"""Verify the saved Freudenthal rank certificate using exact rational arithmetic."""
from fractions import Fraction
from pathlib import Path
import json

def require(value, message):
    if not value:
        raise AssertionError(message)

def row(data):
    return {(i,j): Fraction(c) for i,j,c in data}

def linear_combination(data, coeffs):
    out={}
    for i,c in coeffs:
        c=Fraction(c)
        for m,a in data[i].items():
            out[m]=out.get(m,Fraction(0))+c*a
            if not out[m]:
                del out[m]
    return out

p=Path(__file__).with_name('freudenthal_quadric_rank_certificate.json')
d=json.loads(p.read_text())
a=[row(r) for r in d['original_rows']]
b=[row(r) for r in d['echelon_rows']]
require(len(a)==144 and len(b)==133,'Wrong matrix dimensions')
require(len({min(r) for r in b})==133,'Repeated pivot')
require(all(r[min(r)]==1 for r in b),'Unnormalized pivot')
for r,c in zip(b,d['echelon_from_original']):
    require(r==linear_combination(a,c),'Incorrect forward span identity')
for r,c in zip(a,d['original_from_echelon']):
    require(r==linear_combination(b,c),'Incorrect reverse span identity')
from check_freudenthal_quadrics import rows
require(a==rows(),'Certificate does not match the printed cyclic relations')
print('PASS: rank 133; 133 forward and 144 reverse exact span identities.')