%%%%%%%%%%%%%%%%%
GuessM.txt
%%%%%%%%%%%%%%%%


Help:=proc(): print(`GuessM(F)`):end:

#GuessM(F): inputs a list of integer-tuples of
#the same length (let's call it k) outputs
#a k by k matrix (let's call it M) such that
#F[i+1]=M.F[i]
GuessM:=proc(F) local k,var,eq,i,j,x,X,sol:

k:=nops(F[1]):

if not {seq(nops(F[i]),i=1..nops(F))}={k} then
 ERROR(`bad input`):
fi:

if nops(F)<k^2+3 then
  ERROR(`F too short`):
fi:

var:={seq(seq(x[i][j],j=1..k),i=1..k)}:

#seq(x[i][j]*V[j]=b[i],j=1..k)

eq:=
{seq(seq(
add(x[i][j]*F[i1][j],j=1..k)=F[i1+1][j],i=1..k)
,i1=1..nops(F)-1)}:

X:=[seq([seq(x[i][j],j=1..k)],i=1..k)]:
sol:=solve(eq,var):


if sol=NULL then
 print(`Sorry, you did not beat Andrew W. yet!`):
 RETURN(FAIL):
 else
  print(`Yea, you have a beautiful new proof of FLT for n=3`):
 RETURN(subs(sol,X)):
fi:

end: