#C4.txt: Feb. 1, 2016 ExpMath (Spring 2016) (no relation to explosive)
Help:=proc():  print(` BP(K), Cr(f) , LtoN(L), BAr(f), C(x,N) , BA(x,N) `): end:

Digits:=1000:

#BP(K): the first (prob.) prime after K
BP:=proc(K) local i:

for i from K+1 while not isprime(i) do od:
i:
end:

#Cr(f): Home made continued fraction of a positive fraction f
Cr:=proc(f)  if type(f,integer) then [f] else [trunc(f), op(Cr(1/(f-trunc(f))))] fi end:

#LtoN(L): inpts
LtoN:=proc(L)  if nops(L)=1 then  L[1] else L[1]+ 1/LtoN(L[2..nops(L)]) fi end:

#BAr(f): the sequence of BEST appx. to f with smaller denominators
BAr:=proc(f) local L,i:
L:=Cr(f):

[seq(LtoN(L[1..i]),i=1..nops(L))]:

end:

#C(x,N): Home made first N terms of the continued fraction of any pos. real number x
C:=proc(x,N) local y:

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

y:=trunc(evalf(x)):
if N=1 then
   [y]:
else
 
[y, op(C(1/(x-y)     , N-1))  ]:
fi:



end:
  

#BA(x,N): the sequence of BEST rational (aka Diophantine) appx. to  real number x
BA:=proc(x,N) local L,i:

L:=C(x,N):

[seq(LtoN(L[1..i]),i=1..N)]:

end: