Z transforms

The following functions were developed on the TI-92+ calculator, but should work just fine
on the TI-89 since it does not depend upon the screen size.

The following folder names are used.
al - means "Algebraic"
c  - means "Complex"
is - contains test functions that return true or false
p  - means "Polynomial"
ut - means "Utility"
zt - means "Ztransform"  (Only contains the lookup table.  See "lkup" below)

The Z transform functions are actually a one-sided Z transform.  Any of the answers produced
by the "iz" function can be multiplied by u(n) to convert them to the two-sided function.

The variable n is assumed to be >=0 and is an integer and the variable z is assumed abs(z)>1.

c\zt(ex,n,z) - Takes the one-sided Z transform of the equation or expression "ex".
 ex - an equation or expression in the variable "n"
 n  - The independent variable
 z  - The Z transform variable
 
 Example: c\zt(a^n,n,z)  returns z/(z-a)
 
 c\zt uses zt\tb which is a data variable table of transform forms.
 
c\iz(ex,z,n) - Takes the inverse Z transform of the equation or expression "ex".
 ex - an equation or expression in the variable "z"
 z  - The inverse Z transform variable
 n  - The Z transform variable
 
 Example: c\iz(z/(z-a),z,n) returns a^n
 
i\ci(expr,z) - Takes the Closed Loop Complex Integral of the expression "ex".
 expr - an expression in the variable "z"
 z    - the independent wrt variable.
 
 Example: i\ci(z^2/((z-a)*(z-b)),z) returns [-2b^2*pi/(a-b)*i,b<c;2a^2*pi/(a-b)*i,a<c]

 It assumes that the closed loop is in the counterclockwize direction around the poles.
 It returns a mxn matrix of the "n" values of the integral.  "m" is normally 2 unless
 there are restrictions on the value of z in which case "m" will be 3.  The last item
 is an inequality of the form "v<c" which should be read as "The complex value "v" is
 contained within the contour (closed loop) of the path of the integral".
 
 This function is used by the iz function above.
 
i\allpoles(cia) - Make "ci" answer include all the poles in the contour.
 cia - the answer returned by function ci above i. e. the coutour include both a and b.
       It just sums the first column of the answer matrix.
 
 Example: c\allpoles(ans(1)) returns 2*(a+b)*pi*i where ans(1) is the answer in the
 above example under "i\ci".
 
 ut\form(ex,v) - Makes a form of the expression or equation to be used by "lkup".
  ex - an expression or variable in the variable "v"
  v  - a independent variable
  
  Use this function to make a form to include in a data editor table to be used with
  the look up routine.
  
 ut\lkup(aggregate) - Look Up an function call or an aggregate in a lookup table.
  aggregate - an aggregate (integral,sum,product) or function call with args
  
  The function name should match the folder name where the lookup table is located.
  For aggregates use the following:
   i  - integral
   s  - sum
   p  - product
   
An example of using Z transforms to solve an equation.
<coming soon>