Test A: For I:=1 To 100 Do X := Fact(1000+I); Y := Fact(900+I); Z := X/Y End; _____________________________________________ Tests F, G, Gp: Set Timer; P := (7*y*x^2-3*x*y+11*(x+1)*y^2+5)^4*(3*x-7*y+2)^5; Q := (7*y*x^2-3*x*y+11*(x+1)*y^2+5)^3*(3*x-7*y-2)^6; P3 := (7*y*x^2*z^2-3*x*y*z+11*(x+1)*y^2+5*z+1)^4*(3*x-7*y+2*z-3)^5; Q3 := (7*y*x^2*z^2-3*x*y*z+11*(x+1)*y^2+5*z+1)^3*(3*x-7*y+2*z+3)^6; Use R2 ::= Z/(181) [ x,y,z]; P4 := (7*y*x^2*z^2-3*x*y*z+11*(x+1)*y^2+5*z+1)^4*(3*x-7*y+2*z-3)^5; Q4 := (7*y*x^2*z^2-3*x*y*z+11*(x+1)*y^2+5*z+1)^3*(3*x-7*y+2*z+3)^6; ____________________________________________ Test S; D := Mat[[-517,-540,-90,-353,-1086,-1315,-187,168,-317,-1426,-754,-83,542,-215,538,-1471,-885,-925,373,1344], [ 1210,-716,-1241,-444,50,168,1162,-233,1325,185,769,519,1187,760,1332,849,-795,-956,-956,461], [ -500,1003,-1447,-180,678,-195,446,1447,-342,141,-779,294,879,-119,86,-888,746,911,1209,-85], [ 294,-967,1224,842,1120,803,584,-325,-1257,-1497,50,-343,1088,-293,1491,-841,421,-880,-678,-758], [ -793,-193,290,-1254,14,-713,-1359,-1255,1424,517,785,1157,-640,-873,851,611,669,1450,105,918], [ -1369,515,289,1231,-1206,-991,1342,899,851,-1355,505,-1462,268,376,414,1099,-1297,97,-565,751], [ 178,548,1170,-744,130,-1238,111,-447,-788,-285,374,-293,-424,-1364,-394,899,-1031,-524,403,-436], [ 557,-414,-130,311,-1346,-1439,-293,1341,420,-775,-999,-1457,-1183,-819,303,-661,407,177,-327,820], [ 539,-64,-613,1164,-827,931,1361,1050,1260,362,-977,-634,1105,-1172,653,-658,-1426,-264,507,-272], [ 392,253,92,895,-487,619,1286,-124,-743,-904,824,180,511,-57,1362,642,-14,782,386,-396], [ -685,-934,483,-659,-13,-232,861,1076,-950,-671,1414,-769,260,28,232,-1037,636,-1180,1116,1310], [ 1319,-276,-936,-1149,873,196,-1488,-626,-150,-1172,-1319,-92,-1163,659,345,1036,-265,-587,-959,-986], [ -81,1015,1062,-1162,907,-555,-51,712,-706,277,-300,1061,-1067,449,-1453,-1296,3,1034,-238,383], [ 1150,-460,-1073,-907,255,-1407,-872,-1433,-282,705,925,-263,1367,740,40,1425,88,-418,-86,1175], [ -1491,791,-1476,1150,-496,-809,-781,98,715,1372,157,-397,1460,732,576,1265,-133,1083,-945,95], [-1302,1271,-371,66,-468,484,-217,175,-1254,1274,267,-609,-1161,-1497,-607,-104,-1418,-444,-1403,1259], [ -1015,1351,893,557,-631,1172,1308,-1196,996,104,972,346,-810,198,-690,52,-1137,1373,-708,662], [ 627,-266,-478,1109,-874,1399,735,874,-46,-802,962,1494,1193,-742,524,969,-668,-758,-1346,1207], [ -705,1356,-123,-100,-1343,-603,-756,-643,-637,61,879,15,-1009,244,89,-51,-257,-1289,511,-1093], [ 599,1079,-976,1486,852,-685,-378,-386,1333,814,1483,-1171,-383,845,729,244,304,533,810,-724 ]]; ____________________________________________ Test M1: (For M2, please see mupadall or fermatall.) Set Timer; Use R ::= Q[x[1..5]]; W := Mat [ [ 1, 1, 1, 7, x[4] , 12, x[3] , 17, x[2] , 22, x[1] ], [ 2, 2, 1, 8, x[4] , 13, x[3] , 18, x[2] , 