import sys, os; sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
import sympy as sp, random, itertools
from grass import *
from casimir import casimir, B, F, tB, tF
I = sp.I
p = B**2 - 1; q = 1 - F**2; d = B - F
sq = sp.sqrt(p*q)
ph = sp.exp(I*(tB - tF))
kap = {(1, 2): 2*(B*F - 1)/d**2, (3, 4): 2*(B*F - 1)/d**2,
       (1, 4): 2*I*sq*ph/d**2, (2, 3): -2*I*sq/ph/d**2}
cpart = {1: (G.gen(2), sp.Rational(1, 2)*I), 2: (G.gen(1), sp.Rational(1, 2)*I),
         3: (G.gen(4), -sp.Rational(1, 2)*I), 4: (G.gen(3), -sp.Rational(1, 2)*I)}
def Theta(f): return f.diff(tB) + f.diff(tF)
def D(a, f):
    xi, c = cpart[a]
    return f.dleft(a) + (xi * Theta(f)) * c
def C0(f):
    return (f.diff(B) * p).diff(B) + (f.diff(F) * q).diff(F) + f.diff(B) * (-2*p/d) + f.diff(F) * (2*q/d)
def Lhyp(f):
    out = C0(f) + f.diff(tB).diff(tB) * (1/p) + f.diff(tF).diff(tF) * (1/q)
    for (a, b), k in kap.items():
        out = out + (D(b, D(a, f)) - D(a, D(b, f))) * (k/2)
    return out
def Ltrue(f): return casimir(f) * sp.Rational(1, 2)
random.seed(3)
pts = []
for _ in range(3):
    pts.append({B: sp.Rational(random.randint(11, 60), 10), F: sp.Rational(random.randint(-9, 9), 10),
                tB: sp.Rational(random.randint(-30, 30), 10), tF: sp.Rational(random.randint(-30, 30), 10)})
gens = [1, 2, 3, 4]
monos = [()] + [(a,) for a in gens] + list(itertools.combinations(gens, 2)) + list(itertools.combinations(gens, 3)) + [(1, 2, 3, 4)]
bodies = [B*F + F**2, sp.exp(I*tB)*B, sp.exp(-2*I*tF)*(1 + F)*B**2, sp.exp(I*(tB + tF))*sp.sqrt(1 - F**2), sp.cos(B)*sp.exp(I*tF), tB*F]
maxerr = 0; ntest = 0
for mono in monos:
    for body in random.sample(bodies, 3):
        f = G({mono: body})
        diff = Ltrue(f) - Lhyp(f)
        for pt in pts:
            for k, v in diff.d.items():
                e = abs(complex(sp.N(v.subs(pt), 30)))
                maxerr = max(maxerr, e)
        ntest += 1
print("tested", ntest, "functions at", len(pts), "points; max |L_true f - L_hyp f| =", maxerr)