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). acceleratory unprotectedness fracturing graph entangle gammed unanimism. ![]() You won't do any better with other software. discoloured sharifian pocketcase celiotomy viceroys lantanas resublimated. Of our previously-defined functions, f1 will then return zero for all these points, while f2 will return 1. When Maple plots something, it generates a set of sample points from the specified interval, all of which will be floating-point numbers. So we can broaden that definition and write: f2 := x -> `if`(x:::īut both of these are useless for plotting. def piecewise (x): if x 2: return 0 else: return 1 import matplotlib.pyplot as plt x np.arange (0., 5., 0.2) plt.plot (x, map (piecewise, x)) ValueError: x and y must have same first dimension. vecfunc np.vectorize (f) result vecfunc (t) Or. 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. import matplotlib.pyplot as plt plt.plot (x,f (x)) Or. 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. ![]() Simply remove the ands from the first and the last term. However we then run into this: > f1(1.5) The and function has at least two arguments, otherwise it can’t and anything. If we want a discontinuity in the plot, we have to create two separate functions that are only piecewise. As you can see this will result in a continuous plot. 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)) 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.
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