# End-to-end check of Lemma 3.1 with the actual integer digit columns (r=23, d=3, k=1440). No arguments.
import random, sys
sys.set_int_max_str_digits(0)
from field_encoding import Field, rows, k
r=23; F=Field(r,3)
M=4800*k*k*r**3; P=r*r*(r*M)
def isprime(n):
    for p in [2,3,5,7,11,13,17,19,23,29,31,37]:
        if n%p==0: return n==p
    d=n-1; s=0
    while d%2==0: d//=2; s+=1
    for a in [2,3,5,7,11,13,17,19,23,29,31,37]:
        x=pow(a,d,n)
        if x in (1,n-1): continue
        for _ in range(s-1):
            x=x*x%n
            if x==n-1: break
        else: return False
    return True
B2=600*k*k*r*r*M+1
while not isprime(B2): B2+=1
B=r*B2; assert B-1>=100*6*k*k*P and r*M<B2 and B2*r<=M*M//2
h=r*B**(k-1); tau=B**(k-1)//2
print("k",k,"log2 B",B.bit_length(),flush=True)
rnd=random.Random(7)
def column(xi):
    Pr=rows(F,xi); col=[]
    for i in range(3):
        val=0
        for u in reversed(range(k)):
            res=Pr[i].get(u,0)%r
            if i<2: dg=res if res else r
            else: dg=res+r*rnd.randrange(M) if res else r*rnd.randrange(1,M+1)
            val=val*B+dg
        col.append(val)
    return col
def det3(m):
    return (m[0][0]*(m[1][1]*m[2][2]-m[1][2]*m[2][1])-m[0][1]*(m[1][0]*m[2][2]-m[1][2]*m[2][0])+m[0][2]*(m[1][0]*m[2][1]-m[1][1]*m[2][0]))
fails=0
for t in range(6):
    xis=[[rnd.randrange(r) for _ in range(3)] for _ in range(3)]
    for x in xis:
        if not any(x): x[0]=1
    if t%3==2: xis[2]=xis[0][:]
    distinct=len({tuple(x) for x in xis})==3
    cols=[column(x) for x in xis]
    D=det3([[cols[j][i] for j in range(3)] for i in range(3)])%h; rep=min(D,h-D)
    J= rep<=tau; ok=(not J) if distinct else True; fails+= not ok
    print(t,"distinct" if distinct else "repeated","min|rep|/B**(k-1)=%.4f"%(rep/B**(k-1)),"J" if J else "-","OK" if ok else "FAIL",flush=True)
print("fails",fails,flush=True)