'****************************************************
'*      ROOT  TESTING  PROGRAM FOR POLYNOMIALS      *
'* ------------------------------------------------ *
'* Reference: BASIC Scientific Subroutines, Vol. II *
'* By F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1].*
'*                                                  *
'****************************************************
defint i-n
defdbl a-h,o-z
cls
print
print "  This program will help you determine"
print " where to look for roots of a polynomial."
print
input " What is the degree of the polynomial: ", n
dim A(n)
print
print " Input the polynomial coefficients as prompted:"
print
for i=0 to n
  print "   A(";i;") = "; : input A(i)
next i
print
print
print " There are ";n;" roots."
print
'Find the maximum value of root
aa=A(n-1)*A(n-1)-2*A(n-2)
if aa>0 then goto 100
print " There are at least two complex roots."
goto 500
100 aa=sqr(aa)
print
print " The magnitude of the largest root is <= "; aa
print
aa=-1
if INT(n/2)=n/2  then aa=-aa
aa=A(0)/aa
'b will flag a negative root
b=0
if aa>0 then goto 200
print " There is at least one negative real root."
b=1
200 print
'Test for Descartes rule nø 1
c=0
for i=1 to n
  if A(i-1)*A(i)<0 then c=c+1
next i
if c=1 then print " There is at most one positive ";
if c>1 then print " There are at most ";c;" positive ";
if c=1 then print "real root."
if c>1 then print "real roots."
print
'Test for Descartes rule nø 2
d=0
for i=1 to n
  if A(i-1)*A(i)>0 then d=d+1
next i
if d=1 then print " There is at most one negative ";
if d>1 then print " There are at most ";d;" negative ";
if d=1 then print "real root."
if d>1 then print "real roots."
print
if INT(c/2)=c/2 then goto 300
print " There is at least one positive real root."
300 if INT(d/2)=d/2 then goto 500
print " There is at least one negative real root."
500 print
end

'End of file roottest.bas