"""Exact check that the vector fields of casimir.py reproduce [A, Q] on all sixteen entries
of Q (e:sigma-action), for all sixteen elementary supermatrices A = E_ij (with the auxiliary
odd generator for odd E_ij).  Same rational substitution as verify_op_exact.py."""
import sys, os; sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
import sympy as sp, time
from grass import *
from casimir import basis, apply_v, B, F, tB, tF
from chart import Q
from verify_op_exact import ratsub
ETA = 5
t0 = time.time(); bad = 0; n = 0
for (ij, p, v) in basis:
    i, j = ij
    A = mzero(4)
    A[i][j] = G.c(1) if p == 0 else G.gen(ETA)
    dQ = msub(mmul(A, Q), mmul(Q, A))
    for k in range(4):
        for l in range(4):
            lhs = apply_v(v, Q[k][l]) - dQ[k][l]
            for mono, c in lhs.d.items():
                r = sp.expand(sp.numer(sp.together(ratsub(c))))
                if r != 0:
                    bad += 1; print('NONZERO', ij, (k, l), mono, r)
            n += 1
print('checked', n, 'entries;', bad, 'nonzero coefficients;', round(time.time() - t0, 1), 's')