homework1.html

> restart;

First the Golden ratio program.

> evalf(.5*(1+sqrt(5)));

> Golden:=proc(N)
Phi:=2:
for j from 1 to N-2 do
Phi:=evalf(1+1/Phi):
end do:
end:

Warning, `Phi` is implicitly declared local to procedure `Golden`

Warning, `j` is implicitly declared local to procedure `Golden`

> Golden(3);

> Golden(4);

> Golden(10);

> Golden(11);

> Golden(12);

Now the quadratic formula program.

> quadro:=proc(a,b,c):
if (a=0) then
  if (b=0) then
     print(`Constant function: no roots.`):
  else
     x := -c/b:
     print(`Linear function: one root at `, x):
  end if:
else
  disc := b^2-4*a*c:
  if (disc<0) then
     print(`Negative discriminant: no real roots.`):
  else
     if (disc=0) then
        x := -b/(2*a):
        print(`Zero discriminant: one repeated root at `, x):
     else
        sqd := sqrt(disc):
        if (b<0) then
           x1 := (-b+sqd)/(2*a):
           x2 := (-2*c)/(b-sqd):
        else
           if (b>0) then
              x1 := (-b-sqd)/(2*a):
              x2 := (-2*c)/(b+sqd):
           else
              x1 := sqrt(-c/a):
              x2 := -x1:
           end if:
        end if:
     print(`Two real roots at`, x1, ` and `, x2):
     end if:
  end if:
end if:
end:

Warning, `x` is implicitly declared local to procedure `quadro`

Warning, `disc` is implicitly declared local to procedure `quadro`

Warning, `sqd` is implicitly declared local to procedure `quadro`

Warning, `x1` is implicitly declared local to procedure `quadro`

Warning, `x2` is implicitly declared local to procedure `quadro`

> quadro(1,2,1);

> quadro(1,2,2);

Test that it works for four digits.

> Digits:=4;

> fsolve(2.1*x^2-42.6*x+1.0=0,x);

> quadro(2.1,-42.6,1.0);

> fsolve(2.0*x^2+55*x-1.0=0,x);

> quadro(2.0,55,-1.0);