Equation 677 Database

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Magma 8c3de954cbb4…

magma 8c3de954cbb4
Size
181
Isomorphism class hash
8c3de954cbb4dda8ba3c3bc092489f3cdba76d02b158e6348d849ae74f6721e0
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:26:36
Display reorder
0,1,148,139,27,94,166,40,106,151,14,108,25,104,48,83,85,105,127,29,17,64,129,5,165,55,161,115,144,112,155,51,80,171,73,59,7,82,156,57,22,46,130,21,2,119,169,50,88,67,164,128,125,132,172,103,180,43,69,35,49,31,61,170,146,117,66,52,111,15,33,122,16,160,98,140,116,162,176,68,138,118,97,3,86,6,58,158,62,114,32,167,23,126,30,36,143,141,124,44,10,8,20,93,37,100,63,152,133,81,90,110,109,177,75,34,19,77,39,154,134,41,168,45,76,60,120,70,175,38,149,4,56,71,89,47,42,9,11,84,78,157,79,12,92,87,95,153,145,150,18,137,54,136,142,26,24,102,123,147,174,159,113,91,107,72,173,53,163,179,121,65,101,28,96,99,135,13,131,178,74 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) = 56·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 20:01:20 · history