"""Recompute all eighteen E7 boundary coefficient kernels over Q.

This checks uniqueness on the displayed support sets. The fact that these sets
bound the intrinsic expansions is the separate geometric/support calculation.
"""
from pathlib import Path
import json
namespace={}
exec(Path(__file__).with_name('e7_divisors.py').read_text().split('func=[]')[0],namespace)
s=namespace['s'];v=namespace['v'];W=namespace['W'];first=namespace['first']
F={}
for I,expr in [(namespace['I1'],first[0]),(namespace['I2'],first[1]),(namespace['I3'],first[2]),(namespace['I4'],first[3])]:
 num=s.expand(expr*s.prod(v[j-1] for j in I))
 for i in I:F[i-1]=num
for i,expr in zip([2,3,4,8,9,10],first[4:]):F[i-1]=s.expand(expr*v[i-1])
def exponent(term):return tuple(int(term.as_powers_dict().get(x,0)) for x in v)
records=[]
for j,expr in enumerate(W):
 expr=s.expand(expr);mons=[exponent(t) for t in expr.as_ordered_terms()]
 assert len(set(mons))==len(mons)
 assert all(s.cancel(t/s.prod(x**a for x,a in zip(v,m)))==1 for t,m in zip(expr.as_ordered_terms(),mons))
 rows={}
 for i in range(20):
  terms=s.expand(F[i]).as_ordered_terms();assert len(terms)==2
  aa,bb=map(exponent,terms);delta=tuple(b-a for a,b in zip(aa,bb))
  pivot=next(k for k,d in enumerate(delta) if abs(d)==1)
  for t,m in enumerate(mons):
   if m[i]>=0:continue
   assert m[i]==-1,(j,i,m[i])
   q=m[pivot]*delta[pivot]
   residue=tuple(m[k]-q*delta[k] for k in range(20))
   key=(i,residue)
   rows.setdefault(key,[0]*len(mons))[t]+=1 if q%2==0 else -1
 M=s.Matrix(list(rows.values())) if rows else s.zeros(0,len(mons))
 assert M.rank()==len(mons)-1,(j,M.shape,M.rank())
 assert M*s.ones(len(mons),1)==s.zeros(M.rows,1)
 if len(mons)>1:
  _,I=M.T.rref();I=list(I);_,J=M[I,:].rref();J=list(J)
  det=M[I,J].det();assert abs(det)==1
 else:I=[];J=[];det=1
 records.append({'boundary':j,'support':[list(m) for m in mons], 'rows':[[int(c) for c in row] for row in M.tolist()],'rank':int(M.rank()), 'independent_rows':I,'minor_columns':J,'minor':int(det)})
 print('W'+str(j),'support',len(mons),'rank',M.rank(),'minor',det,flush=True)
Path(__file__).with_name('e7_boundary_certificates.json').write_text(json.dumps({'boundary_cases':records},indent=2))
print('PASS: eighteen normalized coefficient-one kernels.')