23, x[1] ], [ 3, 3, 1, 9, x[4] , 14, x[3] , 19, x[2] , 24, x[1] ], [ 4, 4, 1, 10, x[4] , 15, x[3] , 20, x[2] , 25, x[1] ], [ 5, 5, 1, 26, 1, 1, 0, 1, 0, 1, 0 ], [ 6, 2, x[5] , 6, 1, 12, x[3] , 17, x[2] , 22, x[1] ], [ 7, 3, x[5] , 7, 1, 13, x[3] , 18, x[2] , 23, x[1] ], [ 8, 4, x[5] , 8, 1, 14, x[3] , 19, x[2] , 24, x[1] ], [ 9, 5, x[5] , 9, 1, 15, x[3] , 20, x[2] , 25, x[1] ], [10, 10, 1, 26, 1, 1, 0, 1, 0, 1, 0 ], [11, 2, x[5] , 7, x[4] , 11, 1, 17, x[2] , 22, x[1] ], [12, 3, x[5] , 8, x[4] , 12, 1, 18, x[2] , 23, x[1] ], [13, 4, x[5] , 9, x[4] , 13, 1, 19, x[2] , 24, x[1] ], [14, 5, x[5] , 10, x[4] , 14, 1, 20, x[2] , 25, x[1] ], [15, 15, 1, 26, 1, 1, 0, 1, 0, 1, 0 ], [16, 2, x[5] , 7, x[4] , 12, x[3] , 16, 1, 22, x[1] ], [17, 3, x[5] , 8, x[4] , 13, x[3] , 17, 1, 23, x[1] ], [18, 4, x[5] , 9, x[4] , 14, x[3] , 18, 1, 24, x[1] ], [19, 5, x[5] , 10, x[4] , 15, x[3] , 19, 1, 25, x[1] ], [20, 20, 1, 26, 1, 1, 0, 1, 0, 1, 0 ], [21, 2, x[5] , 7, x[4] , 12, x[3] , 17, x[2] , 21, 1], [22, 3, x[5] , 8, x[4] , 13, x[3] , 18, x[2] , 22, 1], [23, 4, x[5] , 9, x[4] , 14, x[3] , 19, x[2] , 23, 1], [24, 5, x[5] , 10, x[4] , 15, x[3] , 20, x[2] , 24, 1], [25, 25, 1, 26, 1, 1, 0, 1, 0, 1, 0 ], [26, 1, x[5] , 6, x[4] , 11, x[3] , 16, x[2] , 21, x[1] ] ]; M := NewMat(26,26, 0); For I:=1 To 26 Do For J := 1 To 5 Do M[I, W[I, 2*J] ] := W[I, 2*J+1] End; End; ______________________________________________________ Tests P - Q': W := Mat [ [ 1, 1, 1, 12, 9, 22, 8, 32, 7, 42, 6, 52, 5, 62, 4, 72, 3, 82, 2, 92, 1 ], [ 2, 2, 1, 13, 9, 23, 8, 33, 7, 43, 6, 53, 5, 63, 4, 73, 3, 83, 2, 93, 1 ], [ 3, 3, 1, 14, 9, 24, 8, 34, 7, 44, 6, 54, 5, 64, 4, 74, 3, 84, 2, 94, 1 ], [ 4, 4, 1, 15, 9, 25, 8, 35, 7, 45, 6, 55, 5, 65, 4, 75, 3, 85, 2, 95, 1 ], [ 5, 5, 1, 16, 9, 26, 8, 36, 7, 46, 6, 56, 5, 66, 4, 76, 3, 86, 2, 96, 1 ], [ 6, 6, 1, 17, 9, 27, 8, 37, 7, 47, 6, 57, 5, 67, 4, 77, 3, 87, 2, 97, 1 ], [ 7, 7, 1, 18, 9, 28, 8, 38, 7, 48, 6, 58, 5, 68, 4, 78, 3, 88, 2, 98, 1 ], [ 8, 8, 1, 19, 9, 29, 8, 39, 7, 49, 6, 59, 5, 69, 4, 79, 3, 89, 2, 99, 1 ], [ 9, 9, 1, 20, 9, 30, 8, 40, 7, 50, 6, 60, 5, 70, 4, 80, 3, 90, 2, 100, 1 ], [10, 10, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [11, 2, 10, 11, 1, 22, 8, 32, 7, 42, 6, 52, 5, 62, 4, 72, 3, 82, 2, 92, 1 ], [12, 3, 10, 12, 1, 23, 8, 33, 7, 43, 6, 53, 5, 63, 4, 73, 3, 83, 2, 93, 1 ], [13, 4, 10, 13, 1, 24, 8, 34, 7, 44, 6, 54, 5, 64, 4, 74, 3, 84, 2, 94, 1 ], [14, 5, 10, 14, 1, 25, 8, 35, 7, 45, 6, 55, 5, 65, 4, 75, 3, 85, 2, 95, 1 ], [15, 6, 10, 15, 1, 26, 8, 36, 7, 46, 6, 56, 5, 66, 4, 76, 3, 86, 2, 96, 1 ], [16, 7, 10, 16, 1, 27, 8, 37, 7, 47, 6, 57, 5, 67, 4, 77, 3, 87, 2, 97, 1 ], [17, 8, 10, 17, 1, 28, 8, 38, 7, 48, 6, 58, 5, 68, 4, 78, 3, 88, 2, 98, 1 ], [18, 9, 10, 18, 1, 29, 8, 39, 7, 49, 6, 59, 5, 69, 4, 79, 3, 89, 2, 99, 1 ], [19, 10, 10, 19, 1, 30, 8, 