22-b23-b24-b25+b31-b32-b34-b35+b43)*(-c13-c43+c53) 18 | (-a11-a23+a24)*(b11-b12-b13-2*b14-b15-b23-b24-b25-b31+b32+b34)*(c11-c22+c32+c41) 19 | (a11+a13-a14+a24-a34)*(-b11+b12+b14+b15+b21-b22-b23-b24-2*b41+2*b42+b43+2*b44+b45)*(c11+c21-c31+c51) 20 | (-a11-a13+a21+a23)*(-b21+b22+b23+b24+b25-b31+b32+b33+b34+b35)*(-c12-c42+c52) 21 | (a11-a12+a13-a14-a31+a32-a33+a34)*(-b11+b12+b14+b15-b25+b31-b32-b34-b35+b43+b44+b45)*(-c23+c33) 22 | (a11-a12+a13-a24+a33)*(b11-b14-b15-b21+b24+b25-b31+b33+2*b34+2*b35+b43+b44+b45)*(c11-c22-c23+c41+c42+c43) 23 | (a22-a23+a24)*(b12+b13+b22+b23)*(-c11+c22+c31-c41-c42+c52) 24 | (-a32+a33)*(-b11+b14+b15+b21-b22-b23-b24-b25+b31+b33+b42+2*b43+b44+b45)*(c12+c13+c22+c23) 25 | (a32-a33+a34)*(b21-b22-b23-b24+b42+b43)*(c11+c21+c23-c31-c43+c51+c53) 26 | (-a21+a22-a23+a24+a31-a32+a33-a34)*(-b21+b22+b23+b24)*(c13-c33+c43) 27 | (a11-a12+2*a13-2*a14+a24+a32-a33)*(b11-b12-b14-b15-b31+b32+b34+b35)*(c11+c21-c31+c51) 28 | (-a21+a22-a23+a24-a33)*(b11-b14-b15-b21+b22+b23+b24+b25-b31+b32+b33+b34+b35)*(c13-c32-c33+c43+c52) 29 | (-a11+a12-a13+a14-a32)*(-b21+b22+b24+b43+b44+b45)*(c11-c23+c33+c41) 30 | (-a24)*(-b31+b32+b34-b41+b42+b44)*(-2*c11-c12-c21+c31-2*c41-2*c42-c43+c51+2*c52+c53) 31 | (-a31-a33)*(-b11+b14+b15+b21-b22-b23-b24-b25+b31-b32-b34-b35+b43)*(c12+2*c13+c22+c23-c32-c33+c43+c52) 32 | (-a23+a33)*(b22+b23+b32+b33)*(-c32+c52) 33 | (-a11+a12-a13+a24-a32)*(b33+b34+b35+b43+b44+b45)*(-c22-c23+c42+c43) 34 | (a14-a24+a34)*(-b21+b22+b23+b24+b25-b31+b32+b34+b35-b41-b43+b44+b45)*(c11-c13+c21-c31-c43+c51+c53) 35 | (a21+a23-a24)*(-b11+b12+b13+2*b14+b15-b21+b22+b23+2*b24+b25)*(c12+c22-c32+c42) 36 | (a21-a22+a23-a24)*(b11-b12-b13-b14-b15-b21+b22+b23+b24+b25-b31+b32+b33+b34+b35)*(c12+c13-c22-c33+c42+c43) 37 | (-a11-a13+a24)*(b21-b22-b23-b24-b25-b31+b32+b34-2*b41+2*b42+b43+2*b44+b45)*(-2*c11-c12-c21+c31-2*c41-c42+c51+c52) 38 | (-a11-a13+a14)*(2*b21-2*b22-b23-2*b24-b25-2*b41+2*b42+b43+2*b44+b45)*(c11+c21-c31+c41) 39 | (-a14+a24)*(b21-b22-b23-b24-b25-b41+b42+b43+b44+b45)*(2*c11-c13+c21-c31+2*c41-c43-c51+c53) 40 | (-a21-a23+a31+a33)*(-b21+b24-b31+b34)*(c12+c22-c32+c52) 41 | (a11-a12+a13-a14)*(-b21+b22+b24)*(c11-c21-c23+c33+c41) 42 | (-a12+a13-a14+a22-a23+a24)*(b23+b25)*(c11-c31+c41) 43 | (a11+a13-a22+a23-a24)*(b11-b14-b15+b22+b23-b31+b32+b33+b34+b35)*(-c11-c12+c31-c41-c42+c52) 44 | (a24+a32-a33)*(-b22-b23+b42+b43)*(c11+c12+c21+c22) 45 | (a21-a22+a23-a24-a31)*(b12+b13-b21+b22+b23+b24)*(c12+c13+c22-c32-c33+c43+c52) 46 | a11*(b11-b12-b14-b31+b32+b34)*(c11-c22+c32+c51) 47 | a32*(-b11+b14+b15+b22+b23+b24+b31+b33+b43+b44+b45)*(c11+c12+c13+c41+c42+c43) 48 | -------------------------------------------------------------------------------- /solutions/346-56-mod2.exp: -------------------------------------------------------------------------------- 1 | (a14+a24)*(b11+b16+b41+b46)*(c32+c62) 2 | (a12+a13+a14)*(b11+b15+b16+b23+b41+b43+b45+b46)*(c31+c33+c51+c63) 3 | (a11+a13+a14+a21+a22+a31+a33)*(b15+b43+b45+b46)*(c12+c22+c52+c62) 4 | (a12+a32+a33)*(b11+b12+b13+b14+b15+b16+b21+b22+b23+b24+b25+b26+b34+b41+b42+b43+b45+b46)*(c13+c41+c43) 5 | (a12+a13+a14+a32+a34)*(b11+b12+b15+b16+b23+b33+b41+b42+b43+b45+b46)*(c11+c31+c33+c61+c63) 6 | (a11+a13+a21+a22+a24+a31+a33)*(b15+b16+b43+b45+b46)*(c12+c13+c32+c52+c53+c62) 7 | (a11+a13+a14)*(b11+b22+b32+b33+b35+b36+b43+b45+b46)*(c11+c12+c13+c22+c52+c53+c61+c62) 8 | (a11+a13+a14+a23+a31+a33+a34)*(b11+b13+b15+b16+b22+b32)*(c13+c22+c42+c43+c52) 9 | (a12+a14+a32+a34)*(b13+b23+b33)*(c11+c31+c61) 10 | (a22+a24+a32+a34)*(b11+b14+b15+b21+b24+b25+b31+b34+b35)*(c12+c32+c62) 11 | (a21+a24)*(b11+b22+b23+b25+b26+b32+b33+b35+b36)*(c41+c43+c53+c61+c62) 12 | (a21+a23+a31+a33)*(b13+b15+b16+b43+b45+b46)*(c11+c12+c13+c22+c52+c53+c61+c62) 13 | (a12+a21+a22+a24+a32)*(b23+b25+b26)*(c13+c53) 14 | (a11+a12+a14)*(b15+b16+b32+b33+b35+b36+b42)*(c11+c21) 15 | (a21+a22+a24)*(b16+b22+b23+b25+b26+b32+b33+b35+b36)*(c12+c22) 16 | (a22+a23+a24+a32+a33+a34)*(b12+b13+b16+b31+b34+b35+b42)*(c53+c63) 17 | (a12+a21+a24)*(b12+b13+b15+b16+b22+b23+b25+b26+b32+b33+b35+b36)*(c12+c41+c43+c52+c53+c61+c62) 18 | (a31+a33)*(b12+b42)*(c11+c12+c13+c21+c22+c23+c31+c33+c52+c53+c61+c62) 19 | (a11+a13+a14+a21+a22+a24+a31+a33+a34)*(b11+b14+b22+b32+b33+b35+b36+b43+b45+b46)*(c13+c22+c42+c52+c53) 20 | (a22+a23+a24+a32+a34)*(b12+b13+b14+b16+b21+b24+b25+b31+b34+b35+b41+b42+b43+b45+b46)*(c12+c32+c53+c62+c63) 21 | (a11+a13+a14+a21+a23+a24+a31+a33+a34)*(b11+b22+b32+b33+b35+b36+b43+b45+b46)*(c22+c42+c52) 22 | (a13)*(b13+b23+b31+b32+b35+b36+b41+b42+b43+b45+b46)*(c11) 23 | (a12+a22)*(b13+b16+b23+b26+b33+b36)*(c12+c52+c62) 24 | (a12+a13+a32+a33)*(b23+b34+b43+b44)*(c41) 25 | (a14+a22+a23)*(b11+b16+b23+b41+b43+b46)*(c32+c51+c61+c62) 26 | (a11+a14+a31+a34)*(b13+b15+b16+b33+b35+b36)*(c21+c51) 27 | (a23)*(b11+b13+b14+b15+b21+b23+b24+b25+b31+b33+b34+b35)*(c32+c62) 28 | (a12+a13+a14+a32+a33)*(b14+b23+b43+b44)*(c33+c41+c63) 29 | (a11+a13+a14+a31+a34)*(b12+b22+b32)*(c13+c21+c23+c51+c53) 30 | (a11+a13+a31+a33)*(b13)*(c11+c12+c13+c21+c31+c32+c52+c53+c61+c62) 