import sys, os; sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
import sympy as sp, random, itertools
from grass import *
from verify_op import Lhyp, C0, B, F, tB, tF
I = sp.I
def Lang(f): return Lhyp(f) - C0(f)
random.seed(5)
gens = [1, 2, 3, 4]
allmonos = [()] + [m for r in range(1, 5) for m in itertools.combinations(gens, r)]
def rand_f():
    f = G()
    for mono in random.sample(allmonos, 6):
        a, b = random.randint(-2, 2), random.randint(-2, 2)
        f = f + G({mono: sp.exp(I*a*tB + I*b*tF) * sp.Rational(random.randint(-5, 5), 3)})
    return f
pt = {B: sp.Rational(27, 10), F: sp.Rational(-2, 5)}
worst = 0
for trial in range(8):
    f, g = rand_f(), rand_f()
    top = (f * Lang(g) - Lang(f) * g).coeff((1, 2, 3, 4))
    # average over the torus: integrate exp(i(a tB + b tF)) terms
    top = sp.expand(sp.expand(top).subs(pt))
    avg = sp.integrate(sp.integrate(top, (tB, 0, 2*sp.pi)), (tF, 0, 2*sp.pi)) / (4*sp.pi**2)
    worst = max(worst, abs(complex(sp.N(avg))))
print("max |torus average of [f L_ang g - (L_ang f) g]_top| over 8 random pairs:", worst)