Assume to represent a fraction a/b as a pair (a,b). Write the following functions:
val is_posfrac : int * int -> bool = <fun>such that is_posfrac (a,b) is true iff (a,b) is a positive fraction (note: if the denominator is 0, then the pair is not a fraction).
val compare_posfrac : int * int -> int * int -> int = <fun>which compares two positive fractions (failing if one of them is not such). The result of the comparison is:
- 0, if the two fractions are equal (i.e. they represent the same rational number);
- 1, if the first fraction is greater than the second;
- -1, otherwise
For instance, the following assertions must pass:
assert (compare_posfrac (1,2) (2,4) == 0);;
assert (compare_posfrac (1,2) (1,3) == 1);;
assert (compare_posfrac (1,2) (2,3) == -1);;Finally, write a function:
val compare_frac : int * int -> int * int -> int = <fun>which compares two fractions (not necessarily positive).
Warning: it is strictly forbidden to convert the fractions to floats!