31 | (a22+a23)*(b11+b21+b22+b25+b32+b33+b35+b36+b41+b43+b46)*(c42+c51+c52+c61+c62) 32 | (a12+a13+a14+a31+a33)*(b12+b13+b42)*(c11+c21+c31+c33+c61+c63) 33 | (a12)*(b11+b21+b32+b33+b35+b36+b41+b42+b43+b45+b46)*(c11+c12+c13+c41+c43+c51+c52+c61+c62) 34 | (a14)*(b23+b43)*(c31+c32+c41+c61+c62) 35 | (a22+a23+a24+a31+a33)*(b12+b13+b16+b42)*(c12+c22+c52+c53+c62+c63) 36 | (a22+a23+a24)*(b12+b13+b16+b42+b43+b46)*(c32+c52+c53+c63) 37 | (a24+a34)*(b21+b24+b25+b41+b44+b45)*(c42) 38 | (a23)*(b11+b13+b14+b15+b16+b22+b24+b32+b34)*(c12+c13+c42+c43) 39 | (a11+a13+a14)*(b22+b42)*(c11+c12+c13+c21+c22+c23+c41+c43+c51+c52+c61+c62) 40 | (a11+a13+a14+a21+a24)*(b11+b12+b13+b15+b16)*(c12+c22+c41+c43+c52+c53+c61+c62) 41 | (a12+a23+a32)*(b14+b24+b34)*(c13+c43) 42 | (a11+a13+a14+a32+a33)*(b11+b12+b13+b14+b15+b16+b22+b42)*(c13+c23+c41+c43) 43 | (a12+a31+a34)*(b12+b13+b15+b16+b22+b32+b33+b35+b36)*(c13+c21+c51+c53) 44 | (a32+a34)*(b11+b12+b13+b15+b16+b41+b42+b43+b45+b46)*(c11+c12+c13+c31+c32+c33+c61+c62+c63) 45 | (a12+a13+a22+a23)*(b11+b13+b15+b23+b33+b36+b41+b43+b45+b46)*(c51+c61) 46 | (a11+a13+a14+a22+a23)*(b12+b13+b16+b32+b33+b35+b36+b42)*(c12+c22+c51+c52+c61+c62) 47 | (a33)*(b12+b14+b21+b23+b24+b25+b26+b31+b33+b34+b35+b36+b41+b42+b43+b45+b46)*(c13+c53+c63) 48 | (a32+a33)*(b14+b21+b23+b24+b25+b26+b41+b43+b45+b46)*(c41+c43+c53+c63) 49 | (a12+a22+a23)*(b11+b12+b15+b21+b22+b25+b33+b36+b41+b42+b43+b45+b46)*(c12+c51+c52+c61+c62) 50 | (a22+a23+a24+a34)*(b14+b21+b24+b25+b41+b45)*(c42+c53+c63) 51 | (a31+a32+a34)*(b11+b12+b13+b14+b15+b16+b42)*(c13+c23) 52 | (a21+a22+a24)*(b11+b14+b15+b16+b22+b23+b25+b26+b32+b33+b35+b36)*(c13+c22+c52+c53) 53 | (a12+a13+a14+a32+a33+a34)*(b13+b14+b23+b33+b43+b44)*(c33+c63) 54 | (a34)*(b14+b44)*(c33+c42+c43+c63) 55 | (a11+a13+a21+a23+a31+a33)*(b13+b15+b16+b43+b45+b46)*(c11+c12+c13+c32+c52+c53+c61+c62) 56 | (a11+a13+a14+a31+a33+a34)*(b11+b13+b14+b15+b16+b22+b32)*(c22+c23+c42+c43+c52+c53) 57 | -------------------------------------------------------------------------------- /solutions/355-58-mod0.exp: -------------------------------------------------------------------------------- 1 | (a14-a15)*(2*b11+b12-2*b22+b31+b32+b42+b51+3*b52-b53+b54)*(-c11+c13) 2 | (-a12+a14-a15+a22-a32-a35)*(-b22-b24+b42+b44+b52+b54)*(-c11+c13+c33+c41-c43+c51-2*c53) 3 | (-a14+a15-a31+a32+2*a33+a35)*(b11+b12+b15+b53-b54+b55)*(-c13+c51) 4 | (a13-a14+a23)*(-2*b13-b22-b33+b42+b52)*(-c21+c22-c32+c41-c42+c51) 5 | (-a12+a14-a15+2*a34-a35)*(b13+b23)*(-c11+c13-c31+c33-c43+c51-2*c53) 6 | (a24-a25)*b41*c12 7 | (-a12+a14-a15-a32+a34-a35)*(b13-b22+b23-b24+b42+b44+b52+b54)*(-c13-c33+c43+2*c53) 8 | (-a24)*(-b22+b42+b43+b52+b53)*(-c32+c52) 9 | (-a13+a14-a33)*(2*b13-b23+b24-b25+b33+b43-b44+b45+b53-b54+b55)*(-c33+c51) 10 | (-a13+a14+a21-a22-2*a23+a31-a32-3*a33)*(-b23+b24-b25+b43-b44+b45+b53-b54+b55)*c33 11 | (a11-a12-2*a13-a14+a21-a22-2*a23)*(-b21-b22+b23-b24+b41+b42+b44+b51+b52+b54)*(-c11+c12-c31+c51) 12 | (-a21+a22+2*a23+a24-a31+a32+2*a33+a34)*(b12-2*b15-b35+b43-b44+b45+b53-b54+b55)*c52 13 | (a12+a13+a14+a23)*(b12+2*b14-b22+b32+b34)*(-c21+c22+c41+c51) 14 | (-a11+a12+2*a13-a14+a15-a21+a22+2*a23-2*a34+a35)*(b13-b21-b22+b23-b24+b41+b42+b44+b51+b52+b54)*(-c11-c31+c51) 15 | (-a12-a13-a14)*(2*b12+2*b14+b32+b34)*(-c21+c22+c43+c51) 16 | (a13-a14+a23-2*a24+a25-2*a34+a35)*(-b22+b42+b52)*(-c22+c32+c42) 17 | a34*(b22+2*b24-b25-b42-2*b44+b45-b52-b53-2*b54+b55)*(-c33+c53) 18 | (-a12-a13-a14-a21+2*a23-a31+a33)*(b13-b14+b15+b23-b24+b25)*c43 19 | (-a21+2*a23)*(b12+b14)*(-c11+c12+c41-c42+c43+c51) 20 | (-a21+a22+a23+a25)*b12*(c12-c22+c42) 21 | (-a32-a34)*(-b12-2*b13-b15-b22-2*b23-b25+b52+b54)*(c43+c53) 22 | (-a24+a25-a33-a34+a35)*(b12+2*b22-b42-2*b52+b53-b54+b55)*(-c23+c43+c53) 23 | (a11-a12-a13-a14+a33)*(2*b11+b31)*(c11-c21+c41) 24 | (-a33)*(b12-2*b22+b32+b42+2*b52)*(-c11+c13+c21-c23-c41+c43-c51+c53) 25 | (a14-a15+2*a34-a35)*(-b21-b22-b24+b41+b42+b44+b51+b52+b53+b54)*(-c11+c13-c31+c51) 26 | (a11-a12-2*a13-a14)*(b11-b12+b13-b14+b31)*(-c11+c12+c51) 27 | a14*(-2*b13-b21-b22+b23-b24-b33+b41+b42-b43+b44+b51+b52-b53+b54)*(-c31+c51) 28 | (-a32-a35)*(b52+b54)*(-c11+c13+c22-c23+c41+c51) 29 | (-2*a34+a35)*b53*(-c11+c13+c22-c23-c31-c32+c33-c42+c43+c51) 30 | (-a11+a12+2*a13+a14-a21+a22+2*a23+a25)*(-b12+b41+b51)*c12 31 | (-a11+a12+2*a13+a14-a21+2*a23)*(-b11-b12+b13-b14-b21-b22+b23-b24+b42+b44+b52+b54)*(-c11+c12+c41+c51) 32 | (a31-a32-2*a33-a34)*(b12+b15+b53-b54+b55)*(-c13-c52+c53) 33 | (a24-a25+2*a34-a35)*(b22-b42-b52+b53)*(c22-c23-c32-c42+c43+c53) 34 | (-a22)*(-b22-b24+b42+b44+b52+b54)*(-c11-c12+c13+c33+c41+c42-c43+c51+c52-2*c53) 35 | (a24-a25-a31+a32+2*a33+a34)*(b12+b53-b54+b55)*(-c23+c43-c52+c53) 36 | (a21-2*a23+a31-a32-2*a33-a34)*(b12+b13+b15+b23-b24+b25)*(c43+c52) 37 | (a13-a14)*(2*b13+b33)*(-c21+c22+c31-c32-c33+c41-c42+c51) 38 | (a21-a22-2*a23+a31-a32-2*a33-a34)*(-b13-b23+b24-b25+b43-b44+b45+b53-b54+b55)*(-c33+c52) 39 | (a11-a12-2*a13-a15+a31-a32-2*a33-a35)*(3*b11+b12+b13-b14+2*b15-2*b23+2*b24-2*b25+b31+b33-b34+b35+b43-b44+b45+b53-b54+b55)*c51 