40, 7, 50, 6, 60, 5, 70, 4, 80, 3, 90, 2, 100, 1 ], [20, 20, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [21, 2, 10, 12, 9, 21, 1, 32, 7, 42, 6, 52, 5, 62, 4, 72, 3, 82, 2, 92, 1 ], [22, 3, 10, 13, 9, 22, 1, 33, 7, 43, 6, 53, 5, 63, 4, 73, 3, 83, 2, 93, 1 ], [23, 4, 10, 14, 9, 23, 1, 34, 7, 44, 6, 54, 5, 64, 4, 74, 3, 84, 2, 94, 1 ], [24, 5, 10, 15, 9, 24, 1, 35, 7, 45, 6, 55, 5, 65, 4, 75, 3, 85, 2, 95, 1 ], [25, 6, 10, 16, 9, 25, 1, 36, 7, 46, 6, 56, 5, 66, 4, 76, 3, 86, 2, 96, 1 ], [26, 7, 10, 17, 9, 26, 1, 37, 7, 47, 6, 57, 5, 67, 4, 77, 3, 87, 2, 97, 1 ], [27, 8, 10, 18, 9, 27, 1, 38, 7, 48, 6, 58, 5, 68, 4, 78, 3, 88, 2, 98, 1 ], [28, 9, 10, 19, 9, 28, 1, 39, 7, 49, 6, 59, 5, 69, 4, 79, 3, 89, 2, 99, 1 ], [29, 10, 10, 20, 9, 29, 1, 40, 7, 50, 6, 60, 5, 70, 4, 80, 3, 90, 2, 100, 1 ], [30, 30, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [31, 2, 10, 12, 9, 22, 8, 31, 1, 42, 6, 52, 5, 62, 4, 72, 3, 82, 2, 92, 1 ], [32, 3, 10, 13, 9, 23, 8, 32, 1, 43, 6, 53, 5, 63, 4, 73, 3, 83, 2, 93, 1 ], [33, 4, 10, 14, 9, 24, 8, 33, 1, 44, 6, 54, 5, 64, 4, 74, 3, 84, 2, 94, 1 ], [34, 5, 10, 15, 9, 25, 8, 34, 1, 45, 6, 55, 5, 65, 4, 75, 3, 85, 2, 95, 1 ], [35, 6, 10, 16, 9, 26, 8, 35, 1, 46, 6, 56, 5, 66, 4, 76, 3, 86, 2, 96, 1 ], [36, 7, 10, 17, 9, 27, 8, 36, 1, 47, 6, 57, 5, 67, 4, 77, 3, 87, 2, 97, 1 ], [37, 8, 10, 18, 9, 28, 8, 37, 1, 48, 6, 58, 5, 68, 4, 78, 3, 88, 2, 98, 1 ], [38, 9, 10, 19, 9, 29, 8, 38, 1, 49, 6, 59, 5, 69, 4, 79, 3, 89, 2, 99, 1 ], [39, 10, 10, 20, 9, 30, 8, 39, 1, 50, 6, 60, 5, 70, 4, 80, 3, 90, 2, 100, 1 ], [40, 40, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [41, 2, 10, 12, 9, 22, 8, 32, 7, 41, 1, 52, 5, 62, 4, 72, 3, 82, 2, 92, 1 ], [42, 3, 10, 13, 9, 23, 8, 33, 7, 42, 1, 53, 5, 63, 4, 73, 3, 83, 2, 93, 1 ], [43, 4, 10, 14, 9, 24, 8, 34, 7, 43, 1, 54, 5, 64, 4, 74, 3, 84, 2, 94, 1 ], [44, 5, 10, 15, 9, 25, 8, 35, 7, 44, 1, 55, 5, 65, 4, 75, 3, 85, 2, 95, 1 ], [45, 6, 10, 16, 9, 26, 8, 36, 7, 45, 1, 56, 5, 66, 4, 76, 3, 86, 2, 96, 1 ], [46, 7, 10, 17, 9, 27, 8, 37, 7, 46, 1, 57, 5, 67, 4, 77, 3, 87, 2, 97, 1 ], [47, 8, 10, 18, 9, 28, 8, 38, 7, 47, 1, 58, 5, 68, 4, 78, 3, 88, 2, 98, 1 ], [48, 9, 10, 19, 9, 29, 8, 39, 7, 48, 1, 59, 5, 69, 4, 79, 3, 89, 2, 99, 1 ], [49, 10, 10, 20, 9, 30, 8, 40, 7, 49, 1, 60, 5, 70, 4, 80, 3, 90, 2, 100, 1 ], [50, 50, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [51, 2, 10, 12, 9, 22, 8, 32, 7, 42, 6, 51, 1, 62, 4, 72, 3, 82, 2, 92, 1 ], [52, 3, 10, 13, 9, 23, 8, 33, 7, 43, 6, 52, 1, 63, 4, 73, 3, 83, 2, 93, 1 ], [53, 4, 10, 14, 9, 24, 8, 34, 7, 44, 6, 53, 1, 64, 4, 74, 3, 84, 2, 94, 1 ], [54, 5, 10, 15, 9, 25, 8, 35, 7, 45, 6, 54, 1, 65, 4, 75, 3, 85, 2, 95, 1 ], [55, 6, 10, 16, 9, 26, 8, 36, 7, 46, 6, 55, 1, 66, 4, 76, 3, 86, 2, 96, 1 ], [56, 7, 10, 17, 9, 27, 8, 37, 7, 47, 6, 56, 1, 67, 4, 77, 3, 87, 