'****************************************************
'* Program to demonstrate complex series evaluation *
'* It is assumed that the coefficients are obtained *
'* from a subroutine                                *
'* ------------------------------------------------ *
'* Reference: BASIC Scientific Subroutines, Vol. II *
'* By F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1].*
'* ------------------------------------------------ *
'* SAMPLE RUN:                                      *
'*                                                  *
'* Input the complex number as prompted:            *
'*                                                  *
'*   Real part    = 1                               *
'*   Complex part = 0                               *
'*                                                  *
'* Results are:                                     *
'*                                                  *
'*   Z1 =  32                                       *
'*   Z2 =  8E-029                                   *
'*                                                  *
'****************************************************
defint i-n
defdbl a-h,o-z
pi = 4#*ATN(1#)
'Get coefficients
gosub 1000
'input complex number
cls
print
print " Input the complex number as prompted:"
print
input "   Real part    = ", x
input "   Complex part = ", y
gosub 3000
print
print " Results are:"
print
print "   Z1 = "; z1
print "   Z2 = "; z2
print
end

'Coefficients subroutine
1000 m=5
  A(0) = 1
  A(1) = 5
  A(2) = 10
  A(3) = 10
  A(4) = 5
  A(5) = 1
return

'Rectangular to polar conversion
2000 u = sqr(x*x+y*y)
  'Guard against ambiguous vector
  if y=0 then y = (.1)^30
  'Guard against divide by zero
  if x=0 then x = (.1)^30
  v = ATN(y/x)
  'Check quadrant and adjust
  if x<0 then v = v + pi
  if v<0 then v = v + 2# * pi
return

'Polar to rectangular conversion
2100 x = u*cos(v)
     y = u*sin(v)
return

'Polar power
2200 u1 = u^n
  v1 = n * v
  v1 = v1 - 2#*pi * int(v1/2#/pi)
return

'Rectangular complex number power
2300 gosub 2000
  'Polar power
  gosub 2200
  'Change variable for conversion
  u=u1 : v=v1
  'Polar to rectangular conversion
  gosub 2100
return

'********************************************************
'*        Complex series evaluation subroutine          *
'* ---------------------------------------------------- *
'* The series coefficients are A(i), assumed real, the  *
'* order of the polynomial is m. The subroutine uses    *
'* repeated calls to the nth power (Z^N) complex number *
'* subroutine. Inputs to the subroutine are x, y, m and *
'* the A(i). Outputs are z1 (real) and z2 (imaginary).  *
'********************************************************
3000 z1 = A(0) : z2 = 0
  'Store x and y
  a1 = x : a2 = y
  for n = 1 to m
    'Recall original x and y
    x = a1 : y = a2
    'Call Z^N subroutine
    gosub 2300
    'Form partial sum
    z1 = z1 + A(n) * x
    z2 = z2 + A(n) * y
  next
  'Restore x and y
  x = a1 : y = a2
return

'End of file CMPLXSER.BAS