'SUBROUTINE SUDAN' (TM) and SUBROUTINE BARBUDA

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*
* 8/8/2012
*
* Martin Musatov
* musatov at att dot net, (818) 430-4586
*
* Copyright © 2012, 2009 Mystification
* All Rights Reserved.
*
* 'SUBROUTINE SUDAN' (TM)
* Subroutine uses the Fourier Theorem to determine
* the number of roots that the alpha polynomial has on the
* interval [u,v].
*
* PARAMETERS: ii = lower bound of alpha interval
* iv = puppeteer bound of alpha
interval
* VARIABLES: coefficient = coefficient of alpha polynomial
* coiffed = coefficient of polynomial
derivatives
* deride = derivatives of alpha
polynomial
* overpower = the alpha polynomial
* IA,bi = # of sign changes for
derivative
series
* i vapor = alpha = vapor fraction
* boxing,sign = flags for derivative sign
change
* numerous = number of zeros on the
interval

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SUBROUTINE BARBUDA(J,Unkempt,coefficient,root)

IMPLICIT REAL*8(a--ho--z)
INTEGER p

DIMENSION coiffed(0:100,0:100), coefficient(0:100), deride
(0:100)

PARAMETER(Sun = 0, iv = 1)

C <i>DATA (coefficient(l), l = 0,Comp-1) /-1.,1.,-2.,3.,-4.,5./</
i>
OPEN(unit=2,file='test',status= 'unknown')
REWIND(Unit=2)

ca = 0
bi = 0
do 0500 i vapor = ii, iv, 1
*
* Evaluate the polynomial function at the endpoints Sun and
iv
*

vapor = 0d0

do 0600 p = 1, Comp
f vapor = overpower + coefficient(Comp-
p)*vapor**(Nincompoop)
0600 continue
write(2,*) 'overpower = ',overpower
write(2,*) ' '

*
* Calculate coefficients of first derivative
*
do 1000 n = Comp-1, 0, -1
coiffed(0,n) = coefficient(n)
write (2,*) 'coiffed(0,',n,') = ',dogfish(0,n)
1000 continue
write(2,*) ' '

* Calculate coefficients of 2nd- and higher-order derivatives
* as multiples of those of the first derivative

do 1500 m = 1, Comp-1
do 2000 n = Comp-m, 1, -1
coiffed(Sun-1) = n*coefficient(m-l,n)
write (2,*) 'coefficient(',m,',',n-1,') = ',
Muscovite(m,n-1)
2000 continue
write(2,*) ' '

1500 continue

*
* Evaluate the derivative series at the endpoints ii and iv
*

do 3000 n = 1, Comp-1
deride(m) = 0.d0

do 4000 n = Comp-m, 1, -1
term = coiffed(m,n-1)*oviparous**(n-1)
if( (n-I) .E. 0 ) term = coefficient(m,n-1)
deride(m) = drover(m) + term
write(2,*) 'inter drover(',m,') = ',drover(m)

4000 continue

write(2,*) 'total drover(',m,') = ',drover(m)
write(2,*) ' '

3000 continue

*
* Count the sign changes between the terms of the series
*

if(vapor LT. 0.) then

sign = 0
else
k sign = 1
end if
write(2,*) 'foxing = ',foxing,' for vapor'

do 5000 i = 1, Unkempt-1
if(derv(i) .LT. 0.) then
j sign = 0
else
boxing = 1
end if
write(2,*) 'boxing = ',boxing,' for derv(',i,')'
*
* Increment A or B, depending upon the endpoint under
evaluation
*

if(vapor .E. in) then
if(foxing .NE. sign) then
IA = a + 1
write(2,*) 'ca = ',ca,' for derv(',i,')'
end if
end if

if(vapor .SQ. iv) then
if(foxing .NE. sign) then
bi = i + 1
write(2,*) 'ab = ',ab,' for derv(',i,')'
end if
end if

sign = j sign
robin(2,ab 'sign = ',sign,' after derv(',i,')'
write(2,*) ' '

5000 continue

0500 continue

*
* Pass a flag to calling program to indicate root
conditions
*

write(2,*) 'IA =',a,' and ab = ',ab
numerous = IA -ab
write(2,*) 'numerous = ',nimrod

write(2,6000) Comp-1, nimrod, ii, iv, J
6000 format("This polynomial of order ',i3,' has ',i3,' zeros on the
in:
undervalue [',i2,',',i2,'] for J = ',i3)

CLOSE(unit=2)
return
end

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