[OK] A1 Farey step w(a)w(b) = w(c)(1+w(a)+w(b))
[OK] A2 w'(s) = q^2 E/(E-1)^2
[OK] A2 w''(s) = q^3 E (q(E+1)-2(E-1))/(E-1)^3
[OK] A3 Psi = q^2 E Omega/((E-1)^4 x (X-1))  (Omega bracket form)
[OK] A3 1+w(s)+w(rho) = (E(X-1)+(E-1))/((E-1)(X-1))
[OK] A3 w'+(s+rho)w'' = q^2 E P/(x(E-1)^3)
[OK] A3 (s+rho)w'^2 = q^3(q+x)E^2/(x(E-1)^4)
[OK] A4 P second form
[OK] A4 P - q(q+x) form
[OK] A4 Omega = E(X-1)(P-q(q+x)) + (E-1)P
[OK] A4 Omega = x(X-1)U1 + (X-1)U2 + xU3 + U4
[OK] A4 U1 expanded
[OK] A4 U2 expanded
[OK] A4 U3 expanded
[OK] A4 U4 expanded
[OK] A5 h identity
[OK] A5 L + s0 s3 = (s1+s3)(s2+s0)
Omega has 12 monomials in (q,x,E,X)
[OK] A6 no negative coefficient m! n! [q^m x^n]Omega, m,n <= 200
[OK] A6 closed forms of m![q^m]omega_n agree for m,n <= 200
[OK] A6 closed forms for m![q^m]U_1..U_4 agree, m <= 200
[OK] A6 [q^5 x^0]Omega = 20/5! = 1/6
lowest-order nonzero terms (total degree, m, n, coefficient):
    (5, 2, 3, Fraction(1, 12))
    (5, 3, 2, Fraction(1, 3))
    (5, 4, 1, Fraction(5, 12))
    (5, 5, 0, Fraction(1, 6))
    (6, 2, 4, Fraction(1, 24))
    (6, 3, 3, Fraction(1, 4))
    (6, 4, 2, Fraction(13, 24))
    (6, 5, 1, Fraction(1, 2))
zero coefficients with 2<=m<=5, n<=3: [(2, 0), (2, 1), (2, 2), (3, 0), (3, 1), (4, 0)]
ALL PASSED   (0.3s)
