Equation 677 Database

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Magma ddf8aaa4de5b…

magma ddf8aaa4de5b
Size
181
Isomorphism class hash
ddf8aaa4de5b63c69b5e463ffef52f398538147a138758661538cddcf5aacec7
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:26:51
Display reorder
0,1,164,146,68,97,110,34,40,170,61,86,12,38,46,135,169,39,18,70,55,127,20,5,138,109,160,84,96,81,148,49,129,150,145,177,7,163,120,143,9,53,21,17,2,73,116,48,175,133,166,19,79,23,122,37,180,28,167,67,47,63,121,178,130,80,161,50,89,62,65,76,54,98,165,118,85,132,100,105,174,72,103,3,141,6,115,154,93,83,64,172,10,26,71,30,124,90,78,29,57,8,16,125,31,43,155,142,24,101,119,88,87,162,179,66,15,123,33,176,25,35,144,52,151,149,74,139,128,32,136,4,171,111,147,45,27,56,58,107,95,92,157,59,153,113,159,114,158,108,14,112,137,140,152,13,11,36,77,102,156,126,82,91,41,173,94,51,104,106,75,99,44,69,131,42,168,60,22,134,117 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) = 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 20:01:21 · history