Help:=proc(): print(`CF(a), CF1(a,K), IsPeriodic(L,p)`): 
print(` CFtoNu(L),CF1a(a,L), FindPeriod(L) ,GuessUP(L)`):
end:


#CF(a): inputs a positive rational number and outputs
#the list of terms in the (simple)-continued fraction
CF:=proc(a) local b,c,L1:

if a<0 or not type (a,rational)  then
 ERROR(`We are followers of Pythagors`):
fi:

if type(a,integer) then
   RETURN([a]):
fi:

b:=trunc(a):

c:=1/(a-b):

L1:=CF(c):

[b,op(L1)]:



end:


Digits:=100:



#IsPeriodicP(L,p): inputs a list L and a pos. integer p
#and outputs true if L is periodic of period p
#starting at the beginning
IsPeriodicP:=proc(L,p)  local i:

 for i from 1 to nops(L)-p do
   if L[i]<>L[i+p] then
      RETURN(false):
    fi:
od:
true:
end:











#CFtoNu(L): inputs a list of integers and outputs
#the rational number that is represents.
CFtoNu:=proc(L):
if nops(L)=1 then
   L[1]:
else
 L[1]+1/CFtoNu([op(2..nops(L),L)]):
fi:
end:

#AreWeDone(a,L): Given a real number a and a current
#continued fraction appx. L, either returns L
#(if the difference between a and "L" is less than 1/10^(Digits-10)
#or a better L
AreWeDone:=proc(a,L)
if abs(a-CFtoNu(L))<1/10^(Digits-10) then
  true:
else
  false:
fi:


end:



CF1:=proc(a) local a1, b, L:
a1:=evalf(a):
b:=trunc(a1):

L:=[b]:

while not AreWeDone(a,L) do

a1:=1/(a1-b):
b:=trunc(a1):
L:=[op(L),b]:

od:

L:


end:

#FindPeriod(L): inputs a list L and outputs
#its shortest preiod
FindPeriod:=proc(L) local p:

for p from 1 to trunc(nops(L)/2) do
  
 if IsPeriodicP(L,p) then
   RETURN([op(1..p,L)]):
  fi:

od:

FAIL:

end:


#GuessUP(L): Inputs a list of integers L and outputs
#two lists: L1, and L2, such that L=L1(L2)*
GuessUP:=proc(L) local L1, L2,i:

for i from 1 to trunc(nops(L)/2) do
L1:=[op(1..i,L)]:
L2:=[op(i+1..nops(L),L)]:

L2:=FindPeriod(L2):
if L2<>FAIL then
 RETURN(L1,L2):
fi:
od:

FAIL:

end: