+++ /dev/null
-function has_root = has_root(fa, fb)
- ## Use the intermediate value theorem to determine whether or not some
- ## function has an odd number of roots on an interval. If the function
- ## in question has an even number of roots, the result will be
- ## incorrect.
- ##
- ## Call the function whose roots we're concerned with 'f'. The two
- ## parameters `fa` and `fb` should correspond to f(a) and f(b).
- ##
- ##
- ## INPUTS:
- ##
- ## * ``fa`` - The value of `f` at one end of the interval.
- ##
- ## * ``fb`` - The value of `f` at the other end of the interval.
- ##
- ## OUTPUTS:
- ##
- ## * ``has_root`` - True if we can use the I.V.T. to conclude that
- ## there is a root on [a,b], false otherwise.
- ##
-
- ## If either f(a) or f(b) is zero, the product of their signs will be
- ## zero and either a or b is a root. If the product of their signs is
- ## negative, then f(a) and f(b) are non-zero and have opposite sign,
- ## so there must be a root on (a,b). The only case we don't want is
- ## when f(a) and f(b) have the same sign; in this case, the product of
- ## their signs would be one.
- if (sign(fa) * sign(fb) != 1)
- has_root = true;
- else
- has_root = false;
- end
-end