Equation 677 Database

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Magma 2c0a619ddc1b…

magma 2c0a619ddc1b
Size
181
Isomorphism class hash
2c0a619ddc1b123a88bf06021406aa6195ec1abb3f4373825c7df4f9324856fd
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:26:32
Display reorder
0,1,155,58,118,15,38,176,57,93,91,22,171,160,68,168,14,113,143,179,37,28,86,66,139,127,124,99,56,95,145,101,146,100,140,11,144,169,172,94,21,41,73,82,134,98,158,59,123,23,115,126,67,136,138,12,131,83,60,163,13,110,46,45,166,149,54,44,106,178,70,129,142,48,33,112,36,19,31,53,27,167,111,43,85,50,6,159,65,4,170,141,102,39,128,69,90,87,161,92,177,119,74,105,152,175,61,47,55,71,34,32,148,7,117,165,108,75,62,35,154,63,180,18,109,80,17,30,153,120,162,52,103,77,79,26,10,2,16,130,107,150,29,164,132,137,116,42,135,24,173,84,147,96,125,49,20,114,51,5,40,88,156,122,72,8,76,64,81,157,78,3,97,174,25,133,151,89,9,104,121 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) = 122·d when d is a quadratic residue mod 181, and f(d) = 46·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