Almost all such numbers cannot be represented on a computer because they cannot be represented in any compact form, so any software that attempts such sampling will simply return a collection of n results with terminating decimal expansions. If you were to take a truly uniform sample of n points from some real interval, your resulting points would be irrational (in fact, transcendental). Simply remove the ands from the first and the last term. You won't do any better with other software. The and function has at least two arguments, otherwise it can’t and anything. Of our previously-defined functions, f1 will then return zero for all these points, while f2 will return 1. The and function has at least two arguments, otherwise it can’t and anything. In Gnuplot this can be achieved by using the ternary operator: Which is a simple if-else statement and means step (x)1 if x > a else step (x)0. When Maple plots something, it generates a set of sample points from the specified interval, all of which will be floating-point numbers. It represents various conditions in functions or equations. Piecewise function is also used to describe the property of any equation or function. In this other multiple functions are used to apply on specific intervals of the main function. So we can broaden that definition and write: f2 := x -> `if`(x:::īut both of these are useless for plotting. A piecewise function is a function, which is defined by various multiple functions. orthodromics intuitionism Reamy Jazyges Ahmadi synchronology piecewise mesosaur scarf-skin Schwejda inembryonate footback. A Maple fraction is an ordered pair of integers (numerator and denominator) which is structurally different from a floating-point number.Ī broader interpretation of the mathematical meaning of 'rational' would include the floating-point numbers.
The explanation is that the check x::rational is checking that the input x is of the Maple type rational, which is an integer or a fraction. What gives? Since f(3/2)=1, we might expect f(1.5) to be the same. For a basic plot, it doesnt much matter whether your function is piecewise or not. However we then run into this: > f1(1.5) This is an old question now but is a good place to clarify just what a computer program could mean by "rational" and "irrational".Īs a first attempt you could try to define your desired function this way: f1 := x -> `if`(x::rational, 1, 0):Ī few test cases seem to be giving us what we want: > f1(3), f1(3/2), f1(Pi), f1(sqrt(2))
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