Commentary history a9267aade1a1 — Equation 677 Database

Commentary history

6 edits.

dwrensha · 2026-05-16 12:02:52

Linear magma over the ring Z/49Z: x ◇ y = 18x + 10y (mod 49). NOTE: Z/49Z is the ring of integers mod 49, NOT a field — since 49 = 7² is not prime, Z/49Z has zero divisors (e.g. 7·7 = 0 mod 49). The genuine field F_49 = GF(7²) exists as a separate object (and gives different size-49 Eq 677 magmas, e.g. magma#3d9ea61f); this construction uses ring arithmetic mod 49 instead. Coefficients (18, 10) satisfy the Eq 677 polynomial conditions over the ring Z/49Z. Size 49, not fully idempotent, right-cancellative. Companion to magma#bd9c4bf0 (also Z/49Z with coefficients (18, 8)). [text written by Claude]
dwrensha · 2026-05-16 11:52:41

Linear magma over the ring Z/49Z: x ◇ y = 18x + 10y (mod 49). NOTE: Z/49Z is the ring of integers mod 49, NOT a field — since 49 = 7^2 is not prime, Z/49Z has zero divisors (e.g. 7·7 = 0 mod 49). The genuine field F_49 = GF(7^2) exists as a separate object but is not used here; this construction uses ring arithmetic mod 49. [text written by Claude]
dwrensha · 2026-04-29 17:22:26

Linear magma over Z/49Z (the prime field F_49): x ◇ y = 18x + 10y (mod 49).
dwrensha · 2026-04-29 17:19:24

Linear magma over Z/49Z (the prime field F_49): x ◇ y = 18x + 10y (mod 49).
dwrensha · 2026-04-29 13:44:00

Linear magma over Z/49Z (the prime field F_49): x ◇ y = (18,10).
dwrensha · 2026-04-29 13:28:37

Linear over Z/49Z: x◇y = (18,10).