/*

(d4) This program generates the transition curves in


Mathieu's equation via Hill's determinants.  Call it by


typing:


                       HILL()


NOTE: File HILL1.MAC must be loaded before calling HILL().

*/


hill():=(input(),
     IF evenp(n) THEN (findaeven(n,m,n+m),IF n > 0 THEN findbeven(n,m,n+m))
	 ELSE findaodd(n,m,n+m))$
input():=(n:read("ENTER TRANSITION CURVE NUMBER N"),
      m:read("ENTER DEGREE OF TRUNCATION"))$
findaeven(n,m,p):=(d:'d,det:expand(makeaeven(p)),d:n^2/4+k[2]*e^2,
	  for i from 2 step 2 thru m do
	      (loop(i),IF i < m THEN d:d+k[i+2]*e^(i+2)),print("delta=",d),
	  print(" "))$
findbeven(n,m,p):=(d:'d,det:expand(makebeven(p)),d:n^2/4+k[2]*e^2,
	  for i from 2 step 2 thru m do
	      (loop(i),IF i < m THEN d:d+k[i+2]*e^(i+2)),print("delta=",d),
	  print(" "))$
findaodd(n,m,p):=(d:'d,det:expand(makeaodd(p)),d:n^2/4+k[1]*e,
	 for i thru m do (loop(i),IF i < m THEN d:d+k[i+1]*e^(i+1)),
	 print("delta=",d),print(" "),print("delta=",ev(d,e:-e)),print(" "))$
loop(i):=d:ev(d,solve(taylor(ev(det),e,0,i),k[i]))$