rem roots of polynomials - newton's method
cls
print
print "Roots of Polynomials - Newton's Method"
print "input the degree, and then the coefficients"
print "given the form F(x)=A0+A1*x+A2*x^2+...+AN*x^N"
dim a(11)
dim b(11)

for i=1 to 11
 a(i)=0
 b(i)=0
next i

print
input "degree of equation: ";n$
if n$="q" then end
n=val(n$)
print
for i=1 to n+1
 print "coefficent of A(";i-1;")= ";
 input a$
 if a$="q" then end
 a=val(a$)
 a(i)=a
next i

for i=1 to 10
 b(i)=a(i+1)*i
next i

[again]
print
input "Best guess (press q to quit)?  ";x$
if x$="q" then end
x=val(x$)

q=0

[leap]
s=1
f1=0
f0=0
q=q+1

for i=1 to n+1
 f0=f0+a(i)*s
 f1=f1+b(i)*s
 s=s*x
next i

if f1=0 then
 print
 print "derivative = 0 at x= ";x
 print
 goto [again]
end if

s=x-f0/f1
if x=s then
 print
 print "Root =      ";x
 print "Error=      ";f0
 print "Derivative= ";f1
 goto [again]
end if

x=s
if q>1000 then
 print
 print "1000 iterations completed with no clear solution"
 print "x=    ";x
 print "f(x)= ";f0
 print
 [jump]
 input "More iterations (i), new guess (g), quit (q)? ";w$
 if w$="i" then goto [leap]
 if w$="g" then goto [again]
 if w$="q" then end
 goto [jump]
end if
goto [leap]