Equation 677 Database

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Magma 2f9657895c93…

magma 2f9657895c93
Size
181
Isomorphism class hash
2f9657895c93273cfaf7753200a41d127846a5b515e97517c07bf79b308a99c1
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:26:38
Display reorder
0,1,70,121,9,143,46,109,57,101,124,44,39,110,162,84,11,4,26,40,38,20,28,170,129,89,176,99,69,112,153,135,114,134,12,165,29,100,161,48,65,92,23,37,158,163,105,90,175,2,68,75,87,113,173,137,118,78,32,82,147,159,59,157,62,131,141,125,67,83,73,120,17,117,19,24,140,178,136,60,79,7,55,144,133,126,171,86,179,47,8,18,95,156,34,123,106,3,42,152,10,167,76,56,77,22,54,127,41,88,146,71,15,154,160,96,98,149,145,166,142,21,52,97,102,66,43,115,51,104,85,164,63,128,155,31,169,107,6,151,61,111,130,138,172,150,36,50,35,148,139,91,45,122,13,132,5,116,180,58,177,74,168,64,103,33,81,25,93,108,94,27,16,80,72,53,119,30,174,49,14 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) = 139·d when d is a quadratic residue mod 181, and f(d) = 176·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