#GuessPol1(L,n,d): inputs a list of pairs [[input,output], ...] a variable name n
#and a pos. integer d, outputs a polynomial of degree d f such that f(input)=output
GuessPol1:=proc(L,n,d) local a,i,f,var,eq:

if nops(L)<d+1 then
 print(`underdetermined make`, d, `smaller . `):
  RETURN(FAIL):
fi:
#f:=a[0]+a[1]*n+...+a[d]*n^d:
var:={ seq(a[i],i=0..d)}:
f:=add(a[i]*n^i,i=0..d):
# f(L[i][1])=L[i][2]

eq:={seq( subs(n=L[i][1], f)=L[i][2], i=1..nops(L))}:

var:=solve(eq,var):

if var=NULL then
  RETURN(FAIL):
fi:

subs(var,f):

end:

#GuessPol(L,n): inputs a list of pairs [input,output] and tries to guess
#a polynomial of degree <=nops(L)-3
GuessPol:=proc(L,n) local f,d:

for d from 0 to nops(L)-3 do
 f:=GuessPol1([op(1..d+3,L)] ,n,d):
  if f<>FAIL then
   f:=GuessPol1(L,n,d):
     if f<>FAIL then
       RETURN(f):
     fi:
   fi:
od:

print(`Too bad, it did not work out, generate more date, or bad news, it is not a polynomial`):
FAIL:

end: