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Commit 0ec39d33 by Zhenjie Li

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 (**********************************************************************) (* *) (* Ancillary file to "The Three-loop MHV Octagon from Qbar equations" *) (* by Zhenjie Li and Chi Zhang, arXiv:2110.xxxxx. *) (* *) (* This file is a replacement rule of all rational letters of the 3 *) (* loop MHV octagon with the notations: *) (* ab[i,j,k,l] : Plucker coordinate, *) (* ab[a,b,c,cap[{d,e},{f,g,h}]] := ab[a,b,c,d] ab[e,f,g,h] *) (* - ab[a,b,c,e] ab[d,f,g,h], *) (* ab[a,cap1[{b,c},{d,e},{f,g}]] := ab[a,b,d,e] ab[a,c,f,g] *) (* - ab[a,b,f,g] ab[a,c,d,e], *) (* ab[a,b,cap2[{r,s,t},{u,v,w}]] := ab[a,b,s,t] ab[r,u,v,w] *) (* - ab[a,b,r,t] ab[s,u,v,w] *) (* + ab[a,b,r,s] ab[t,u,v,w] . *) (* *) (**********************************************************************) {a[1] -> ab[1, 2, 3, 4], a[2] -> ab[1, 2, 3, 5], a[3] -> ab[1, 2, 3, 6], a[4] -> ab[1, 2, 3, 7], a[5] -> ab[1, 2, 3, 8], a[6] -> ab[1, 2, 4, 5], a[7] -> ab[1, 2, 4, 6], a[8] -> ab[1, 2, 4, 7], a[9] -> ab[1, 2, 4, 8], a[10] -> ab[1, 2, 5, 6], a[11] -> ab[1, 2, 5, 7], a[12] -> ab[1, 2, 5, 8], a[13] -> ab[1, 2, 6, 7], a[14] -> ab[1, 2, 6, 8], a[15] -> ab[1, 2, 7, 8], a[16] -> ab[1, 3, 4, 5], a[17] -> ab[1, 3, 4, 6], a[18] -> ab[1, 3, 4, 7], a[19] -> ab[1, 3, 4, 8], a[20] -> ab[1, 3, 5, 6], a[21] -> ab[1, 3, 5, 8], a[22] -> ab[1, 3, 6, 7], a[23] -> ab[1, 3, 6, 8], a[24] -> ab[1, 3, 7, 8], a[25] -> ab[1, 4, 5, 6], a[26] -> ab[1, 4, 5, 7], a[27] -> ab[1, 4, 5, 8], a[28] -> ab[1, 4, 6, 7], a[29] -> ab[1, 4, 6, 8], a[30] -> ab[1, 4, 7, 8], a[31] -> ab[1, 5, 6, 7], a[32] -> ab[1, 5, 6, 8], a[33] -> ab[1, 5, 7, 8], a[34] -> ab[1, 6, 7, 8], a[35] -> ab[2, 3, 4, 5], a[36] -> ab[2, 3, 4, 6], a[37] -> ab[2, 3, 4, 7], a[38] -> ab[2, 3, 4, 8], a[39] -> ab[2, 3, 5, 6], a[40] -> ab[2, 3, 5, 7], a[41] -> ab[2, 3, 5, 8], a[42] -> ab[2, 3, 6, 7], a[43] -> ab[2, 3, 6, 8], a[44] -> ab[2, 3, 7, 8], a[45] -> ab[2, 4, 5, 6], a[46] -> ab[2, 4, 5, 7], a[47] -> ab[2, 4, 5, 8], a[48] -> ab[2, 4, 6, 7], a[49] -> ab[2, 4, 7, 8], a[50] -> ab[2, 5, 6, 7], a[51] -> ab[2, 5, 6, 8], a[52] -> ab[2, 5, 7, 8], a[53] -> ab[2, 6, 7, 8], a[54] -> ab[3, 4, 5, 6], a[55] -> ab[3, 4, 5, 7], a[56] -> ab[3, 4, 5, 8], a[57] -> ab[3, 4, 6, 7], a[58] -> ab[3, 4, 6, 8], a[59] -> ab[3, 4, 7, 8], a[60] -> ab[3, 5, 6, 7], a[61] -> ab[3, 5, 6, 8], a[62] -> ab[3, 5, 7, 8], a[63] -> ab[3, 6, 7, 8], a[64] -> ab[4, 5, 6, 7], a[65] -> ab[4, 5, 6, 8], a[66] -> ab[4, 5, 7, 8], a[67] -> ab[4, 6, 7, 8], a[68] -> ab[5, 6, 7, 8], a[69] -> ab[1, 2, cap2[{3, 4, 5}, {6, 7, 8}]], a[70] -> ab[1, 8, cap2[{2, 3, 4}, {5, 6, 7}]], a[71] -> ab[2, 3, cap2[{1, 7, 8}, {4, 5, 6}]], a[72] -> ab[3, 4, cap2[{1, 2, 8}, {5, 6, 7}]], a[73] -> ab[4, 5, cap2[{1, 2, 3}, {6, 7, 8}]], a[74] -> ab[5, 6, cap2[{1, 7, 8}, {2, 3, 4}]], a[75] -> ab[6, 7, cap2[{1, 2, 8}, {3, 4, 5}]], a[76] -> ab[7, 8, cap2[{1, 2, 3}, {4, 5, 6}]], a[77] -> ab[1, cap1[{2, 3}, {4, 5}, {6, 7}]], a[78] -> ab[1, cap1[{2, 3}, {4, 5}, {6, 8}]], a[79] -> ab[1, cap1[{2, 3}, {4, 5}, {7, 8}]], a[80] -> ab[1, cap1[{2, 3}, {4, 6}, {7, 8}]], a[81] -> ab[1, cap1[{2, 3}, {5, 6}, {7, 8}]], a[82] -> ab[1, cap1[{2, 4}, {5, 6}, {7, 8}]], a[83] -> ab[1, cap1[{2, 8}, {3, 4}, {5, 6}]], a[84] -> ab[1, cap1[{2, 8}, {3, 4}, {5, 7}]], a[85] -> ab[1, cap1[{2, 8}, {3, 4}, {6, 7}]], a[86] -> ab[1, cap1[{2, 8}, {3, 5}, {6, 7}]], a[87] -> ab[1, cap1[{2, 8}, {4, 5}, {6, 7}]], a[88] -> ab[1, cap1[{3, 4}, {5, 6}, {7, 8}]], a[89] -> ab[2, cap1[{1, 3}, {4, 5}, {6, 7}]], a[90] -> ab[2, cap1[{1, 3}, {4, 5}, {6, 8}]], a[91] -> ab[2, cap1[{1, 3}, {4, 5}, {7, 8}]], a[92] -> ab[2, cap1[{1, 3}, {4, 6}, {7, 8}]], a[93] -> ab[2, cap1[{1, 3}, {5, 6}, {7, 8}]], a[94] -> ab[2, cap1[{1, 7}, {3, 4}, {5, 6}]], a[95] -> ab[2, cap1[{1, 8}, {3, 4}, {5, 6}]], a[96] -> ab[2, cap1[{1, 8}, {3, 4}, {6, 7}]], a[97] -> ab[2, cap1[{1, 8}, {3, 5}, {6, 7}]], a[98] -> ab[2, cap1[{1, 8}, {4, 5}, {6, 7}]], a[99] -> ab[2, cap1[{3, 4}, {5, 6}, {7, 8}]], a[100] -> ab[2, cap1[{3, 4}, {5, 7}, {8, 1}]], a[101] -> ab[3, cap1[{1, 2}, {4, 5}, {6, 7}]], a[102] -> ab[3, cap1[{1, 2}, {4, 5}, {7, 8}]], a[103] -> ab[3, cap1[{1, 2}, {4, 6}, {7, 8}]], a[104] -> ab[3, cap1[{1, 2}, {5, 6}, {7, 8}]], a[105] -> ab[3, cap1[{1, 7}, {2, 4}, {5, 6}]], a[106] -> ab[3, cap1[{1, 8}, {2, 4}, {5, 6}]], a[107] -> ab[3, cap1[{1, 8}, {2, 4}, {5, 7}]], a[108] -> ab[3, cap1[{1, 8}, {2, 4}, {6, 7}]], a[109] -> ab[3, cap1[{1, 8}, {4, 5}, {6, 7}]], a[110] -> ab[3, cap1[{2, 4}, {5, 6}, {7, 8}]], a[111] -> ab[3, cap1[{2, 8}, {4, 5}, {6, 7}]], a[112] -> ab[3, cap1[{4, 5}, {6, 8}, {1, 2}]], a[113] -> ab[4, cap1[{1, 2}, {3, 5}, {6, 7}]], a[114] -> ab[4, cap1[{1, 2}, {3, 5}, {6, 8}]], a[115] -> ab[4, cap1[{1, 2}, {3, 5}, {7, 8}]], a[116] -> ab[4, cap1[{1, 2}, {5, 6}, {7, 8}]], a[117] -> ab[4, cap1[{1, 3}, {5, 6}, {7, 8}]], a[118] -> ab[4, cap1[{1, 8}, {2, 3}, {5, 6}]], a[119] -> ab[4, cap1[{1, 8}, {2, 3}, {5, 7}]], a[120] -> ab[4, cap1[{1, 8}, {2, 3}, {6, 7}]], a[121] -> ab[4, cap1[{1, 8}, {3, 5}, {6, 7}]], a[122] -> ab[4, cap1[{2, 3}, {5, 6}, {7, 8}]], a[123] -> ab[4, cap1[{2, 8}, {3, 5}, {6, 7}]], a[124] -> ab[4, cap1[{5, 6}, {7, 1}, {2, 3}]], a[125] -> ab[5, cap1[{1, 2}, {3, 4}, {6, 7}]], a[126] -> ab[5, cap1[{1, 2}, {3, 4}, {6, 8}]], a[127] -> ab[5, cap1[{1, 2}, {3, 4}, {7, 8}]], a[128] -> ab[5, cap1[{1, 2}, {4, 6}, {7, 8}]], a[129] -> ab[5, cap1[{1, 3}, {4, 6}, {7, 8}]], a[130] -> ab[5, cap1[{1, 7}, {2, 3}, {4, 6}]], a[131] -> ab[5, cap1[{1, 8}, {2, 3}, {4, 6}]], a[132] -> ab[5, cap1[{1, 8}, {2, 3}, {6, 7}]], a[133] -> ab[5, cap1[{1, 8}, {2, 4}, {6, 7}]], a[134] -> ab[5, cap1[{1, 8}, {3, 4}, {6, 7}]], a[135] -> ab[5, cap1[{2, 3}, {4, 6}, {7, 8}]], a[136] -> ab[5, cap1[{6, 7}, {8, 2}, {3, 4}]], a[137] -> ab[6, cap1[{1, 2}, {3, 4}, {5, 7}]], a[138] -> ab[6, cap1[{1, 2}, {3, 4}, {7, 8}]], a[139] -> ab[6, cap1[{1, 2}, {3, 5}, {7, 8}]], a[140] -> ab[6, cap1[{1, 2}, {4, 5}, {7, 8}]], a[141] -> ab[6, cap1[{1, 7}, {2, 3}, {4, 5}]], a[142] -> ab[6, cap1[{1, 8}, {2, 3}, {4, 5}]], a[143] -> ab[6, cap1[{1, 8}, {2, 3}, {5, 7}]], a[144] -> ab[6, cap1[{1, 8}, {2, 4}, {5, 7}]], a[145] -> ab[6, cap1[{1, 8}, {3, 4}, {5, 7}]], a[146] -> ab[6, cap1[{2, 3}, {4, 5}, {7, 8}]], a[147] -> ab[6, cap1[{2, 8}, {3, 4}, {5, 7}]], a[148] -> ab[6, cap1[{7, 8}, {1, 3}, {4, 5}]], a[149] -> ab[7, cap1[{1, 2}, {3, 4}, {5, 6}]], a[150] -> ab[7, cap1[{1, 2}, {3, 4}, {6, 8}]], a[151] -> ab[7, cap1[{1, 2}, {3, 5}, {6, 8}]], a[152] -> ab[7, cap1[{1, 2}, {4, 5}, {6, 8}]], a[153] -> ab[7, cap1[{1, 3}, {4, 5}, {6, 8}]], a[154] -> ab[7, cap1[{1, 8}, {2, 3}, {4, 5}]], a[155] -> ab[7, cap1[{1, 8}, {2, 3}, {4, 6}]], a[156] -> ab[7, cap1[{1, 8}, {2, 3}, {5, 6}]], a[157] -> ab[7, cap1[{1, 8}, {3, 4}, {5, 6}]], a[158] -> ab[7, cap1[{2, 3}, {4, 5}, {6, 8}]], a[159] -> ab[7, cap1[{2, 8}, {3, 4}, {5, 6}]], a[160] -> ab[7, cap1[{8, 1}, {2, 4}, {5, 6}]], a[161] -> ab[8, cap1[{1, 2}, {3, 4}, {5, 6}]], a[162] -> ab[8, cap1[{1, 2}, {3, 4}, {5, 7}]], a[163] -> ab[8, cap1[{1, 2}, {3, 4}, {6, 7}]], a[164] -> ab[8, cap1[{1, 2}, {3, 5}, {6, 7}]], a[165] -> ab[8, cap1[{1, 2}, {4, 5}, {6, 7}]], a[166] -> ab[8, cap1[{1, 3}, {4, 5}, {6, 7}]], a[167] -> ab[8, cap1[{1, 7}, {2, 3}, {4, 5}]], a[168] -> ab[8, cap1[{1, 7}, {2, 3}, {4, 6}]], a[169] -> ab[8, cap1[{1, 7}, {2, 3}, {5, 6}]], a[170] -> ab[8, cap1[{1, 7}, {2, 4}, {5, 6}]], a[171] -> ab[8, cap1[{1, 7}, {3, 4}, {5, 6}]], a[172] -> ab[8, cap1[{2, 3}, {4, 5}, {6, 7}]], a[173] -> ab[cap2[{1, 2, 3}, {3, 4, 5}], cap2[{5, 6, 8}, {7, 8, 1}]], a[174] -> ab[cap2[{1, 2, 3}, {3, 4, 5}], cap2[{6, 8, 1}, {5, 6, 7}]], a[175] -> ab[cap2[{1, 2, 7}, {6, 7, 8}], cap2[{2, 3, 5}, {4, 5, 6}]], a[176] -> ab[cap2[{1, 2, 7}, {6, 7, 8}], cap2[{3, 5, 6}, {2, 3, 4}]], a[177] -> ab[cap2[{2, 3, 4}, {4, 5, 6}], cap2[{6, 7, 1}, {8, 1, 2}]], a[178] -> ab[cap2[{2, 3, 4}, {4, 5, 6}], cap2[{7, 1, 2}, {6, 7, 8}]], a[179] -> ab[cap2[{2, 3, 8}, {7, 8, 1}], cap2[{3, 4, 6}, {5, 6, 7}]], a[180] -> ab[cap2[{2, 3, 8}, {7, 8, 1}], cap2[{4, 6, 7}, {3, 4, 5}]], a[181] -> ab[cap2[{3, 4, 1}, {8, 1, 2}], cap2[{4, 5, 7}, {6, 7, 8}]], a[182] -> ab[cap2[{3, 4, 1}, {8, 1, 2}], cap2[{5, 7, 8}, {4, 5, 6}]], a[183] -> ab[cap2[{3, 4, 5}, {5, 6, 7}], cap2[{7, 8, 2}, {1, 2, 3}]], a[184] -> ab[cap2[{3, 4, 5}, {5, 6, 7}], cap2[{8, 2, 3}, {7, 8, 1}]], a[185] -> ab[cap2[{3, 4, 6}, {5, 6, 7}], cap2[{2, 7, 8}, {1, 2, 3}]], a[186] -> ab[cap2[{4, 5, 2}, {1, 2, 3}], cap2[{5, 6, 8}, {7, 8, 1}]], a[187] -> ab[cap2[{4, 5, 6}, {6, 7, 8}], cap2[{1, 3, 4}, {8, 1, 2}]], a[188] -> ab[cap2[{4, 5, 6}, {6, 7, 8}], cap2[{8, 1, 3}, {2, 3, 4}]], a[189] -> ab[cap2[{4, 5, 7}, {6, 7, 8}], cap2[{3, 8, 1}, {2, 3, 4}]], a[190] -> ab[cap2[{5, 6, 3}, {2, 3, 4}], cap2[{6, 7, 1}, {8, 1, 2}]], a[191] -> ab[cap2[{5, 6, 7}, {7, 8, 1}], cap2[{1, 2, 4}, {3, 4, 5}]], a[192] -> ab[cap2[{5, 6, 7}, {7, 8, 1}], cap2[{2, 4, 5}, {1, 2, 3}]], a[193] -> ab[cap2[{5, 6, 8}, {7, 8, 1}], cap2[{4, 1, 2}, {3, 4, 5}]], a[194] -> ab[cap2[{6, 7, 1}, {8, 1, 2}], cap2[{5, 2, 3}, {4, 5, 6}]], a[195] -> ab[cap2[{6, 7, 4}, {3, 4, 5}], cap2[{7, 8, 2}, {1, 2, 3}]], a[196] -> ab[cap2[{6, 7, 8}, {8, 1, 2}], cap2[{2, 3, 5}, {4, 5, 6}]], a[197] -> ab[cap2[{6, 7, 8}, {8, 1, 2}], cap2[{3, 5, 6}, {2, 3, 4}]], a[198] -> ab[cap2[{7, 8, 1}, {1, 2, 3}], cap2[{3, 4, 6}, {5, 6, 7}]], a[199] -> ab[cap2[{7, 8, 1}, {1, 2, 3}], cap2[{4, 6, 7}, {3, 4, 5}]], a[200] -> ab[cap2[{7, 8, 5}, {4, 5, 6}], cap2[{8, 1, 3}, {2, 3, 4}]], a[201] -> ab[cap2[{8, 1, 2}, {2, 3, 4}], cap2[{4, 5, 7}, {6, 7, 8}]], a[202] -> ab[cap2[{8, 1, 2}, {2, 3, 4}], cap2[{5, 7, 8}, {4, 5, 6}]], a[203] -> ab[cap2[{8, 1, 6}, {5, 6, 7}], cap2[{1, 2, 4}, {3, 4, 5}]], a[204] -> ab[cap2[{8, 1, 6}, {5, 6, 7}], cap2[{2, 4, 5}, {1, 2, 3}]]}
F2.m 0 → 100644
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F3.m 0 → 100644
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F4.m 0 → 100644
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algebraic_part.m 0 → 100644
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