#C18.txt March 26, 2018, ExpMath (RU)
Help:=proc(): print(`RatToCF(x),NuToCF(x,n) , EvalCF(L), SymCF(a,n) `):end:

#RatToCF(x): converts a pos. rational number x into a continued fraction
RatToCF:=proc(x) local a,x1:
 if not (x>0 and type(x,rational)) then
  RETURN(FAIL):
 fi:

a:=trunc(x):

if a=x then
  RETURN([a]):
fi:

x1:=1/(x-a):

[a, op(RatToCF(x1))]:


end:


#NuToCF(x,n): appx. a pos. number x into a continued fraction with <=n terms
NuToCF:=proc(x,n) local a,x1:

 
 if not (x>0 and type(n,integer) and n>=1) then
  RETURN(FAIL):
 fi:


a:=trunc(x):

if n=1 then
  RETURN([a]):
fi:
  
if x=a then
  RETURN([a]):
fi:

x1:=1/(x-a):

[a,op(NuToCF(x1,n-1))]:
end:

#EvalCF(L): evaluates the simple continued 
EvalCF:=proc(L) local L1,x:
if not (type(L,list) and nops(L)>0) then
  RETURN(FAIL):
fi:

if nops(L)=1 then
 RETURN(L[1]):
fi:

L1:=[op(2..nops(L),L)]:

x:=EvalCF(L1):

normal(L[1]+1/x):
end:

#SymCF: the rational function of a[1], ..., a[n] describing EvalCF([a[1], ..., a[n]]):
#the numerator followed by the denominator
SymCF:=proc(a,n) local i,yonah:
yonah:=EvalCF([seq(a[i],i=1..n)]):

numer(yonah),denom(yonah):
end:

#The a-analog of the Fibonacci numbers, the numerator
P:=proc(a,n) option remember:

if n=0 then
 1:
elif n=1 then
  a[1]:
else
expand(a[n]*P(a,n-1)+ P(a,n-2)):
 end:


Q:=proc(a,n)
end: