"""Check C_1 = -Delta_D^s exactly, coefficient by coefficient, at two points."""
import itertools
import os
import sys

sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))

import sympy as sp
from grass import G
from casimir import casimir, B, F, tB, tF


def radial_laplacian(f):
    d = B - F
    p = B**2 - 1
    q = 1 - F**2
    return (sp.diff(p * sp.diff(f, B), B)
            + sp.diff(q * sp.diff(f, F), F)
            - 2 * p / d * sp.diff(f, B)
            + 2 * q / d * sp.diff(f, F))


points = [
    {B: sp.Rational(23, 10), F: sp.Rational(3, 10),
     tB: sp.Rational(7, 10), tF: sp.Rational(-4, 10)},
    {B: sp.Rational(51, 10), F: sp.Rational(-7, 10),
     tB: sp.Rational(1, 3), tF: sp.Rational(2)},
]
monomials = [mono for degree in range(5)
             for mono in itertools.combinations(range(1, 5), degree)]
checked = 0
for f in [B, F, B**2, B * F, F**2, sp.exp(B) * sp.cos(F)]:
    # casimir.py returns -2*C_1, while the manuscript uses C_1 = -Delta_D^s.
    actual = casimir(G.c(f)) * sp.Rational(-1, 2)
    expected = -radial_laplacian(f)
    for point in points:
        for mono in monomials:
            difference = actual.coeff(mono) - (expected if not mono else 0)
            residual = sp.simplify(sp.sympify(difference).subs(point))
            assert residual == 0, (f, point, mono, residual)
            checked += 1
    print(f"ok {f}: C_1 = -Delta_D^s at both points, all 16 coefficients")
print(f"passed {checked} exact coefficient checks in 12 function-point pairs")