import sys
from fractions import Fraction as F
from system import System, ERRDIMS
from hosts import proof_hosts
def exact_proj(t, hosts=None, order=("E3","E25","E2","b","a")):
    S=System(t,verbose=False); S.run(hosts if hosts is not None else proof_hosts(t))
    cols={}
    for r in S.rows:
        for c in r:
            if c[0]=="nu" and c not in cols: cols[c]=len(cols)
    N=len(cols); o=N
    for n in order:
        for i in range(ERRDIMS[n]): cols[("err",n,i)]=o+i
        o+=ERRDIMS[n]
    piv={}
    for r in S.rows:
        r={cols[c]:F(v) for c,v in r.items() if v!=0}
        while r:
            c=min(r)
            if c in piv:
                pr=piv[c]; f=r[c]
                for cc,vv in pr.items():
                    nv=r.get(cc,0)-f*vv
                    if nv: r[cc]=nv
                    else: r.pop(cc,None)
            else:
                inv=1/r[c]; piv[c]={cc:vv*inv for cc,vv in r.items()}; break
    npe=sum(1 for c in piv if c>=N)
    res={}
    start=N
    for j,n in enumerate(order):
        res["/".join(order[j:])]=(o-start)-sum(1 for c in piv if c>=start)
        start+=ERRDIMS[n]
    return res, len(S.reps), S.skipped
for tv in sys.argv[1:]:
    print(tv, exact_proj(F(tv)))