Equation 677 Database

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Magma 7580f29f9f1b…

magma 7580f29f9f1b
Size
181
Isomorphism class hash
7580f29f9f1b81ce8cffad189b0e4037b0ea5d85764cbbe1e6876ffe003b584a
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:26:34
Display reorder
0,1,14,17,78,138,21,75,168,119,62,96,150,61,51,139,120,18,68,172,41,171,72,16,175,84,146,90,5,170,177,31,131,22,166,106,124,59,26,4,24,174,108,159,134,34,112,162,100,145,117,157,58,179,114,153,129,48,73,50,35,169,151,121,46,176,55,132,125,74,135,101,15,130,85,3,126,65,127,44,87,165,94,27,37,105,141,38,164,123,6,45,93,9,86,83,70,69,148,110,80,47,13,39,104,67,32,97,140,173,66,91,81,107,54,160,163,158,154,7,122,133,102,53,49,77,88,2,40,111,89,98,92,161,57,10,52,99,60,180,36,144,28,79,33,116,137,143,20,156,64,71,19,8,25,29,147,178,167,76,109,113,118,115,30,152,12,136,42,128,95,142,56,43,149,63,82,23,11,155,103 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-181 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. Tao Type II piecewise-linear construction on F_181 (181 prime): x ◇ y = x + f(y − x) in F_181, where f(0) = 0, f(d) = 139·d when d is a quadratic residue mod 181, and f(d) = 122·d when d is a non-residue. So the multiplier on the difference y − x depends only on its QR/NQR class. The display reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-181 magma automorphism τ (the hidden additive translation by 1 in F_181), making the magma fully translation-invariant in the rendered table: every row is a horizontal shift of row 0. [text written by Claude]

last edited by dwrensha at 2026-05-14 20:01:20 · history