#Data check by Apecs:
#Note; Apecs runs under MAPLE V  (not, e.g. Maple 8)

Qdjr:=[0, ndjr^2, 0, -72*ndjr, -64*ndjr^3-432]:
read sofar: ONEA:={seq(idjr[1],idjr=ONE)}:TWOA:={seq(idjr[1],idjr=TWO)}:
PTS:=array(1..200):for idjr to 200 do PTS[idjr]:=[idjr,[]]:od:
 for idjr in [op(ONE),op(TWO)]  do PTS[idjr[1]][2]:=idjr[2]:od:

read apecs:

for idjr from 4 to 200 do 
 conductr:=substring(ein(subs(ndjr=idjr,Qdjr))[2],2..-1):
 if member(idjr,ONEA) then App(trcw(PTS[idjr][2])):fi:
 if member(idjr,TWOA) then App(trcw(PTS[idjr][2][1])):App(trcw(PTS[idjr][2][2])):fi:
 Isog();
 ein(cat(`C`,conductr));RkNC(); ein(cat(`B`,conductr));RkNC(); ein(cat(`A`,conductr));RkNC(); 
od:

for idjr in MEST do ein(subs(ndjr=idjr[1],Qdjr)):Mest(idjr[2]): od:
for idjr in LSET do ein(subs(ndjr=idjr,Qdjr)):Rk(); od;

# Check ranks are right:
for idjr from 4 to 200 do ein(op(subs(ndjr=idjr,Qdjr))):lprint(idjr,nops(RR),r1,r4);Rk();od;
# Note: Shows uses of parity conj; 
#  repeat last line to get briefer summary of ranks.

# Check to make sure the advertised points really do make a basis:
for idjr in ONE do ein(op(subs(ndjr=idjr[1],Qdjr))):Expr(trcw(idjr[2])):od:
for idjr in TWO do ein(op(subs(ndjr=idjr[1],Qdjr))):Expr(trcw(idjr[2][1])):Expr(trcw(idjr[2][2])):lprint(idjr[1]):od:

# Look for points in original coordinates with max(|x|,|y|,|z|)<10^20:
sdjr:=[-1/2*(ndjr*X+36-Y)/(3*X+4*ndjr^2), -1/2*(ndjr*X+36+Y)/(3*X+4*ndjr^2),1]:
#
for idjr in ONE do ein(op(subs(ndjr=idjr[1],Qdjr))):lprint(idjr[1]):
 for jdjr to 10 do XYdjr:=trwc(mult(jdjr,RR[1])):
 subs({X=%[1],Y=%[2],ndjr=idjr[1]},sdjr):sort(expand(%*denom(%[2]))):
 if abs(%[1])<10^20 and abs(%[2])<10^20 then lprint(` `,jdjr,%):fi:od:
od:
#
for idjr in TWO do ein(op(subs(ndjr=idjr[1],Qdjr))):lprint(idjr[1]):
 for jdjr to 8 do for kdjr from -8 to 8 do
  XYdjr:=trwc(eadd(mult(jdjr,RR[1]),mult(kdjr,RR[2]))):
  subs({X=%[1],Y=%[2],ndjr=idjr[1]},sdjr):sort(expand(%*denom(%[2]))):
  if abs(%[1])<10^20 and abs(%[2])<10^20 then lprint(` `,jdjr,kdjr,%):fi:
 od:od:
 for kdjr to 8 do
  XYdjr:=trwc(mult(kdjr,RR[2])):
  subs({X=%[1],Y=%[2],ndjr=idjr[1]},sdjr):sort(expand(%*denom(%[2]))):
  if abs(%[1])<10^20 and abs(%[2])<10^20 then lprint(` `,0,kdjr,%):fi:
 od:
od:
#
#Warning: this misses the generators if they themselves are large!

#The rank-2 ones will likely be way out of sorted order. Probably should
#do something like this (not tested):
#sz:=proc(a,b) length(a)<length(b):end: #boolean function: is a shorter than b?
#Start with SOL:=[]:  replace lprint(...) with SOL:=[op(SOL),[...]]: 
#Then end with  
#  SOL:=sort(SOL,sz): for kdjr in SOL do lprint(kdjr): od: