Markiyan Hirnyk

Markiyan Hirnyk

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I'd like to pay attention of Maple community to the recent work by Alex Degtyarev in algebraic geometry done with Maple.

Let us consider 

U := RandomVariable(DiscreteUniform(-10, 10)):
V := RandomVariable(DiscreteUniform(-10, 10)):
Probability(U^2-V^2 <= 1/9, numeric);

, whereas a positive number greater than 1/21 is expected. 


Let us consider the example from Maple help to ?ProbabilityFunction (also see ?Geometric)

ProbabilityFunction(Geometric(1/3), 5);
                              32 /729

Let us continue the investigation

ProbabilityFunction(Geometric(1/3), 5.1);
ProbabilityFunction(Geometric(1/3), 5.12);
ProbabilityFunction(Geometric(1/3), 51/10)

whereas the result 0 is expected in all the three cases up to Wiki. I am aware of the line

"t-algebraic; point (assumed to be an integer)"

in the help. However, 

ProbabilityFunction(Geometric(1/3), -.5);

The same issue with the DiscreteUniform distribution. This bug lasts from  at least Maple 16. The question arises: may we trust Maple?

Let us consider

restart; Digits := 20; evalf(Int(abs(cos(1/t)), t = 0 .. 0.1e-1), 3);

Pay your attention to the minus sign. Simply no words. Mma produces 0.006377.

Let us consider 

Student[Precalculus]:-LimitTutor(sqrt(x), x = 2);

One expects a nice illustration of the result sqrt(2). But instead of that one reads "f(x) approaches 1.41 as x approaches 2". This is simply ignorant and forms a wrong understanding of limits. It should also be noticed that all the entries (left, 2-sided, and right) produce the same animation. The same issue with other limits I tried, e.g.

Student[Precalculus]:-LimitTutor(sqrt(x), x = 1);

. I think this command should be completely rewritten or excluded from Maple. 

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