dly wrote: [Interesting history deleted] > In general linear programming models the results can assume any > values in the feasible region and are allowed to be continuous. > Altho for some problems such as transportation assignment or network > flow, integer solutions can be obtained automatically, the extreme > points of a general linear programming problem is not ordinarily > restricted to having only integer-valued components. Moreover one > cannot merely round the fractional values of an optimal solution and > expect it to produce the optimal value solution. In a mixed integer- > continuous variable problem only some of the variables are required > to be integers. >
Donna: Thanks for this information. I guess I misunderstood (or am misunderstanding now): you first raised the linear programming/vector processor issue as an example as to why 111r333 contained more information than 1r3. I completely agree that approximating a rational number by a floating point number may be inappropriate in some circumstances, however if we are talking about rational numbers (which are defined as equivalence classes), I still don't see the difference between representatives. The rational type in J can be useful, but it is easily added to any language. In fact a rational number class is a common exercise in OOP courses, especially if the language has operator overloading. By the way, floating point numbers are rational, too: in fact 64 bit floating point numbers represent more rational numbers than <32 bit integers>r<32 bit integers>. So you also have the reverse problem: approximating a floating point number by a rational. More generally, the fact that finitely many rational numbers tell us anything about uncountably many real numbers is remarkable in itself. Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