2, 97, 1 ], [57, 8, 10, 18, 9, 28, 8, 38, 7, 48, 6, 57, 1, 68, 4, 78, 3, 88, 2, 98, 1 ], [58, 9, 10, 19, 9, 29, 8, 39, 7, 49, 6, 58, 1, 69, 4, 79, 3, 89, 2, 99, 1 ], [59, 10, 10, 20, 9, 30, 8, 40, 7, 50, 6, 59, 1, 70, 4, 80, 3, 90, 2, 100, 1 ], [60, 60, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [61, 2, 10, 12, 9, 22, 8, 32, 7, 42, 6, 52, 5, 61, 1, 72, 3, 82, 2, 92, 1 ], [62, 3, 10, 13, 9, 23, 8, 33, 7, 43, 6, 53, 5, 62, 1, 73, 3, 83, 2, 93, 1 ], [63, 4, 10, 14, 9, 24, 8, 34, 7, 44, 6, 54, 5, 63, 1, 74, 3, 84, 2, 94, 1 ], [64, 5, 10, 15, 9, 25, 8, 35, 7, 45, 6, 55, 5, 64, 1, 75, 3, 85, 2, 95, 1 ], [65, 6, 10, 16, 9, 26, 8, 36, 7, 46, 6, 56, 5, 65, 1, 76, 3, 86, 2, 96, 1 ], [66, 7, 10, 17, 9, 27, 8, 37, 7, 47, 6, 57, 5, 66, 1, 77, 3, 87, 2, 97, 1 ], [67, 8, 10, 18, 9, 28, 8, 38, 7, 48, 6, 58, 5, 67, 1, 78, 3, 88, 2, 98, 1 ], [68, 9, 10, 19, 9, 29, 8, 39, 7, 49, 6, 59, 5, 68, 1, 79, 3, 89, 2, 99, 1 ], [69, 10, 10, 20, 9, 30, 8, 40, 7, 50, 6, 60, 5, 69, 1, 80, 3, 90, 2, 100, 1 ], [70, 70, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [71, 2, 10, 12, 9, 22, 8, 32, 7, 42, 6, 52, 5, 62, 4, 71, 1, 82, 2, 92, 1 ], [72, 3, 10, 13, 9, 23, 8, 33, 7, 43, 6, 53, 5, 63, 4, 72, 1, 83, 2, 93, 1 ], [73, 4, 10, 14, 9, 24, 8, 34, 7, 44, 6, 54, 5, 64, 4, 73, 1, 84, 2, 94, 1 ], [74, 5, 10, 15, 9, 25, 8, 35, 7, 45, 6, 55, 5, 65, 4, 74, 1, 85, 2, 95, 1 ], [75, 6, 10, 16, 9, 26, 8, 36, 7, 46, 6, 56, 5, 66, 4, 75, 1, 86, 2, 96, 1 ], [76, 7, 10, 17, 9, 27, 8, 37, 7, 47, 6, 57, 5, 67, 4, 76, 1, 87, 2, 97, 1 ], [77, 8, 10, 18, 9, 28, 8, 38, 7, 48, 6, 58, 5, 68, 4, 77, 1, 88, 2, 98, 1 ], [78, 9, 10, 19, 9, 29, 8, 39, 7, 49, 6, 59, 5, 69, 4, 78, 1, 89, 2, 99, 1 ], [79, 10, 10, 20, 9, 30, 8, 40, 7, 50, 6, 60, 5, 70, 4, 79, 1, 90, 2, 100, 1 ], [80, 80, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [81, 2, 10, 12, 9, 22, 8, 32, 7, 42, 6, 52, 5, 62, 4, 72, 3, 81, 1, 92, 1 ], [82, 3, 10, 13, 9, 23, 8, 33, 7, 43, 6, 53, 5, 63, 4, 73, 3, 82, 1, 93, 1 ], [83, 4, 10, 14, 9, 24, 8, 34, 7, 44, 6, 54, 5, 64, 4, 74, 3, 83, 1, 94, 1 ], [84, 5, 10, 15, 9, 25, 8, 35, 7, 45, 6, 55, 5, 65, 4, 75, 3, 84, 1, 95, 1 ], [85, 6, 10, 16, 9, 26, 8, 36, 7, 46, 6, 56, 5, 66, 4, 76, 3, 85, 1, 96, 1 ], [86, 7, 10, 17, 9, 27, 8, 37, 7, 47, 6, 57, 5, 67, 4, 77, 3, 86, 1, 97, 1 ], [87, 8, 10, 18, 9, 28, 8, 38, 7, 48, 6, 58, 5, 68, 4, 78, 3, 87, 1, 98, 1 ], [88, 9, 10, 19, 9, 29, 8, 39, 7, 49, 6, 59, 5, 69, 4, 79, 3, 88, 1, 99, 1 ], [89, 10, 10, 20, 9, 30, 8, 40, 7, 50, 6, 60, 5, 70, 4, 80, 3, 89, 1, 100, 1 ], [90, 90, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [91, 2, 10, 12, 9, 22, 8, 32, 7, 42, 6, 52, 5, 62, 4, 72, 3, 82, 2, 91, 1 ], [92, 3, 10, 13, 9, 23, 8, 33, 7, 43, 6, 53, 5, 63, 4, 73, 3, 83, 2, 92, 1 ], [93, 4, 10, 14, 9, 24, 8, 34, 7, 44, 6, 54, 5, 64, 4, 74, 3, 84, 2, 93, 1 ], [94, 5, 10, 15, 9, 25, 8, 