procedure verifyrat(p,r1,r2)  #: verification tests for rational procedures
return write("Testing ",p,"( ",rat2str(r1),", ",rat2str(\r2) | &null," ) ==> ","returned " || rat2str(p(r1,r2)) | "failed")
end

procedure makerat(x)          #: make rational (from integer, real, or strings)
local n,d
static c
initial c := &digits++'+-'

   return case type(x) of {
             "real"    : real2rat(x)
             "integer" : ratred(rational(x,1,1))
             "string"  : if x ? ( n := integer(tab(many(c))), ="/", d := integer(tab(many(c))), pos(0)) then
                            ratred(rational(n,d,1))
                         else
                            makerat(numeric(x))
          }
end

procedure absrat(r1)          #: abs(rational)
   r1 := ratred(r1)
   r1.sign := 1
   return r1
end

invocable all                 #  for string invocation

procedure xoprat(op,r1,r2)    #: support procedure for binary operations that cross denominators
   local numer, denom, div

   r1 := ratred(r1)
   r2 := ratred(r2)

   return if op(r1.numer * r2.denom,r2.numer * r1.denom) then r2   # return right argument on success
end

procedure eqrat(r1,r2)        #: rational r1 = r2
return xoprat("=",r1,r2)
end

procedure nerat(r1,r2)        #: rational r1 ~= r2
return xoprat("~=",r1,r2)
end

procedure ltrat(r1,r2)        #: rational r1 < r2
return xoprat("<",r1,r2)
end

procedure lerat(r1,r2)        #: rational r1 <= r2
return xoprat("<=",r1,r2)
end

procedure gerat(r1,r2)        #: rational r1 >= r2
return xoprat(">=",r1,r2)
end

procedure gtrat(r1,r2)        #: rational r1 > r2
return xoprat(">",r1,r2)
end

link rational