PASS alpha^2 + 3 alpha - 2 = 0 in F
PASS table: i^2 = -1
PASS table: j^2 = -3
PASS table: ij = k and ji = -k
PASS table is associative on the basis
PASS identity xi_a eta_0 = - eta_0 xi_b
PASS identity xi_b eta_0 = - eta_0 xi_c
PASS identity xi_c eta_0 =   eta_1 xi_a
PASS identity xi_a eta_1 =   eta_1 xi_c
PASS identity xi_b eta_1 =   eta_1 xi_b
PASS identity xi_c eta_1 =   eta_0 xi_a
PASS negative control: xi_a eta_0 = + eta_0 xi_b is FALSE
PASS negative control: xi_c eta_0 = eta_0 xi_a is FALSE
PASS negative control: xi_c eta_1 = eta_1 xi_a is FALSE
PASS trd xi_a = 0
PASS nrd xi_a = rho (algebra and formula)
PASS xi_a^2 = -rho (scalar)
PASS trd xi_b = 0
PASS nrd xi_b = rho (algebra and formula)
PASS xi_b^2 = -rho (scalar)
PASS trd xi_c = 0
PASS nrd xi_c = rho (algebra and formula)
PASS xi_c^2 = -rho (scalar)
PASS trd eta_0 = -6 alpha
PASS trd eta_1 = -12
PASS nrd eta_0 = 36(2 - alpha)
PASS nrd eta_1 = 36(2 - alpha)
PASS eta_1 = 6 (xi_b - 1)
trd(eta_0)^2/nrd(eta_0) = (Fraction(1, 2), Fraction(-1, 2))   trd(eta_1)^2/nrd(eta_1) = (Fraction(5, 2), Fraction(1, 2))   (pairs p + q alpha)
PASS trd(eta_0)^2/nrd(eta_0) = (1 - alpha)/2
PASS trd(eta_1)^2/nrd(eta_1) = (5 + alpha)/2
PASS the two values differ
PASS (2 - alpha)(1 - alpha) = 2 alpha^2
PASS (2 - alpha)(5 + alpha) = 8
PASS -2 is not a root of X^2+3X-2

SUMMARY r2_1_quaternions: 0 failed