40 | (-a14+a15+a32+a35)*(b11-b13+b21-b23+b52+b54)*(-c11+c13+c41+c51) 41 | (a24-a25)*(-b12-b53+b54)*(c22-c23-c42+c43-c52+c53) 42 | (-a24+a25+a32+a35)*(-b12-b22+b52+b54)*(c22-c23+c43+c53) 43 | (-a23)*(b12-2*b13+2*b14-b33+b34)*(-c21+c22+c41-c42+c51) 44 | (-a22)*(b13+b23)*(-c12-c32+c52) 45 | (-a13-a14+a15-a23)*(2*b11+b12-2*b22+b31+b32+b42+b52)*(-c21+c41+c51) 46 | (-a12-a14)*(-b11+b12+b13+b14-b21-b22+b23-b24+b32+b34)*(c41+c51) 47 | (a31-a32-a33-a35)*(b53-b54+b55)*(-c23+c43+c51) 48 | (-a11+a12+3*a13+a15-a31+a32+3*a33+a35)*(2*b11+b13-b14+b15-2*b23+2*b24-2*b25+b31+b33-b34+b35+b43-b44+b45+b53-b54+b55)*c51 49 | (a22+a24)*(-b12-b22+b42+b44+b52+b54)*(c42+c52) 50 | (a21-a22-2*a23)*b13*(-c11+c12-c31+c32-c33+c51) 51 | (a11-2*a13-a14+a15+a21-2*a23+a32+a35)*(-b11+b13-b21-b22+b23-b24+b42+b44+b52+b54)*(-c11+c41+c51) 52 | (a14-a15-a33)*(2*b11+b12-2*b22+b31+b32+b42+2*b52)*(c11-c13-c21+c41+c51) 53 | (-a11+a12+2*a13+a14+a23)*(2*b11+b12+b31)*(c12-c21+c41+c51) 54 | (-a21+a22+3*a23+a24-a31+a32+2*a33+a34)*(2*b15+b35)*c52 55 | a33*(2*b12+2*b15+b32+b35+b53-b54+b55)*(-c51+c53) 56 | (-a14+a15-a34+a35)*(b12+b13+b15-2*b21-b22+b23-b24+b41+b42+b44+2*b51+b52+b53+b55)*c13 57 | (a12+a13+a14+a33)*(2*b12+b13+b14+b15+b23-b24+b25+b32+b34)*(c43+c51) 58 | (a12+a13+a14+a22+a23+a25+a32+a35)*(b12+b22)*c22 59 | -------------------------------------------------------------------------------- /solutions/356-71-mod2.exp: -------------------------------------------------------------------------------- 1 | (a14+a25)*(b42+b44+b45+b52+b54+b55+b56)*(c11+c13+c32+c51+c53+c61+c62) 2 | (a13)*(b31+b32+b33+b35+b42+b51+b52+b55)*(c21+c22+c23+c61+c62+c63) 3 | (a12+a22+a23+a32+a33)*(b24+b25+b26+b32+b34+b35+b36)*(c23+c43+c61+c63) 4 | (a21+a23+a25)*(b33+b35)*(c22+c23+c52+c53) 5 | (a13+a33)*(b21+b25+b31+b32+b33+b34+b35)*(c22+c23+c62+c63) 6 | (a22+a23+a24)*(b42+b43+b46)*(c22+c23+c42+c43+c63) 7 | (a13+a21+a23)*(b21+b25+b31+b33)*(c12+c13+c22+c23+c62+c63) 8 | (a11+a25+a35)*(b12+b14+b15+b23+b25+b51+b53)*(c13+c21+c61) 9 | (a22)*(b22+b24+b26+b32+b33+b34+b35+b36)*(c12+c32+c52+c62) 10 | (a12+a15)*(b52+b53+b54+b55+b56)*(c31+c32+c33) 11 | (a15+a35)*(b22+b23+b24+b51+b52+b53+b54+b55)*(c41+c61) 12 | (a11)*(b11+b12+b14+b15+b16+b23+b25+b51+b53)*(c11+c13+c41+c43+c51+c53) 13 | (a21)*(b11+b15+b21+b25+b31+b35+b41+b45)*(c42+c52) 14 | (a25+a35)*(b14+b15+b23+b25+b52+b53+b56)*(c21+c23+c41+c43) 15 | (a11+a14+a31+a34)*(b41+b45)*(c11+c31+c61) 16 | (a25+a35)*(b12+b14+b15+b23+b25+b52+b53+b54+b55)*(c21+c23+c61+c63) 17 | (a13+a15+a25+a35)*(b42+b51+b52+b55)*(c21+c41) 18 | (a11+a22+a23+a31+a32+a33)*(b12+b13+b14+b15+b16+b21+b25)*(c13+c31+c41+c51) 19 | (a21+a23+a25+a31+a33+a35)*(b14+b15+b23+b25)*(c23+c53) 20 | (a11+a31)*(b11+b12+b15+b21+b25+b41+b45)*(c43+c53) 21 | (a24+a34)*(b12+b14+b15+b16+b42+b43+b44+b45)*(c32+c62) 22 | (a11+a25+a35)*(b14+b15+b23+b25+b53+b55)*(c21+c41+c43+c53) 23 | (a22+a23+a33)*(b24+b25+b26+b32+b33+b35+b36)*(c22+c23+c42+c43) 24 | (a12+a13+a14+a22+a23+a32+a33)*(b32+b34+b35+b36)*(c61) 25 | (a21+a23+a33)*(b14+b15+b33+b35)*(c13+c42+c53+c62+c63) 26 | (a23+a33)*(b12+b14+b15+b22+b24+b32+b33+b34+b35)*(c22+c62) 27 | (a22+a23+a33)*(b22+b24+b33)*(c13+c33+c42+c43+c53+c62) 28 | (a23+a33)*(b14+b15+b22+b25+b26+b32+b33+b36)*(c22+c42) 29 | (a14)*(b41+b43+b45+b52+b54+b55+b56)*(c41+c42+c43+c51+c52+c53) 30 | (a11+a31)*(b11+b12+b13+b14+b15+b21+b25)*(c13+c43+c53) 31 | (a25)*(b33+b34+b42+b54)*(c11+c12+c13+c41+c42+c43+c51+c52+c53) 32 | (a25)*(b34+b35+b44+b45+b54+b55)*(c11+c12+c13+c51+c52+c53+c61+c62+c63) 33 | (a12+a14+a15+a32+a34+a35)*(b42+b44+b45)*(c12+c13+c22+c23+c32+c33+c42+c43+c52+c53) 34 | (a21+a23+a25+a31+a33+a35)*(b12+b14+b15+b23+b25)*(c13+c23+c63) 35 | (a13+a25)*(b34+b35+b42+b52)*(c22+c23+c41+c61+c62+c63) 36 | (a11)*(b11+b13+b15+b51+b55)*(c41+c43+c51+c53) 37 | (a13+a25)*(b33+b35+b51+b55)*(c11+c12+c13+c41+c51) 38 | (a12+a15+a32+a35)*(b22+b23+b24+b42+b44+b45)*(c13+c33+c53+c63) 39 | (a14+a15+a24+a25+a34+a35)*(b22+b24+b25+b26+b32+b34+b35+b36+b42)*(c23+c43+c63) 40 | (a13+a22+a23)*(b21+b25+b33)*(c12+c13+c31+c41+c51) 41 | (a21+a24+a31+a34)*(b12+b14+b15+b16)*(c11+c13+c31+c33+c61+c63) 42 | (a14+a22+a23)*(b32+b34+b35+b36+b42+b43+b44+b45+b46)*(c31+c32+c33+c41+c42+c43+c51+c52+c53+c62+c63) 43 | (a21+a24)*(b41+b42+b44+b45)*(c11+c12+c13+c31+c32+c33+c61+c62+c63) 44 | (a12+a15+a35)*(b22+b23+b24+b53)*(c13+c33+c41+c53+c61+c63) 45 | (a22+a23+a25)*(b33+b34+b44+b45)*(c22+c23+c42+c43) 46 | (a22+a23)*(b32+b33+b34+b35+b36+b42+b43+b44+b45+b46)*(c31+c32+c33+c41+c42+c43+c51+c52+c53) 47 | (a14)*(b32+b34+b35+b36+b41+b46+b52+b54+b55+b56)*(c31+c32+c33+c41+c42+c43+c51+c52+c53+c61+c62+c63) 48 | (a22+a23+a31+a32+a33)*(b12+b13+b14+b15+b16)*(c31+c32+c33+c41+c43+c51+c53) 49 | (a12+a14+a15+a24+a25+a32+a34+a35)*(b22+b24+b25+b26+b32+b34+b35+b36+b42+b44+b45)*(c12+c22+c23+c32+c42+c43+c52+c63) 50 | (a22+a23+a24)*(b42+b43+b44+b45+b46)*(c22+c23+c42+c43+c62+c63) 51 | (a21)*(b11+b21+b25+b31+b33+b41+b42+b44+b45)*(c12+c42+c52) 52 | (a11+a13+a15)*(b51+b55)*(c21+c51) 53 | (a21+a24+a34)*(b12+b14+b15+b16+b41+b42+b44+b45)*(c13+c32+c33+c43+c53+c62+c63) 54 | (a12)*(b21+b23+b25+b53)*(c11+c21+c23+c31+c43+c51+c61+c63) 55 | (a13)*(b31+b33+b35+b51+b55)*(c11+c12+c13+c21+c22+c23+c61+c62+c63) 56 | (a11+a12+a13+a31+a32+a33)*(b21+b25)*(c31+c41+c51) 57 | (a12+a15+a25)*(b23+b25+b52+b53+b54+b55+b56)*(c11+c13+c32+c51+c53+c61+c63) 58 | (a14+a15+a25+a35)*(b42+b52+b54+b55+b56)*(c21+c23+c41+c43+c63) 59 | (a22+a23+a32+a33)*(b12+b13+b14+b15+b16+b22+b24)*(c13+c33+c43+c53) 60 | (a12)*(b21+b22+b23+b25+b52+b53+b54+b55+b56)*(c21+c23+c41+c43+c61+c63) 61 | (a14+a34)*(b41+b43)*(c32+c33+c62+c63) 62 | (a12+a14+a15+a22+a24+a25+a32+a34+a35)*(b22+b24+b25+b26+b32+b34+b35+b36)*(c12+c22+c32+c42+c52) 63 | (a11+a15+a25)*(b23+b25+b51+b53)*(c11+c51+c61) 64 | (a12+a14+a15)*(b52+b54+b55+b56)*(c11+c13+c21+c23+c31+c33+c41+c43+c51+c53) 65 | (a11+a21+a24+a31+a34)*(b12+b14+b15+b16+b41+b45)*(c11+c31+c43+c53+c61) 66 | (a14+a21+a24)*(b42+b44)*(c11+c31+c42+c43+c52+c53+c61) 67 | (a21+a22+a23+a31+a32+a33)*(b12+b13+b14+b15+b16+b23+b25)*(c32) 68 | (a22+a23+a34)*(b42+b43+b46)*(c63) 69 | (a12+a15+a21+a23+a25+a31+a32+a33)*(b23+b25)*(c13+c32+c53+c63) 70 | (a21+a23+a33)*(b12+b21+b25+b31+b35)*(c13+c22+c23+c62+c63) 71 | (a22+a23+a32+a33)*(b24+b25+b26)*(c61+c63) 72 | -------------------------------------------------------------------------------- /solutions/366-85-mod2.exp: -------------------------------------------------------------------------------- 1 | (a32+a36)*(b61+b64+b66)*(c32+c33+c52+c53+c62+c63) 2 | (a23+a25+a33+a35)*(b12+b13+b14+b15+b52+b53+b54+b55)*(c33) 3 | (a35)*(b34+b46+b56)*(c22+c23+c33+c41+c42+c63) 4 | (a23+a25+a33)*(b12+b13+b14+b15+b22+b23+b24+b25+b33+b36+b42+b43+b44+b45+b52+b53+b54+b55+b63+b66)*(c31+c32+c33+c61+c62) 5 | (a23+a26)*(b13+b16+b62+b64+b65+b66)*(c32+c33+c52+c53) 6 | (a22+a24)*(b13+b16+b22+b23+b24+b26+b63+b65)*(c22) 7 | (a11+a12+a23+a24)*(b11+b12+b13+b16+b51+b52+b53+b56)*(c11+c12) 8 | (a14+a15+a24+a25)*(b41+b44+b46)*(c11+c41+c61) 9 | (a34)*(b22+b24+b25+b26+b42+b45)*(c33+c53) 10 | (a22+a23+a24+a26+a32+a33+a34+a36)*(b13+b16+b23+b26+b63+b65)*(c22+c32+c52) 11 | (a24)*(b12+b14+b25+b26+b32+b34+b45+b46+b52+b54+b62+b64)*(c31+c32+c41+c42+c61+c62) 12 | (a12+a16+a23+a24+a31+a36)*(b61+b64)*(c12+c13+c32+c33+c52+c53+c62+c63) 13 | (a33)*(b32+b34+b35+b36+b62+b64+b65+b66)*(c11+c13+c31+c32+c33+c62+c63) 14 | (a11+a12+a16+a21+a22+a26+a32+a36)*(b11+b14+b16)*(c23+c32+c43+c52+c62) 15 | (a11+a12+a14+a15)*(b32+b35+b52+b55)*(c21) 16 | (a11+a12+a24+a25)*(b15+b16+b23+b26+b31+b33+b36+b41+b43+b46+b55+b63+b66)*(c11+c12+c31) 17 | (a21+a25+a31+a35)*(b13+b15+b23+b25+b63+b65)*(c23+c53) 18 | (a13+a14+a15+a23+a24+a25+a33+a34)*(b34+b44+b54)*(c31+c33+c41+c43+c61) 19 | (a16+a26+a31+a36)*(b11+b61+b64)*(c12+c13+c23+c32+c43+c52+c62) 20 | (a32)*(b26+b61+b64+b66)*(c13+c23+c33+c43+c53+c63) 21 | (a12+a14)*(b45)*(c21+c51) 22 | (a12+a22)*(b24)*(c12+c22+c32+c42+c52+c62) 23 | (a21+a22+a24+a25+a31+a32+a34+a35)*(b13+b16+b23+b25+b63+b65)*(c52) 24 | (a12+a16+a23+a24+a33)*(b32+b35+b62+b64+b65+b66)*(c11+c13+c33+c53+c61+c63) 25 | (a11+a12+a16+a21+a22+a26+a31+a32+a36)*(b11+b14+b16+b21+b24)*(c23+c43) 26 | (a16+a26+a36)*(b11+b21+b26+b64+b66)*(c13+c23+c43) 27 | (a31)*(b16+b61+b64)*(c23+c33+c43+c53+c63) 28 | (a11+a16+a21+a26+a31+a36)*(b11+b21+b24)*(c12+c32+c52+c62) 29 | (a13+a16)*(b35+b55)*(c21+c51) 30 | (a31+a32+a34+a35)*(b12+b13+b14+b15)*(c52+c53) 31 | (a33+a34)*(b34)*(c11+c12+c31+c42+c43+c62+c63) 32 | (a11+a21)*(b14)*(c22+c32+c42+c52+c62) 33 | (a16)*(b32+b35+b62+b65)*(c11+c12+c21+c22+c41+c42) 34 | (a13+a15+a23+a25+a33)*(b31+b34+b36+b41+b51)*(c11+c13+c61) 35 | (a11+a13+a14+a15+a23+a24)*(b31+b32+b33+b35+b36)*(c31) 36 | (a11+a13+a15+a16)*(b55)*(c21+c51) 37 | (a12+a14)*(b31+b33+b36+b41+b43+b46)*(c31) 38 | (a11+a25)*(b13+b16+b23+b26+b31+b33+b36+b41+b43+b46+b51+b53+b56+b63+b66)*(c11+c12+c31) 39 | (a11+a12+a24+a25+a34+a35)*(b22+b24+b32+b42+b62+b64)*(c23+c53) 40 | (a11+a15)*(b31+b33+b36+b51+b53+b56)*(c31) 41 | (a13+a15+a23+a25+a33+a34)*(b34+b41+b46)*(c13+c31+c41+c61) 42 | (a12+a16+a22+a26+a32+a36)*(b11+b14+b16+b21+b26)*(c32+c52+c62) 43 | (a11+a25+a35)*(b12+b14+b22+b24+b32+b42+b52+b62+b64)*(c22+c41+c42) 44 | (a23+a26+a33+a36)*(b13+b16+b23+b26+b63+b66)*(c33+c53) 45 | (a25)*(b13+b16+b22+b23+b24+b25+b33+b36+b42+b43+b44+b45+b53+b56+b63+b66)*(c11+c12+c61+c62) 46 | (a13+a15+a23+a25+a33+a35)*(b34+b46+b51)*(c13) 47 | (a11)*(b12+b15+b22+b35+b42+b52+b55+b65)*(c11+c12+c21+c22+c41+c42) 48 | (a12+a14)*(b42+b45+b52+b55)*(c21) 49 | (a11+a12+a24+a25+a35)*(b15+b16+b22+b24+b32+b42+b55+b62+b64)*(c22+c23+c41+c42+c53) 50 | (a12+a16+a23+a24+a32+a33+a34+a36)*(b62+b63+b64+b65)*(c22+c23+c32+c33+c52+c53) 51 | (a12+a16)*(b35+b65)*(c11+c12+c21+c22+c31+c32+c41+c42+c51+c52+c61+c62) 52 | (a11)*(b15+b55)*(c11+c12+c21+c22+c31+c32+c41+c42+c51+c52+c61+c62) 53 | (a21+a25)*(b12+b14+b63+b65)*(c22+c23+c52+c53) 54 | (a13+a23+a33)*(b31+b41+b44+b46+b51)*(c11+c61) 55 | (a11+a12+a24+a25)*(b15+b16+b55)*(c11+c12+c22+c23+c32+c41+c42+c52+c53+c61+c62) 56 | (a24+a25)*(b12+b14+b22+b23+b24+b25+b32+b34+b42+b43+b44+b45+b52+b54+b62+b64)*(c31+c32+c41+c42+c61+c62) 