Equation 677 Database

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Magma 3beeddeed1cd…

magma 3beeddeed1cd
Size
181
Isomorphism class hash
3beeddeed1cde1c1424a9062aa9dd6ab2a12b2c89b1b1f58fabb13ec511eb9fb
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:26:49
Display reorder
0,1,103,33,32,109,80,168,135,44,39,137,157,118,56,40,123,52,69,164,115,6,136,91,54,89,51,66,122,12,174,30,17,64,38,141,22,53,26,88,50,158,48,85,35,4,29,166,92,172,143,108,21,110,98,163,113,159,82,179,124,154,167,37,149,62,126,111,146,114,3,76,9,55,27,129,112,63,175,116,58,20,77,176,104,75,31,140,49,169,170,43,177,93,119,121,90,84,99,165,81,73,78,125,10,142,19,150,127,94,97,162,151,46,130,60,11,47,42,160,15,153,161,105,173,57,71,134,171,5,72,144,145,41,155,128,139,180,79,68,18,101,7,87,132,178,34,74,131,117,36,45,24,16,152,23,102,107,148,120,70,106,14,25,86,2,67,13,156,83,147,65,138,133,95,28,8,96,100,61,59 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-181 idempotent non-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) = 48·d when d is a quadratic residue mod 181, and f(d) = 139·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 20:01:21 · history