Equation 677 Database

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Magma f7d15e60b5af…

magma f7d15e60b5af
Size
655
Isomorphism class hash
f7d15e60b5af8d42c59d7add8a648ff9aaa19763bd844467b1536a65b1dc1cd1
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Submitted by
omegaestable
Submitted at
2026-08-17 04:08:16
Display reorder
652,399,398,396,397,653,444,447,446,445,606,108,109,111,110,589,185,186,187,184,591,244,245,247,246,626,20,22,23,21,536,423,420,421,422,578,411,409,408,410,600,78,77,76,79,588,180,183,182,181,608,442,440,441,443,582,94,93,92,95,564,0,1,3,2,629,322,323,320,321,647,206,204,205,207,543,393,395,394,392,651,401,400,402,403,535,257,259,256,258,643,141,143,142,140,601,82,81,83,80,561,278,279,277,276,526,522,520,521,523,524,514,512,515,513,541,191,190,189,188,586,150,148,151,149,587,153,155,152,154,553,28,30,31,29,528,415,412,413,414,620,369,371,370,368,531,483,482,480,481,567,67,64,65,66,558,289,291,290,288,619,160,163,162,161,563,492,495,493,494,595,235,232,234,233,579,406,404,405,407,574,308,311,310,309,547,45,47,46,44,544,330,329,328,331,603,470,471,468,469,557,262,260,261,263,542,391,390,389,388,617,275,274,273,272,551,55,53,52,54,559,287,285,284,286,645,119,116,118,117,598,71,69,70,68,604,384,386,387,385,594,230,229,228,231,642,145,147,144,146,605,381,382,380,383,537,426,424,425,427,634,360,361,363,362,571,465,464,467,466,648,375,372,374,373,570,460,463,462,461,546,49,48,50,51,525,510,511,509,508,625,197,199,198,196,638,453,452,454,455,568,169,171,170,168,640,102,100,101,103,549,339,337,338,336,545,327,325,324,326,556,267,265,266,264,585,342,341,340,343,599,72,73,74,75,627,18,16,17,19,576,129,131,130,128,649,377,378,376,379,630,172,174,175,173,637,349,350,351,348,550,59,58,56,57,527,517,519,516,518,581,90,91,88,89,631,176,179,177,178,532,39,37,38,36,613,491,489,490,488,654,25,24,27,26,548,333,332,334,335,597,132,134,135,133,566,62,60,61,63,646,211,209,208,210,592,8,10,9,11,615,293,292,295,294,572,216,217,219,218,565,4,6,7,5,584,347,344,345,346,641,107,106,105,104,562,496,497,499,498,534,254,252,255,253,650,448,450,451,449,621,367,364,366,365,610,307,305,304,306,614,299,296,297,298,575,314,315,313,312,633,435,434,432,433,573,214,215,212,213,560,280,281,283,282,590,250,248,249,251,611,302,300,301,303,635,356,359,358,357,583,99,96,97,98,636,353,355,354,352,569,165,164,167,166,602,474,472,475,473,540,193,194,195,192,577,124,126,127,125,529,418,417,416,419,539,503,500,501,502,533,43,40,41,42,580,86,84,87,85,624,200,202,203,201,616,269,268,270,271,552,33,35,34,32,607,113,114,115,112,622,243,241,240,242,538,505,506,504,507,609,438,436,439,437,612,486,485,484,487,639,459,458,457,456,644,120,122,121,123,530,476,478,479,477,628,316,318,319,317,554,220,221,223,222,623,239,236,237,238,632,430,428,431,429,596,136,139,137,138,555,226,227,225,224,593,12,14,15,13,618,156,158,159,157 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Carrier: F_131 x F_5, encoded by 5*x+u. QR/NQR fiber extension. Base operation on F_131: x o y = 54x + 78y (mod 131), where beta=53 is a primitive 5th root and both -1 and beta+1 are quadratic non-residues. For d=y-x: the fiber law is 2u+4v (mod 5) when d=0, right projection v when d is a nonzero quadratic residue, and -u-v (mod 5) when d is a non-residue. Direct check of the 655x655 table: Eq 677 and Eq 255 hold; fully idempotent; left-cancellative; not right-cancellative; nonmedial. Right-cancellation witness: 10*0=540=11*0. Medial witness: (0*0)*(1*5)=290, while (0*1)*(0*5)=291. This is not a direct product: the fiber operation depends on the QR/NQR class of the base difference.

last edited by omegaestable at 2026-08-17 04:08:23 · history