35, 7, 45, 6, 55, 5, 65, 4, 75, 3, 85, 2, 94, 1 ], [95, 6, 10, 16, 9, 26, 8, 36, 7, 46, 6, 56, 5, 66, 4, 76, 3, 86, 2, 95, 1 ], [96, 7, 10, 17, 9, 27, 8, 37, 7, 47, 6, 57, 5, 67, 4, 77, 3, 87, 2, 96, 1 ], [97, 8, 10, 18, 9, 28, 8, 38, 7, 48, 6, 58, 5, 68, 4, 78, 3, 88, 2, 97, 1 ], [98, 9, 10, 19, 9, 29, 8, 39, 7, 49, 6, 59, 5, 69, 4, 79, 3, 89, 2, 98, 1 ], [99, 10, 10, 20, 9, 30, 8, 40, 7, 50, 6, 60, 5, 70, 4, 80, 3, 90, 2, 99, 1 ], [100, 100, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [101, 1, 10, 11, 9, 21, 8, 31, 7, 41, 6, 51, 5, 61, 4, 71, 3, 81, 2, 91, 1 ] ]; M := NewMat(101,101, 0); For I:=1 To 101 Do For J := 1 To 10 Do M[I, W[I, 2*J] ] := W[I, 2*J+1] End; End; N := M; For I:=1 To 101 Do N[I,I] := N[I,I]-t End; M2 := M; For I:=1 To 101 Do A := M2[I,1]; For J := 1 To 100 Do M2[I, J] := M2[I, J+1] End; M2[I,101] := A End; For I:=1 To 101 Do For J := 1 To 101 Do If M[I,J] <> 0 Then M2[I, J] := M[I, J] End; End; End; N2 := M2; For I:=1 To 101 Do N2[I,I] := N2[I,I]-t End; S ::= Z/(181) [t,x]; K := S::N; L := S::M; ____________________________________________ Test N: Use Q ::= Q[ q[1..4], n[1..2], g, p[1..4], a[1..3] ]; Set Timer; R1:=p[1]*p[4]*q[1]^2*q[4]^2-p[2]*p[3]*q[1]^2*q[4]^2-n[2]*p[1]*p[4]*q[1]*q[4]^2+2*n[1]*p[1]*p[4]*q[1]*q[4]^2- p[1]*p[4]*q[1]*q[4]^2+n[2]*p[2]*p[3]*q[1]*q[4]^2-2*n[1]*p[2]*p[3]*q[1]*q[4]^2+p[2]*p[3]*q[1]*q[4]^2+2*g^2* p[1]*p[4]*q[4]^2-2*n[1]*n[2]*p[1]*p[4]*q[4]^2+2*n[2]*p[1]*p[4]*q[4]^2+2*n[1]*p[1]*p[4]*q[4]^2-2*p[1]*p[4]* q[4]^2-2*g^2*p[2]*p[3]*q[4]^2+2*n[1]*n[2]*p[2]*p[3]*q[4]^2-2*n[2]*p[2]*p[3]*q[4]^2-2*n[1]*p[2]*p[3]*q[4]^2+ 2*p[2]*p[3]*q[4]^2-n[1]*p[4]*q[1]*q[2]*q[3]*q[4]+g*p[3]*q[1]*q[2]*q[3]*q[4]+g*p[2]*q[1]*q[2]*q[3]*q[4]-n[2]*p[1]* q[1]*q[2]*q[3]*q[4]-g^2*p[4]*q[2]*q[3]*q[4]+n[1]*n[2]*p[4]*q[2]*q[3]*q[4]-n[1]*p[4]*q[2]*q[3]*q[4]-2*g*p[3]*q[2]*q[3]* q[4]+g*p[2]*q[2]*q[3]*q[4]+2*g^2*p[1]*q[2]*q[3]*q[4]-2*n[1]*n[2]*p[1]*q[2]*q[3]*q[4]+2*n[2]*p[1]*q[2]*q[3]*q[4]-n[1]* p[4]*q[1]*q[3]*q[4]+p[4]*q[1]*q[3]*q[4]+g*p[3]*q[1]*q[3]*q[4]-2*g*p[2]*q[1]*q[3]*q[4]+2*n[2]*p[1]*q[1]*q[3]*q[4]-2*p[1]* q[1]*q[3]*q[4]-g^2*p[4]*q[3]*q[4]+n[1]*n[2]*p[4]*q[3]*q[4]-n[2]*p[4]*q[3]*q[4]-n[1]*p[4]*q[3]*q[4]+p[4]*q[3]*q[4]- 4*g^2*p[1]*q[3]*q[4]+4*n[1]*n[2]*p[1]*q[3]*q[4]-4*n[2]*p[1]*q[3]*q[4]-4*n[1]*p[1]*q[3]*q[4]+4*p[1]*q[3]*q[4]+ n[2]*p[1]*p[4]*q[1]*q[2]*q[4]-2*n[1]*p[1]*p[4]*q[1]*q[2]*q[4]+2*n[1]*p[4]*q[1]*q[2]*q[4]-n[2]*p[2]*p[3]*q[1]*q[2]* q[4]+2*n[1]*p[2]*p[3]*q[1]*q[2]*q[4]+g*p[3]*q[1]*q[2]*q[4]-2*g*p[2]*q[1]*q[2]*q[4]-n[2]*p[1]*q[1]*q[2]*q[4]-4*g^2* p[1]*p[4]*q[2]*q[4]+4*n[1]*n[2]*p[1]*p[4]*q[2]*q[4]-2*n[2]*p[1]*p[4]*q[2]*q[4]-2*n[1]*p[1]*p[4]*q[2]*q[4]+2*g^2* p[4]*q[2]*q[4]-2*n[1]*n[2]*p[4]*q[2]*q[4]+2*n[1]*p[4]*q[2]*q[4]+4*g^2*p[2]*p[3]*q[2]*q[4]-4*n[1]*n[2]*p[2]*p[3]* q[2]*q[4]+2*n[2]*p[2]*p[3]*q[2]*q[4]+2*n[1]*p[2]*p[3]*q[2]*q[4]-2*g*p[3]*q[2]*q[4]-2*g*p[2]*q[2]*q[4]+2*g^2*p[1]* q[2]*q[4]-2*n[1]*n[2]*p[1]*q[2]*q[4]+2*n[2]*p[1]*q[2]*q[4]-p[1]*p[4]*q[1]^2*q[4]-p[4]*q[1]^2*q[4]+p[2]*p[3]*q[1]^2* q[4]+2*p[1]*q[1]^2*q[4]-n[2]*p[1]*p[4]*q[1]*q[4]-4*n[1]*p[1]*p[4]*q[1]*q[4]+5*p[1]*p[4]*q[1]*q[4]+n[2]*p[4]*q[1]* q[4]-p[4]*q[1]*q[4]+n[2]*p[2]*p[3]*q[1]*q[4]+4*n[1]*p[2]*p[3]*q[1]*q[4]-5*p[2]*p[3]*q[1]*q[4]+g*p[3]*q[1]*q[4]+ 4*g*p[2]*q[1]*q[4]+4*n[1]*p[1]*q[1]*q[4]-4*p[1]*q[1]*q[4]-g^2*q[2]^2*q[3]^2+n[1]*n[2]*q[2]^2*q[3]^2+g^2* q[2]*q[3]^2-n[1]*n[2]*q[2]*q[3]^2-n[2]*q[2]*q[3]^2+2*n[1]*q[2]*q[3]^2+2*g^2*q[3]^2-2*n[1]*n[2]*q[3]^2+2*n[2]* q[3]^2+2*n[1]*q[3]^2-2*q[3]^2+g^2*p[4]*q[2]^2*q[3]-n[1]*n[2]*p[4]*q[2]^2*q[3]-2*g^2*p[1]*q[2]^2*q[3]+2*n[1]* n[2]*p[1]*q[2]^2*q[3]+g^2*q[2]^2*q[3]-n[1]*n[2]*q[2]^2*q[3]+2*n[1]*p[4]*q[1]*q[2]*q[3]-2*g*p[3]*q[1]*q[2]*q[3]+ g*p[2]*q[1]*q[2]*q[3]-n[2]*p[1]*q[1]*q[2]*q[3]+n[2]*q[1]*q[2]*q[3]-2*n[1]*q[1]*q[2]*q[3]+g^2*p[4]*q[2]*q[3]-n[1]* n[2]*p[4]*q[2]*q[3]+n[2]*p[4]*q[2]*q[3]+4*g*p[3]*q[2]*q[3]+g*p[2]*q[2]*q[3]+4*g^2*p[1]*q[2]*q[3]-4*n[1]*n[2]* p[1]*q[2]*q[3]+4*n[1]*p[1]*q[2]*q[3]-5*g^2*q[2]*q[3]+5*n[1]*n[2]*q[2]*q[3]-n[2]*q[2]*q[3]-4*n[1]*q[2]*q[3]+2*n[1]* p[4]*q[1]*q[3]-2*p[4]*q[1]*q[3]-2*g*p[3]*q[1]*q[3]-2*g*p[2]*q[1]*q[3]+2*n[2]*p[1]*q[1]*q[3]-2*p[1]*q[1]*q[3]-2*n[2]* q[1]*q[3]-2*n[1]*q[1]*q[3]+4*q[1]*q[3]+2*g^2*p[1]*p[4]*q[2]^2-2*n[1]*n[2]*p[1]*p[4]*q[2]^2-2*g^2*p[4]*q[2]^2+ 2*n[1]*n[2]*p[4]*q[2]^2-2*g^2*p[2]*p[3]*q[2]^2+2*n[1]*n[2]*p[2]*p[3]*q[2]^2-2*g^2*p[1]*q[2]^2+2*n[1]* n[2]*p[1]*q[2]^2+2*g^2*q[2]^2-2*n[1]*n[2]*q[2]^2+n[2]*p[1]*p[4]*q[1]*q[2]+4*n[1]*p[1]*p[4]*q[1]*q[2]-n[2]* p[4]*q[1]*q[2]-4*n[1]*p[4]*q[1]*q[2]-n[2]*p[2]*p[3]*q[1]*q[2]-4*n[1]*p[2]*p[3]*q[1]*q[2]-n[2]*p[1]*q[1]*q[2]-4* n[1]*p[1]*q[1]*q[2]+n[2]*q[1]*q[2]+4*n[1]*q[1]*q[2]-2*p[1]*p[4]*q[1]^2+2*p[4]*q[1]^2+2*p[2]*p[3]*q[1]^2+2*p[1]* q[1]^2-2*q[1]^2; S1 := (4*g*a[3]^3-g*a[1]*a[2]*a[3]^2-4*n[2]*a[2]*a[3]^2+4*n[1]*a[2]*a[3]^2+7*g*a[1]*a[3]^2+4*g^2*a[3]^2- 4*n[1]*n[2]*a[3]^2+4*n[1]*a[3]^2+n[2]*a[1]*a[2]^2*a[3]-n[1]*a[1]*a[2]^2*a[3]-4*g*a[2]^2*a[3]- g*a[1]^2*a[2]*a[3]-5*g^2*a[1]*a[2]*a[3]+5*n[1]*n[2]*a[1]*a[2]*a[3]-7*n[2]*a[1]*a[2]*a[3]+2*n[1]*a[1]* a[2]*a[3]-4*g*a[2]*a[3]+3*g*a[1]^2*a[3]+3*g^2*a[1]*a[3]-3*n[1]*n[2]*a[1]*a[3]+3*n[1]*a[1]*a[3]+g* a[1]*a[2]^3+g^2*a[1]^2*a[2]^2-n[1]*n[2]*a[1]^2*a[2]^2+n[2]*a[1]^2*a[2]^2-2*g*a[1]*a[2]^2-3*g^2* a[1]^2*a[2]+3*n[1]*n[2]*a[1]^2*a[2]-3*n[2]*a[1]^2*a[2]-3*g*a[1]*a[2])/(3*g*a[1]*a[2]*a[3]^2-3*n[2]* a[2]*a[3]^2+g*a[1]*a[3]^2-n[2]*a[3]^2+3*n[1]*a[1]*a[2]^2*a[3]-3*g*a[2]^2*a[3]+5*g*a[1]^2*a[2]* a[3]-5*n[2]*a[1]*a[2]*a[3]+4*n[1]*a[1]*a[2]*a[3]-4*g*a[2]*a[3]+g*a[1]^2*a[3]-n[2]*a[1]*a[3]+n[1]* a[1]*a[3]-g*a[3]+2*n[1]*a[1]^2*a[2]^2-2*g*a[1]*a[2]^2+2*g*a[1]^3*a[2]-2*n[2]*a[1]^2*a[2]+2*n[1]* a[1]^2*a[2]-2*g*a[1]*a[2]); S2 := (4*g*a[1]*a[3]^2-4*n[2]*a[3]^2+4*a[3]^2-g*a[1]^2*a[2]*a[3]+n[2]*a[1]*a[2]*a[3]+4*n[1]*a[1]*a[2]* a[3]-5*a[1]*a[2]*a[3]-4*g*a[2]*a[3]+3*g*a[1]^2*a[3]-3*n[2]*a[1]*a[3]+3*a[1]*a[3]-n[1]*a[1]^2*a[2]^2+ a[1]^2*a[2]^2+g*a[1]*a[2]^2+3*n[1]*a[1]^2*a[2]-3*a[1]^2*a[2]-3*g*a[1]*a[2])/(2*g*a[1]*a[3]^2- 2*n[2]*a[3]^2+g*a[1]^2*a[2]*a[3]-n[2]*a[1]*a[2]*a[3]+2*n[1]*a[1]*a[2]*a[3]-2*g*a[2]*a[3]+2*g*a[1]^2* a[3]-2*n[2]*a[1]*a[3]+2*n[1]*a[1]*a[3]-2*g*a[3]+n[1]*a[1]^2*a[2]^2-g*a[1]*a[2]^2+g*a[1]^3*a[2]- n[2]*a[1]^2*a[2]+n[1]*a[1]^2*a[2]-g*a[1]*a[2]); S3 := (4*p[3]*a[3]^3-p[3]*a[1]*a[2]*a[3]^2-4*p[4]*a[2]*a[3]^2+4*p[1]*a[2]*a[3]^2+7*p[3]*a[1]*a[3]^2-4* p[1]*p[4]*a[3]^2+4*p[2]*p[3]*a[3]^2+4*p[1]*a[3]^2+p[4]*a[1]*a[2]^2*a[3]-p[1]*a[1]*a[2]^2*a[3]-4* p[2]*a[2]^2*a[3]-p[3]*a[1]^2*a[2]*a[3]+5*p[1]*p[4]*a[1]*a[2]*a[3]-7*p[4]*a[1]*a[2]*a[3]-5*p[2]*p[3]* a[1]*a[2]*a[3]+2*p[1]*a[1]*a[2]*a[3]-4*p[2]*a[2]*a[3]+3*p[3]*a[1]^2*a[3]-3*p[1]*p[4]*a[1]*a[3]+3*p[2]* p[3]*a[1]*a[3]+3*p[1]*a[1]*a[3]+p[2]*a[1]*a[2]^3-p[1]*p[4]*a[1]^2*a[2]^2+p[4]*a[1]^2*a[2]^2+p[2]* p[3]*a[1]^2*a[2]^2-2*p[2]*a[1]*a[2]^2+3*p[1]*p[4]*a[1]^2*a[2]-3*p[4]*a[1]^2*a[2]-3*p[2]*p[3]*a[1]^2* a[2]-3*p[2]*a[1]*a[2])/(3*p[3]*a[1]*a[2]*a[3]^2-3*p[4]*a[2]*a[3]^2+p[3]*a[1]*a[3]^2-p[4]*a[3]^2+ 3*p[1]*a[1]*a[2]^2*a[3]-3*p[2]*a[2]^2*a[3]+5*p[3]*a[1]^2*a[2]*a[3]-5*p[4]*a[1]*a[2]*a[3]+4*p[1]*a[1]* a[2]*a[3]-4*p[2]*a[2]*a[3]+p[3]*a[1]^2*a[3]-p[4]*a[1]*a[3]+p[1]*a[1]*a[3]-p[2]*a[3]+2*p[1]*a[1]^2* a[2]^2-2*p[2]*a[1]*a[2]^2+2*p[3]*a[1]^3*a[2]-2*p[4]*a[1]^2*a[2]+2*p[1]*a[1]^2*a[2]-2*p[2]*a[1]*a[2]); S4 := (4*p[3]*a[1]*a[3]^2-4*p[4]*a[3]^2+4*a[3]^2-p[3]*a[1]^2*a[2]*a[3]+p[4]*a[1]*a[2]*a[3]+4*p[1]*a[1]* a[2]*a[3]-5*a[1]*a[2]*a[3]-4*p[2]*a[2]*a[3]+3*p[3]*a[1]^2*a[3]-3*p[4]*a[1]*a[3]+3*a[1]*a[3]-p[1]*a[1]^2* a[2]^2+a[1]^2*a[2]^2+p[2]*a[1]*a[2]^2+3*p[1]*a[1]^2*a[2]-3*a[1]^2*a[2]-3*p[2]*a[1]*a[2])/(2*p[3]* a[1]*a[3]^2-2*p[4]*a[3]^2+p[3]*a[1]^2*a[2]*a[3]-p[4]*a[1]*a[2]*a[3]+2*p[1]*a[1]*a[2]*a[3]-2*p[2]* a[2]*a[3]+2*p[3]*a[1]^2*a[3]-2*p[4]*a[1]*a[3]+2*p[1]*a[1]*a[3]-2*p[2]*a[3]+p[1]*a[1]^2*a[2]^2-p[2]* a[1]*a[2]^2+p[3]*a[1]^3*a[2]-p[4]*a[1]^2*a[2]+p[1]*a[1]^2*a[2]-p[2]*a[1]*a[2]); Subst(R1, [ [q4,S4], [q3, S3], [q2, S2], [q1,S1] ]); ________________________________________________ Tests O1 and O2: Use R ::= Q[ a[1..6], b[1..6], c[1..6], w, x, y, z]; F := a[6]*y^2 + a[5]*y*z + a[4]*y*w + a[3]*z^2 + a[2]*z*w + a[1]*w^2; G := b[6]*y^2 + b[5]*y*z + b[4]*y*w + b[3]*z^2 + b[2]*z*w + b[1]*w^2; H := c[6]*y^2 + c[5]*y*z + c[4]*y*w + c[3]*z^2 + c[2]*z*w + c[1]*w^2; D1 := Mat[ [ a[6], a[5], a[4], a[3], a[2], a[1], 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, a[6], 0, a[5], a[4], 0, a[3], a[2], a[1], 0, 0, 0, 0, 0], [0, a[6], 0, a[5], a[4], 0, a[3], a[2], a[1], 0, 0, 0, 0, 0, 0], [0, 0, 0, a[6], 0, 0, a[5], a[4], 0, 0, a[3], a[2], a[1], 0, 0], [0, 0, 0, 0, a[6], 0, 0, a[5], a[4], 0, 0, a[3], a[2], a[1], 0], [0, 0, 0, 0, 0, a[6], 0, 0, a[5], a[4], 0, 0, a[3], a[2], a[1]], [0, 0, 0, b[6], 0, 0, b[5], b[4], 0, 0, b[3], b[2], b[1], 0, 0], [0, 0, 0, 0, b[6], 0, 0, b[5], b[4], 0, 0, b[3], b[2], b[1], 0], [0, b[6], 0, b[5], b[4], 0, b[3], b[2], b[1], 0, 0, 0, 0, 0, 0], [0, 0, b[6], 0, b[5], b[4], 0, b[3], b[2], b[1], 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, b[6], 0, 0, b[5], b[4], 0, 0, b[3], b[2], b[1]], [0, 0, 0, 0, 0, c[6], 0, 0, c[5], c[4], 0, 0, c[3], c[2], c[1]], [0, 0, c[6], 0, c[5], c[4], 0, c[3], c[2], c[1], 0, 0, 0, 0, 0], [0, c[6], 0, c[5], c[4], 0, c[3], c[2], c[1], 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, c[6], 0, 0, c[5], c[4], 0, 0, c[3], c[2], c[1], 0 ] ]; D2 := Mat[[ b[6], b[5], b[4], b[3], b[2], b[1], 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, b[6], 0, b[5], b[4], 0, b[3], b[2], b[1], 0, 0, 0, 0, 0], [0, b[6], 0, b[5], b[4], 0, b[3], b[2], b[1], 0, 0, 0, 0, 0, 0], [0, 0, 0, b[6], 0, 0, b[5], b[4], 0, 0, b[3], b[2], b[1], 0, 0], [0, 0, 0, 0, b[6], 0, 0, b[5], b[4], 0, 0, b[3], b[2], b[1], 0], [0, 0, 0, 0, 0, b[6], 0, 0, b[5], b[4], 0, 0, b[3], b[2], b[1]], [0, 0, 0, c[6], 0, 0, c[5], c[4], 0, 0, c[3], c[2], c[1], 0, 0], [0, 0, 0, 0, c[6], 0, 0, c[5], c[4], 0, 0, c[3], c[2], c[1], 0], [0, c[6], 0, c[5], c[4], 0, c[3], c[2], c[1], 0, 0, 0, 0, 0, 0], [0, 0, c[6], 0, c[5], c[4], 0, c[3], c[2], c[1], 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, c[6], 0, 0, c[5], c[4], 0, 0, c[3], c[2], c[1]], [0, 0, 0, 0, 0, a[6], 0, 0, a[5], a[4], 0, 0, a[3], a[2], a[1]], [0, 0, a[6], 0, a[5], a[4], 0, a[3], a[2], a[1], 0, 0, 0, 0, 0], [0, a[6], 0, a[5], a[4], 0, a[3], a[2], a[1], 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, a[6], 0, 0, a[5], a[4], 0, 0, a[3], a[2], a[1], 0 ] ]; D3 := Mat[ [ c[6], c[5], c[4], c[3], c[2], c[1], 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, c[6], 0, c[5], c[4], 0, c[3], c[2], c[1], 0, 0, 0, 0, 0], [0, c[6], 0, c[5], c[4], 0, c[3], c[2], c[1], 0, 0, 0, 0, 0, 0], [0, 0, 0, c[6], 0, 0, c[5], c[4], 0, 0, c[3], c[2], c[1], 0, 0], [0, 0, 0, 0, c[6], 0, 0, c[5], c[4], 0, 0, c[3], c[2], c[1], 0], [0, 0, 0, 0, 0, c[6], 0, 0, c[5], c[4], 0, 0, c[3], c[2], c[1]], [0, 0, 0, a[6], 0, 0, a[5], a[4], 0, 0, a[3], a[2], a[1], 0, 0], [0, 0, 0, 0, a[6], 0, 0, a[5], a[4], 0, 0, a[3], a[2], a[1], 0], [0, a[6], 0, a[5], a[4], 0, a[3], a[2], a[1], 0, 0, 0, 0, 0, 0], [0, 0, a[6], 0, a[5], a[4], 0, a[3], a[2], a[1], 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, a[6], 0, 0, a[5], a[4], 0, 0, a[3], a[2], a[1]], [0, 0, 0, 0, 0, b[6], 0, 0, b[5], b[4], 0, 0, b[3], b[2], b[1]], [0, 0, b[6], 0, b[5], b[4], 0, b[3], b[2], b[1], 0, 0, 0, 0, 0], [0, b[6], 0, b[5], b[4], 0, b[3], b[2], b[1], 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, b[6], 0, 0, b[5], b[4], 0, 0, b[3], b[2], b[1], 0 ] ]; ______________________________________ Tests X and Y: can't be done in CoCoA.