The main purpose of the Mathematica codes EIGENIND-SLP is to
compute the index or indices of a given approximate
eigenvalue of a self-adjoint Sturm-Liouville problem. The
boundary condition in the problem can be either separated or
coupled.

In addition to this README file, the codes consist of the
following 7 files:
  Phi-matrix-pc,
  Phi-matrix-rglr,
  a-b-in-computations,
  compare-angles,
  compute-indices-pc,
  compute-indices-rglr, and
  count-zeros,
with compute-indices-pc and compute-indices-rglr being the
main files. (After having down-loaded these files, please
remember to up-date, inside these files, the route in your
computer to these files.)

If the Sturm-Liouville problem has piece-wise constant
coefficient functions, then the index or indices can be
computed by calling the file compute-indices-pc. In this
case, the input has the following 9 items.
  npieces: number of pieces
     a[i]: end points of subintervals, with i running from
           0 to npieces
     f[i]: values of leading coefficient function f, with i
           varying from 1 to npieces
     q[i]: values of potential function
     w[i]: values of weight function
      mAB: coefficient matrix of boundary condition
   nterms: number of terms in given partial sequence of
           consecutive approximate eigenvalues
    ev[i]: approximate values of eigenvalues, with i running
           from 1 to nterms
    mt[i]: multiplicities of eigenvalues
The optional input consists of any of the following 3 items.
    psiYY: partial sequence index of eigenvalue used
           in the main part of computation, its defaulted
           value is the partial sequence index
           corresponding to the approximate eigenvalue
           having smallest absolute value
    inpYY: initial number of points in interval used, its
           defaulted value is 8
     czYY: counting-zero indicator, its defaulted value is
           -1, causing counting-zero part of codes not
           activated
In addition to print-outs, the output has the following 6
items.
     beta0YY: value of beta0
    beta0KYY: value of beta0K
     beta1YY: value of beta1
    beta1KYY: value of beta1K
  indexYY[i]: index or smaller index of ev[i]

If the Sturm-Liouville problem has general coefficient
functions, then the index or indices can be computed by
calling the files a-b-in-computations and
compute-indices-rglr (in this order). In this case, the
input has the following 11 items.
       a: left end point of interval of differential
          equation
      ta: type of a, its value is 00 if a is finite and all
          three coefficient functions are bounded at a, 01
          if a is finite and one coefficient function is
          unbounded at a, and 10 if a is infinite
       b: right end point of interval
      tb: type of b, its value is 00 if b is finite and all
          three coefficient functions are bounded at b, 01
          if b is finite and one coefficient function is
          unbounded at b, and 10 if b is infinite
   f[t_]: leading coefficient function
   q[t_]: potential function
   w[t_]: weight function
     mAB: coefficient matrix of boundary condition
  nterms: number of terms in given partial sequence of
          consecutive approximate eigenvalues
   ev[i]: approximate values of eigenvalues, with i varying
          from 1 to nterms
   mt[i]: multiplicities of eigenvalues
After calling the file a-b-in-computations, the following
two numbers are created.
  aa: approximation of left end point a
  bb: approximation of right end point b
The optional input and the output in this case are the same
as the piece-wise constant case.


Copyright by Hongyou Wu (Registration number TXu 1-344-422)