1/* Filename hill1.mac 2 3 *************************************************************** 4 * * 5 * <package name> * 6 * <functionality description> * 7 * * 8 * from: Computer Algebra in Applied Math. * 9 * by Rand (Pitman,1984) * 10 * Programmed by Richard Rand * 11 * These files are released to the public domain * 12 * * 13 *************************************************************** 14*/ /* 15(d4) This program generates truncated Hill's determinants 16 17 18for Mathieu's equation. To call it, type one of: 19 20 21 MAKEAEVEN(P) 22 23 24 or MAKEBEVEN(P) 25 26 27 or MAKEAODD(P) 28 29 30where P is the truncation size. 31 32*/ 33 34makeaeven(p):=(icaeven(),for k from 2 thru p do (w:eqeven(),v:u,u:w),u)$ 35makebeven(p):=(icbeven(),for k from 3 thru p do (w:eqeven(),v:u,u:w),u)$ 36makeaodd(p):=(icaodd(),for k from 3 thru p do (w:eqodd(),v:u,u:w),u)$ 37eqeven():=(d-k^2)*u-e^2/4*v$ 38eqodd():=(d-(2*k-1)^2/4)*u-e^2/4*v$ 39icaeven():=(u:d*(d-1)-e^2/2,v:d)$ 40icbeven():=(u:(d-1)*(d-4)-e^2/4,v:d-1)$ 41icaodd():=(u:(d-1/4+e/2)*(d-9/4)-e^2/4,v:d-1/4+e/2)$ 42