57 | (a24)*(b22+b24+b25+b26+b42+b44+b45+b46)*(c11+c12+c31+c32+c41+c42) 58 | (a15+a25)*(b31+b34+b36+b41+b44+b46+b51+b54+b56)*(c31+c61) 59 | (a34+a35)*(b34+b46)*(c13+c33+c43+c63) 60 | (a21+a22+a23+a24+a25+a26)*(b13+b16+b63+b65)*(c32) 61 | (a11+a12+a13+a14+a15+a16)*(b32+b35)*(c21+c31) 62 | (a23+a26+a31+a32+a34+a35)*(b13+b16)*(c33+c52+c53) 63 | (a23+a26+a32+a33+a34+a36)*(b13+b16+b23+b26+b62+b63+b64+b65)*(c22+c32+c33+c52+c53) 64 | (a16+a26)*(b64)*(c12+c13+c22+c23+c42+c43) 65 | (a16+a26+a32+a36)*(b21+b26+b61+b64+b66)*(c13+c23+c32+c43+c52+c62) 66 | (a35)*(b12+b14+b15+b16+b34+b46+b52+b55+b56)*(c22+c23+c33+c41+c42) 67 | (a23+a25+a33+a34)*(b22+b23+b24+b25+b32+b34+b42+b43+b44+b45+b62+b64)*(c11+c12+c33+c41+c42+c61+c62) 68 | (a12+a16+a23+a24+a33+a34)*(b32+b62+b64)*(c11+c12+c23+c33+c41+c42+c53+c61+c62) 69 | (a23+a25)*(b32+b33+b34+b36+b62+b63+b64+b66)*(c11+c12+c31+c32+c33) 70 | (a12+a23+a24)*(b11+b12+b13+b16+b21+b22+b23+b25+b26+b31+b32+b33+b35+b36+b41+b42+b43+b45+b46+b51+b52+b53+b56+b61+b62+b63+b65+b66)*(c11+c12) 71 | (a23+a24+a33+a34)*(b22+b23+b24+b25+b42+b43+b44+b45)*(c11+c12+c41+c42+c61+c62) 72 | (a12+a24)*(b15+b16+b25+b26+b35+b45+b55+b65+b66)*(c31+c32+c52+c61+c62) 73 | (a21+a25+a31+a32+a34+a35)*(b12+b13+b14+b15+b23+b25+b63+b65)*(c23+c52+c53) 74 | (a13+a14+a15+a23+a24+a25+a33)*(b44+b46)*(c11+c33+c43+c61) 75 | (a12+a16+a23+a24)*(b35+b61+b62+b63+b66)*(c22+c23+c31+c32+c33+c52+c53) 76 | (a11+a12+a16+a21+a22+a26+a31+a36)*(b21+b24)*(c12+c23+c32+c43+c52+c62) 77 | (a13+a14+a15+a23+a24+a25+a33+a34+a35)*(b34+b46+b54)*(c33+c43) 78 | (a13+a15+a23+a25)*(b31+b34+b36)*(c11+c13+c31) 79 | (a11+a12)*(b22+b35+b42+b65)*(c11+c12+c21+c22+c41+c42) 80 | (a12+a16+a23+a24)*(b32+b35+b61+b62+b65+b66)*(c11+c13+c22+c23+c31+c62+c63) 81 | (a23+a33)*(b12+b13+b14+b15+b22+b23+b24+b25+b32+b33+b34+b35+b42+b43+b44+b45+b52+b53+b54+b55+b62+b63+b64+b65)*(c31+c32+c61+c62) 82 | (a13+a14+a23+a24+a33+a34)*(b34+b41+b44+b46+b54)*(c31+c41+c61) 83 | (a12)*(b25+b35+b45+b65)*(c11+c12+c31+c32+c51+c52+c61+c62) 84 | (a32+a34)*(b12+b13+b14+b15+b22+b23+b24+b25+b62+b63+b64+b65)*(c23) 85 | (a23+a24)*(b21+b22+b23+b25+b26+b35+b41+b42+b43+b45+b46+b65)*(c11+c12) 86 | (a21+a25+a32+a33+a34+a36)*(b63+b65)*(c22+c23+c32+c52+c53) 87 | -------------------------------------------------------------------------------- /solutions/444-47-mod2.exp: -------------------------------------------------------------------------------- 1 | (a14)*(b12+b13+b14+b22+b23+b24+b31+b33+b34+b42+b43+b44)*(c14+c22+c24+c32+c34+c41+c42+c44) 2 | (a14+a23+a41+a42+a43)*(b12+b13+b22+b23+b31+b33+b34+b42+b43)*(c14+c22+c24+c31+c32+c34+c41+c42+c44) 3 | (a41+a43+a44)*(b11+b12+b21+b22+b24+b34+b41+b42)*(c14+c44) 4 | (a11+a14+a33)*(b11+b12+b31+b32)*(c13+c21+c23+c31+c33+c43) 5 | (a22+a24+a34+a41+a44)*(b11+b14+b21+b22+b24+b32+b42+b43)*(c14+c22+c24+c32+c33+c34+c43) 6 | (a42+a43)*(b12+b13+b21+b22+b24+b31+b33+b34+b42+b43)*(c34) 7 | (a33)*(b11+b12+b21+b23+b24+b32+b33+b34)*(c14+c21+c23+c31+c34+c43) 8 | (a11+a14+a21+a23+a31)*(b12+b32)*(c13+c23+c33+c43) 9 | (a12+a14+a33+a41+a43)*(b21+b23+b24+b31+b33+b34)*(c14+c21+c23+c31+c33+c34+c43) 10 | (a23+a24+a34+a41+a44)*(b11+b14+b21+b22+b24+b32+b41+b42+b44)*(c22+c32) 11 | (a41+a43)*(b11+b12+b22+b23+b24+b31+b33+b34+b41+b42)*(c14+c21+c23+c31+c33+c43) 12 | (a34)*(b11+b12+b21+b32+b43+b44)*(c14+c22+c24+c32+c34+c43) 13 | (a12+a14+a31+a32+a33)*(b21+b32)*(c11+c21+c23+c31+c33+c43) 14 | (a11+a14+a21+a22+a31+a32+a33)*(b11+b14+b32)*(c12+c32) 15 | (a11+a14+a23)*(b14+b31+b32)*(c12+c31+c32+c41) 16 | (a12+a13+a14+a23+a41+a42+a43)*(b31+b32+b34)*(c31+c41) 17 | (a12+a14+a32+a41+a43)*(b22+b32)*(c23+c33+c43) 18 | (a21+a23+a34)*(b11+b12+b21+b32+b41)*(c13+c22+c23+c32+c33+c43) 19 | (a11+a12+a13+a14+a21+a23+a31+a32+a33)*(b32)*(c11+c21+c31) 20 | (a31+a33+a34)*(b11+b12+b21+b32)*(c13+c43) 21 | (a22+a24+a34+a41+a42+a43+a44)*(b11+b14+b21+b22+b24+b32+b41+b44)*(c14+c24+c34) 22 | (a12+a14+a33+a41+a42)*(b21+b22+b24+b31+b32+b34)*(c14+c34) 23 | (a11+a13+a14)*(b31+b32)*(c11+c41) 24 | (a41+a44)*(b11+b12+b21+b22+b24+b34+b42+b43)*(c14+c22+c24+c32+c33+c43) 25 | (a14+a41+a43)*(b11+b12+b21+b22+b41+b42)*(c14+c21+c24+c31+c34+c44) 26 | (a22+a24+a31+a32+a33)*(b11+b14+b21+b32)*(c12+c32+c33+c43) 27 | (a31+a32+a33)*(b11+b12+b13+b14+b21+b32)*(c11+c12+c13+c21+c23+c31+c32+c43) 28 | (a21+a23)*(b12+b13+b14+b21+b32+b41)*(c11+c12+c13+c21+c23+c31+c33+c43) 29 | (a11+a14)*(b12+b13+b14+b31+b32)*(c11+c12+c13+c21+c23+c32+c33+c43) 30 | (a12+a13)*(b31+b33+b34)*(c31) 31 | (a33+a41+a44)*(b11+b12+b21+b22+b24+b34)*(c14+c33+c34+c43) 32 | (a22+a23)*(b11+b14+b22+b23+b32+b42+b43)*(c32) 33 | (a22+a24+a41+a42+a43)*(b11+b14+b21+b32+b41+b44)*(c14+c22+c24+c32+c34+c42) 34 | (a34+a41+a43)*(b11+b12+b21+b32+b41+b42)*(c14+c23+c24+c33+c34+c43) 35 | (a12+a14)*(b22+b23+b24+b31+b33+b34)*(c14+c21+c23+c33+c34+c43) 36 | (a14+a22+a41+a42+a43)*(b11+b14+b21+b24+b32+b41+b44)*(c22+c32+c42) 37 | (a22+a24+a32+a33+a34+a41+a44)*(b11+b14+b21+b22+b24+b32)*(c33+c43) 38 | (a22+a24)*(b11+b14+b21+b32+b42+b43)*(c14+c22+c24+c33+c34+c43) 39 | (a23+a41+a44)*(b11+b12+b21+b22+b24+b34+b41+b42+b44)*(c14+c22+c24+c32+c34+c44) 40 | (a14+a23+a41)*(b11+b12+b14+b21+b22+b24+b41+b42+b44)*(c14+c24+c34+c44) 41 | (a11+a14+a21+a23+a31+a32+a33)*(b11+b12+b13+b14+b32)*(c11+c12+c13+c21+c23+c31+c32+c33+c43) 42 | (a21+a23+a24)*(b11+b14+b21+b32+b41)*(c12+c42) 43 | (a14+a21+a23)*(b11+b21+b32+b41)*(c11+c21+c22+c31+c32+c42) 44 | (a12+a14+a41+a42+a43)*(b24+b31+b32+b34)*(c14+c31+c34+c41) 45 | (a32+a33)*(b11+b12+b13+b14+b21+b23+b24+b32)*(c33) 46 | (a41+a42+a43)*(b12+b13+b22+b23+b24+b31+b33+b34+b42+b43)*(c14+c22+c24+c31+c32+c41+c42+c44) 47 | (a23)*(b12+b13+b14+b22+b23+b31+b33+b42+b43)*(c14+c22+c24+c31+c34+c41+c42+c44) 48 | -------------------------------------------------------------------------------- /solutions/444-49-mod0.exp: -------------------------------------------------------------------------------- 1 | (-a32+a33+a34+a42-a43-a44)*(2*b12-2*b14-b22+b24-b32+b34-b42+b44)*(c31-c33-c41+c43) 2 | (a31-2*a32+2*a33+2*a34)*(-b12+b13+b14)*(c23+2*c43) 3 | (-2*a22+a23+a24)*(-b41+b42)*(c22+2*c42) 4 | (a11-3*a12+2*a13+a21-3*a22+2*a23+a31-3*a32+2*a33-a41+3*a42-2*a43)*(-2*b22+2*b23+b24-2*b32+2*b33+b34)*(c23+c43) 5 | (-a21-3*a22+a23+a42-a43)*(-b11-3*b13-b14+b21+b22+2*b31+2*b32)*(-c14+c32-2*c42) 6 | (-a11-2*a12-a21-2*a22)*(b11-b21-2*b31+b41)*(c11+c31-2*c41) 7 | (-a11-a13-a14)*(-b12+b22+2*b32)*(-c11+c12-c21+c22-c31+c32) 8 | (-a11+a12-a13-a21+3*a22-2*a23-a31+a32-a33+a41-3*a42+2*a43)*(b11-2*b12+b13+b14-2*b22+2*b23+b24-2*b32+2*b33+b34)*(c14+c23+c24+c43+c44) 9 | (-2*a12+a13)*(-2*b11+b21+b31+b41)*(-c11+c13) 10 | (-2*a22+a23+a44)*(2*b12-6*b13-2*b14-b22+3*b23+b24-b32+3*b33+b34+b41+b42)*(-c23+c24-c41-c42-c43+c44) 11 | (-a12+a13-a32+a33)*(-2*b11+2*b12-b14+2*b21-2*b22+b24+4*b31-4*b32+2*b34+2*b41-2*b42+b44)*(-c31+c41) 12 | (2*a22-a23)*(-b31-b32+b41+b42)*(c12+c14) 13 | (a42-a43-a44)*(-2*b13+b23+2*b33)*(c31-c32-c33-c34-c41+c42+c43+c44) 14 | (2*a32-a33-a34+2*a42-a43-a44)*(-b13+b23+b33)*(c14+c34-2*c44) 15 | (-a12+a13-a14+a24-a32+a33-a34-a44)*(-b11+2*b12-b13-b14+b21-2*b22+b23+b24+2*b31-4*b32+2*b33+2*b34+2*b41-2*b42+b44)*(c31+c42) 16 | (-a41+2*a42-2*a43-2*a44)*(b12-2*b13-b14-b22+2*b23+b24-b32+2*b33+b34)*(c24+2*c44) 17 | (-a21-2*a22)*(b11-b12-b21+b22-2*b31+2*b32)*(-c11+c12-c31+c32+2*c41-2*c42) 18 | (a21-3*a22+2*a23-a41+3*a42-2*a43)*(b11-2*b12+b13+b14)*(c23+c24+c43+c44) 19 | (a41+a43+a44)*(-b22+2*b23+b24-b32+2*b33+b34)*(-c13+c14-c23+c24-c33+c34) 20 | (-a11-5*a12+2*a13+a21+5*a22-2*a23-a32+a33-a34-a42+a43-a44)*(-2*b13-b14+b22+2*b32)*(-c14+c24+c32-3*c42+c44) 21 | (-a32+a33+a42-a43)*(b32-b34-b42+b44)*(c42+c44) 22 | (a11-a12+a13+a21-a22+a23+a31-a32+a33-a41+a42-a43)*(-2*b12+2*b13+b14-2*b22+2*b23+b24-2*b32+2*b33+b34)*(c14+c24+c44) 23 | (-a11-3*a12+a13-a21-a22)*(2*b11-b21-2*b31-b32+b42)*(-c12-c14-c21+c22+c23+c24-c41+c42+c43+c44) 24 | (-a32+a33)*(2*b12-2*b13-2*b14-b22+b23+b24-2*b32+2*b33+2*b34)*(-c41+c42+c43+c44) 25 | (a12-a13+a14-a22+a23-a24+a32-a33+a34+a42-a43+a44)*(-b11+2*b12-b13-b14+b21-2*b22+b23+b24+2*b31-4*b32+2*b33+2*b34)*c42 26 | (a24-a44)*(-b41+b43)*(c31+c32) 27 | (-a11+a12-a13-a31+a32-a33)*(-b11+b13)*(c13+c14+c23+c24+c43+c44) 28 | (-2*a22+a23+2*a42-a43)*(b11-2*b12+b13+b14+b21-2*b22+b23+b24+b31-2*b32+b33+b34)*c14 29 | (-2*a32+a33+a34-a41-a43-a44)*(-b13-b22+2*b23+b24-b32+2*b33+b34)*(-c13+c14-c23-c33+c34-2*c44) 30 | (a12-a13+a14+a32-a33+a34)*(2*b41-2*b42+b44)*(c41+c42) 31 | (a22-a23-a42+a43)*(b11-b13-b21+b23-2*b31+2*b33)*(-c32+c42) 32 | (a11+3*a12-a13+a21+3*a22-a23)*(-b32+b42)*(-c12-c14+c22+c24+c42+c44) 33 | (a32-a33-a42+a43+a44)*(2*b12-2*b13-2*b14-b22+b23+b24-b32+2*b33+b34-b42+b44)*(c31-c33-c41+c42+c43+c44) 34 | (-a11-3*a12+a13)*(-2*b11+b21+2*b31)*(c11-c12-c13-c14-c21+c22+c23+c24-c41+c42+c43+c44) 35 | a44*(-b33+b43)*(c32+c34) 36 | (-a11-5*a12+2*a13+2*a22-a23-a32+a33-a34-a44)*(b14-b22+b23-2*b32+b33+b41)*(-c14-c23+c24+c32-c41-3*c42-c43+c44) 37 | (-a11-a13-a14-a21-2*a22)*(b12-b22-2*b32+b41)*(-c11+c12+c22-c31+c32+2*c41) 38 | (a11+5*a12-2*a13+a32-a33+a34)*(-2*b13+b23+b33+b41)*(c13-c14-c23+c24+c31+c32-3*c41-3*c42-c43+c44) 39 | (-a21-a22)*(-2*b11-2*b12+b21+b22+2*b31+2*b32)*(-c21+c22+c23+c24-c41+c42+c43+c44) 40 | (-2*a12+a13+a14)*(b12-b22-2*b32+b42)*(c21+2*c41) 41 | (a14-a24+a34+a44)*(-b11+2*b12-b13-b14+b21-2*b22+b23+b24+2*b31-4*b32+2*b33+2*b34+b41-2*b42+b43+b44)*c31 42 | (-a11-3*a12+a13-a32+a33)*(-b11-3*b13+b21+b23+2*b31+b33+b41)*(c13+c31-2*c41) 43 | (2*a32-a33-a34)*(-b22+b23+b24-b32+b33+b34)*(-c13+c14-c33+c34+2*c43-2*c44) 44 | a34*(2*b12-2*b13-2*b14-b22+b23+b24-b32+b33+b34-b42+b43+b44)*(-c31+c33) 45 | (2*a12-a13-2*a22+a23+a34+a44)*(2*b12-6*b13-3*b14+2*b23+b24+b32+2*b33+b34+b42)*(c23+c41+c43) 46 | (a11+a12+a21+a22)*(-2*b12+b22+b32+b42)*(-c21+c23-c41+c43) 47 | (a31+a33+a34+a41+a43+a44)*b13*(c13+c23+c33) 48 | (-2*a12+a13-2*a32+a33)*(-b21+b23-b31+b33)*c13 49 | (a11+a13+a14+a21+a23+a24)*b41*(c12+c22+c32) 50 | -------------------------------------------------------------------------------- /solutions/445-60-mod2.exp: -------------------------------------------------------------------------------- 1 | (a12+a13+a14+a23+a24+a42+a43)*(b32+b35)*(c21+c22+c51+c53) 2 | (a12)*(b11+b13+b15+b24+b25+b43+b45)*(c11+c13+c32+c33+c41+c42+c44+c51+c53) 3 | (a21+a41+a43)*(b11+b15+b35)*(c14+c21+c22+c24+c51+c52+c53+c54) 4 | (a42+a44)*(b11+b12+b13+b41+b42+b43)*(c14+c31+c32+c33+c41+c42+c43+c54) 5 | (a11+a13+a14+a21+a23+a24)*(b31+b32+b33)*(c21+c51+c53) 6 | (a12+a14+a22+a24)*(b21+b23+b24+b32+b35+b41+b42+b45)*(c11+c13+c32+c33+c42+c43+c51+c53) 7 | (a22+a32+a42)*(b24+b44)*(c21+c23+c32+c33+c42+c43+c44+c51+c53) 8 | (a11+a12+a21+a41+a42+a44)*(b11+b13+b15+b21+b22+b23+b41+b42+b43)*(c21+c22+c24+c34) 9 | (a11+a12+a21+a42+a43)*(b21+b22+b25+b41+b42+b45)*(c21+c22+c24+c34+c51+c53) 10 | (a22+a44)*(b25+b41)*(c14+c21+c22+c24+c51+c52) 11 | (a12+a13+a14+a22+a24+a32+a33+a34)*(b35+b41+b45)*(c13+c21+c22+c23+c51+c52) 12 | (a11+a12+a21+a22+a32+a41+a44)*(b21+b22+b23+b31+b32+b33+b41+b42+b43)*(c32) 13 | (a13)*(b12+b14+b34+b35+b41+b42+b45)*(c11+c13+c21+c31+c32+c33+c41+c42+c43+c51+c53) 14 | (a12+a13+a14+a21+a22+a23+a24+a32+a33+a34+a41+a43)*(b35)*(c21+c22+c51+c52+c53) 15 | (a12+a14+a22+a24+a31+a32+a34)*(b11+b12+b13+b31+b32+b33)*(c31+c32+c33) 16 | (a12+a14+a22+a24+a32+a34+a42+a44)*(b11+b12+b13+b41+b42+b43)*(c31+c32+c33+c41+c42+c43) 17 | (a12+a14+a22+a24+a32+a41+a44)*(b21+b22+b23+b31+b32+b33+b41+b42+b43)*(c32+c33) 18 | (a11+a12+a21+a22+a23+a32+a33)*(b33+b34)*(c21+c32+c51+c53) 19 | (a12+a14+a22+a24+a32+a34)*(b11+b13+b14+b35+b43+b44+b45)*(c13+c31+c32+c33+c41+c42+c43+c53) 20 | (a11+a12+a31+a42+a44)*(b11+b13+b15+b25+b43+b44+b45)*(c31+c32+c41+c42+c44) 21 | (a12+a13+a14+a22+a24+a32+a33)*(b22+b24+b31+b32+b33+b42+b44)*(c21+c23+c32+c33+c51+c53) 22 | (a12+a14+a22+a24)*(b21+b22+b23)*(c32+c33+c42+c43) 23 | (a12+a13+a14+a24+a33+a42)*(b22+b24+b32+b35+b41+b42+b44+b45)*(c21+c23+c32+c33+c42+c43+c51+c53) 24 | (a11+a13+a21)*(b12+b14+b31+b32+b34)*(c11+c13+c21+c31+c32+c33+c51+c53) 25 | (a12+a13+a14+a22+a24)*(b32+b35+b41+b42+b45)*(c11+c13+c22+c23+c51+c53) 26 | (a11+a21)*(b11+b14+b15+b21+b22+b25+b31+b32+b34+b41+b42+b45)*(c22+c24+c42+c44) 27 | (a22+a42)*(b22+b32+b35+b41+b42+b45)*(c14+c21+c23+c24+c32+c33+c42+c43+c51+c53) 28 | (a22+a24)*(b41)*(c11+c12+c51+c52) 29 | (a11+a12+a14+a22+a24+a31+a32+a34)*(b11+b13+b14+b43+b44)*(c13+c31+c32+c33+c53) 30 | (a13+a33)*(b22+b24+b32+b34+b35+b41+b42+b44+b45)*(c13+c21+c32+c33+c42+c43+c51+c53) 31 | (a11+a12+a22+a31+a32+a41+a43)*(b11+b15)*(c21+c22+c24+c34+c51+c52+c53+c54) 32 | (a23+a33+a43)*(b34)*(c21+c32+c42+c51+c53) 33 | (a22)*(b21+b41)*(c12+c13+c14+c21+c22+c24+c32+c33+c51+c53) 34 | (a12+a13+a14+a22+a24+a31+a32+a34)*(b12+b14+b31+b32+b33)*(c23+c31+c32+c33) 35 | (a11+a12+a22+a31+a32)*(b11+b15+b25+b45)*(c13+c21+c22+c24+c33+c34+c51+c52+c53+c54) 36 | (a12+a13+a14+a22+a32+a33+a34+a44)*(b41+b45)*(c21+c22+c51+c52) 37 | (a21)*(b11)*(c11+c12+c13+c14+c21+c22+c24+c31+c32+c33+c51+c52+c53+c54) 38 | (a12+a13+a22+a32+a33)*(b22+b24+b31+b32+b34+b42+b44)*(c13+c21+c32+c33+c51+c53) 39 | (a21+a31+a41)*(b14)*(c23+c31+c32+c33+c41+c42+c43+c44) 40 | (a21+a41)*(b12+b35+b41+b42+b45)*(c14+c23+c24+c31+c32+c33+c41+c42+c43+c54) 41 | (a11+a21+a41+a42+a44)*(b11+b12+b13+b21+b22+b23+b41+b42+b43)*(c21+c22+c24) 42 | (a11+a21)*(b12+b13+b14+b15+b23+b25+b31+b32+b34+b43+b45)*(c11+c13+c21+c22+c24+c31+c32+c33+c51+c53) 43 | (a22+a24+a32+a34+a42+a44)*(b44)*(c31+c32+c41+c42) 44 | (a11+a12+a21+a22+a32+a43)*(b11+b15+b21+b22+b25+b31+b32+b34+b41+b42+b45)*(c21+c32+c42+c44+c51+c53) 45 | (a11+a12+a22+a31+a32+a44)*(b25+b45)*(c21+c22+c24+c34+c51+c52+c54) 46 | (a12+a13+a14+a21+a41+a42+a44)*(b41+b42+b45)*(c21+c22) 47 | (a41+a44)*(b21+b22+b23+b31+b32+b33+b41+b42+b43)*(c33+c34) 48 | (a43)*(b11+b15+b21+b22+b25+b31+b32+b41+b42+b45)*(c14+c21+c32+c34+c42+c44+c51+c53) 49 | (a12+a22+a32)*(b11+b15+b21+b22+b24+b25+b31+b32+b34+b41+b42+b44+b45)*(c13+c21+c32+c33+c42+c44+c51+c53) 50 | (a14+a22+a24)*(b21+b23+b24+b41)*(c11+c13+c32+c33+c51+c53) 51 | (a31+a33+a34+a41+a43+a44)*(b31+b32+b33)*(c34) 52 | (a11+a12+a21)*(b11+b13+b15+b23+b25+b43+b45)*(c11+c13+c21+c22+c24+c31+c33+c34+c51+c53) 53 | (a42+a44)*(b11+b13+b15+b25+b43+b45)*(c14+c31+c32+c34+c41+c42+c44+c54) 54 | (a31+a33+a34)*(b31+b32+b33)*(c23+c34) 55 | (a11+a12+a22+a24+a31+a32+a34)*(b43+b44)*(c31+c32) 56 | (a23)*(b31)*(c12+c21+c51+c53) 57 | (a11+a31)*(b11+b13+b14+b15+b25+b43+b44+b45)*(c13+c31+c32+c33+c41+c42+c44+c53) 58 | (a22+a42+a43)*(b21+b22+b25+b32+b35+b41+b42+b45)*(c14+c21+c22+c24+c51+c53) 59 | (a12+a13+a14+a21+a22+a24+a32+a34+a41)*(b12+b14+b35+b41+b42+b45)*(c23+c31+c32+c33+c41+c42+c43) 60 | (a21+a41+a42+a44)*(b12+b15+b41+b42+b45)*(c14+c21+c22+c24+c54) 61 | -------------------------------------------------------------------------------- /solutions/555-95-mod2.exp: -------------------------------------------------------------------------------- 1 | (a22)*(b24)*(c12+c42+c44) 2 | (a22+a42+a43)*(b23+b33+b34)*(c32+c44) 3 | (a22+a42+a45)*(b22+b52+b54)*(c22+c44) 4 | (a22+a41+a42)*(b14+b15+b25)*(c44+c52) 5 | (a21)*(b14)*(c42+c45+c52) 6 | (a21+a51+a53)*(b13+b33+b34)*(c32+c45) 7 | (a22+a42)*(b14+b15+b22+b23+b24+b25+b33+b34+b52+b54)*(c44) 8 | (a23)*(b34)*(c32+c41+c42) 9 | (a11+a13+a23)*(b14+b15+b35)*(c41+c52) 10 | (a13+a23)*(b14+b15+b21+b24+b31+b32+b34+b35+b52+b54)*(c41) 11 | (a13+a15+a23)*(b32+b52+b54)*(c22+c41) 12 | (a21+a51+a55)*(b12+b52+b54)*(c22+c45) 13 | (a12+a13+a23)*(b21+b24+b31)*(c12+c41) 14 | (a13+a15+a21+a22+a23+a25+a42+a45+a51+a55)*(b52+b54)*(c22) 15 | (a21+a51)*(b11+b12+b13+b14+b21+b24+b33+b34+b52+b54)*(c45) 16 | (a21+a51+a52)*(b11+b21+b24)*(c12+c45) 17 | (a25)*(b54)*(c22+c42+c43) 18 | (a25+a35)*(b14+b15+b21+b24+b33+b34+b51+b53+b54+b55)*(c43) 19 | (a25+a32+a35)*(b21+b24+b51)*(c12+c43) 20 | (a25+a33+a35)*(b33+b34+b53)*(c32+c43) 21 | (a11+a13+a21+a22+a23+a25+a31+a35+a41+a42)*(b14+b15)*(c52) 22 | (a21+a22+a23+a25+a33+a35+a42+a43+a51+a53)*(b33+b34)*(c32) 23 | (a25+a31+a35)*(b14+b15+b55)*(c43+c52) 24 | (a33)*(b31+b33+b35+b44+b45+b53)*(c31+c33+c43) 25 | (a24+a31+a34+a44+a45+a54+a55)*(b55)*(c23+c24+c44+c52+c53+c54) 26 | (a24+a31+a34)*(b13+b43+b44)*(c32+c33+c35+c43+c53+c55) 27 | (a11+a14+a24+a31+a34+a41+a44+a51+a53)*(b13+b35+b42+b44)*(c31) 28 | (a11+a13+a31+a33+a41+a43+a51+a53)*(b35)*(c31+c51+c52) 29 | (a43)*(b23+b32+b33+b35)*(c31+c34+c44) 30 | (a24+a44+a54)*(b41)*(c12+c13) 31 | (a24+a33+a34)*(b35+b44+b45)*(c31+c33+c43+c51+c52+c53) 32 | (a24+a34)*(b13+b35+b43+b44+b45)*(c31+c33+c43+c53+c55) 33 | (a44)*(b41)*(c12+c13+c14+c23+c24+c34+c44+c54+c55) 34 | (a14+a24+a34+a54)*(b41)*(c13+c31) 35 | (a24+a54+a55)*(b43+b44+b53)*(c23+c25+c32+c33+c35+c45) 36 | (a11)*(b11+b12+b15+b35+b42+b44)*(c41+c51+c55) 37 | (a42+a43)*(b23)*(c13+c14+c15+c32+c33+c34+c35+c43+c45) 38 | (a14+a15+a34+a35+a44+a45+a54+a55)*(b32+b53)*(c23+c24+c34+c44+c52+c53) 39 | (a44)*(b41+b42+b43+b45)*(c23+c24+c31+c34+c44+c54+c55) 40 | (a31)*(b11+b13+b15+b43+b44+b55)*(c43+c53+c55) 41 | (a11+a12+a31+a41+a42+a51+a52)*(b11+b25)*(c11+c13+c14+c41+c43+c51+c53) 42 | (a12)*(b21+b22+b25+b31)*(c11+c14+c41) 43 | (a42+a43+a52)*(b23+b31)*(c13+c14+c15+c31+c33+c35+c43+c45) 44 | (a11+a12+a41+a42)*(b11)*(c11+c13+c41+c43+c51+c53) 45 | (a32)*(b21+b23+b25+b51)*(c13+c43) 46 | (a11+a31+a51+a52)*(b11+b25)*(c11+c14+c41+c51+c55) 47 | (a11+a12+a31+a32+a51+a52)*(b25)*(c13+c43+c53) 48 | (a24+a31+a34+a41+a51+a53)*(b13+b35+b42+b44)*(c31+c34+c44+c54+c55) 49 | (a12+a13+a33+a42+a43+a52)*(b23+b31)*(c13+c31+c33+c43) 50 | (a12+a32+a35+a42+a45+a52+a55)*(b22+b51)*(c11+c14+c21+c41) 51 | (a32+a35)*(b51)*(c11+c12+c13+c15+c21+c23+c25+c41+c45) 52 | (a52)*(b11+b21+b22+b23)*(c14+c15+c45) 53 | (a42+a43+a52+a53)*(b31)*(c15+c35+c45) 54 | (a55)*(b12+b43+b44+b51+b52+b53)*(c23+c25+c45) 55 | (a32+a35+a55)*(b22+b51)*(c14+c15+c23+c25+c45) 56 | (a13+a15+a33+a35+a43+a45+a53+a55)*(b32)*(c21+c22+c31) 57 | (a41)*(b12+b13+b15+b25)*(c44+c54+c55) 58 | (a45)*(b22+b52+b53+b55)*(c23+c24+c44) 59 | (a11+a14+a31+a34+a41+a44+a51+a54)*(b45+b55)*(c21+c41+c51) 60 | (a14+a15+a24+a33+a34+a44)*(b32+b44+b45+b53)*(c23+c24+c31+c34+c44) 61 | (a42+a45)*(b22)*(c11+c14+c21+c22+c24+c41) 62 | (a24+a31+a34+a41+a44+a54+a55)*(b12)*(c22+c24+c25+c44+c54+c55) 63 | (a14+a15+a24+a33+a34)*(b44+b45)*(c23+c24+c31+c34+c44+c51+c52+c53) 64 | (a24+a34+a44+a54)*(b12+b22+b32+b42+b52)*(c23) 65 | (a24+a53+a54)*(b32+b42+b44)*(c21+c22+c25+c31+c35+c45) 66 | (a24+a31+a34+a51+a53)*(b13)*(c32+c34+c35+c44+c54+c55) 67 | (a54)*(b41)*(c11+c12+c13+c15+c31) 68 | (a24+a54)*(b32+b42+b43+b44+b53)*(c23+c25+c35+c45) 69 | (a12+a42+a52)*(b11+b21+b31+b51)*(c14) 70 | (a24)*(b44)*(c21+c22+c25+c32+c33+c35+c41+c42+c43+c45+c51+c52+c53) 71 | (a14+a15+a24)*(b44+b45+b55)*(c21+c41+c51+c52+c53) 72 | (a12+a13)*(b31)*(c11+c12+c13+c31+c33+c43) 73 | (a53)*(b13+b31+b32+b33+b42+b44)*(c35+c45) 74 | (a24+a31+a34+a41+a44+a51+a53)*(b42+b44)*(c22+c25+c34+c44+c54+c55) 75 | (a15)*(b32+b44+b45+b51+b52+b55)*(c21+c41) 76 | (a24+a31+a34+a54+a55)*(b43+b44)*(c23+c24+c32+c33+c35+c44+c54+c55) 77 | (a32+a35+a52+a55)*(b22)*(c11+c15+c21+c25+c41+c45) 78 | (a41+a42)*(b25)*(c11+c13+c14+c41+c43+c51+c52+c53+c54) 79 | (a24+a31+a34+a41+a44+a51+a54)*(b12+b42+b44)*(c21+c22+c25+c41+c51+c55) 80 | (a51+a52)*(b11)*(c12+c13+c15+c43+c53+c55) 81 | (a24+a31+a34+a41+a43+a51+a53)*(b35)*(c31+c34+c44+c51+c52+c54) 82 | (a24+a33+a35+a54+a55)*(b53)*(c23+c24+c32+c33+c34+c44) 83 | (a13+a33+a43)*(b13+b23+b33+b41+b43+b53)*(c31) 84 | (a12+a13+a32+a33+a42+a43)*(b23)*(c13+c33+c43) 85 | (a24+a31+a34+a44+a54+a55)*(b12+b43+b44+b55)*(c23+c24+c44+c54+c55) 86 | (a13+a14+a24+a33+a34+a43+a44)*(b13+b32+b35+b41+b43+b53)*(c31) 87 | (a11+a24+a31+a34+a41+a44+a51+a54)*(b12+b42+b44+b45+b55)*(c21+c41+c51+c55) 88 | (a12+a13+a21+a22+a23+a25+a32+a35+a51+a52)*(b21+b24)*(c12) 89 | (a24+a34+a35+a44+a45+a54+a55)*(b22+b32+b52)*(c23) 90 | (a24+a33+a35+a43+a45+a54+a55)*(b32)*(c21+c22+c24+c31+c34+c44) 91 | (a14+a15+a34+a35+a44+a45+a54+a55)*(b32+b53+b55)*(c52+c53) 92 | (a12+a15+a42+a45+a52+a55)*(b51)*(c11+c21+c41) 93 | (a11+a14+a24+a53+a54)*(b42+b44)*(c21+c31) 94 | (a11+a31+a41+a51)*(b15+b25+b35+b45+b55)*(c55) 95 | (a14+a54)*(b41)*(c11+c13) 96 | --------------------------------------------------------------------------------