/*  

(d12) This program uses recursive functions to find 


the transition curves in Mathieu's equation.  To call it,


type:


                        TC()

*/


tc():=(input(),sign:1,find(),IF n > 0 THEN (sign:-1,find()))$
input():=(n:read("ENTER TRANSITION CURVE NUMBER N"),
      m:read("ENTER DEGREE OF TRUNCATION"))$
find():=(delta:n^2/4,for i thru m do delta:delta+d(i)*e^i,
     print("delta=",delta),print(" "))$
a(j,k):=IF j < 0 OR k < 0 THEN 0
   ELSE (IF j = 0 AND k = n THEN 1
	     ELSE (IF j = 0 THEN 0
		       ELSE (IF k = n THEN 0
				 ELSE (IF k = 0
					   THEN (-a(j-1,2)/2
					   -sum(d(i)*a(j-i,0),i,1,j))
					   /(n^2/4)
					   ELSE (-(a(j-1,k-2)
					   +a(j-1,k+2)+sign*a(j-1,2-k))
					   /2
					   -sum(d(i)*a(j-i,k),i,1,j))
					   /((n^2-k^2)/4)))))$

d(j):=IF n = 0 THEN -a(j-1,2)/2
   ELSE -(a(j-1,n-2)+a(j-1,n+2)+sign*a(j-1,2-n))/2$