vv

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These are questions asked by vv

 

During the computation of a series, I needed the value Psi(1/12)  of the digamma function at a rational point. 

simplify, convert/elementary or other usual convertions do not help.

But Maple knows the formula for Psi(r) when r is rational:

 

FunctionAdvisor(special_values, Psi)[24][1]: convert(%,`global`);

Psi(n+p/q) = q*(Sum(1/(k*q+p), k = 0 .. n-1))+2*(Sum(cos(2*Pi*p*k/q)*ln(sin(Pi*k/q)), k = 1 .. floor((1/2)*q+1/2)-1))-(1/2)*Pi*cot(Pi*p/q)-ln(2*q)-gamma

(1)

(simplify@value)(eval(%, [n=0, p=1, q=12]));

Psi(1/12) = ((2*3^(1/2)-6)*ln(2+3^(1/2))+(-Pi-2*gamma-6*ln(2)-3*ln(3))*3^(1/2)-Pi+2*gamma+6*ln(2)+3*ln(3))/(2*3^(1/2)-2)

(2)

evalf(%);

-12.44790533 = -12.44790533

(3)

The question is: why does not Maple use this formula when asked? Or, is there a convertion which I was missing?

 

Here is a known probability riddle:

A and B are two lists of 100 binary numbers:

A:=[0,1,0,1,0,1,1,0,1,1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,1,0]:
B:=[0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,1,0,1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,1,0]:

One was obtained by tossing a coin (1 for a head, 0 for a tail), and the other by a human, who was asked to simulate tossing a coin.

Question: which one comes from a human brain?
The standard answer: B was produced using a coin, because (among other things) the probabilty of obtaining a "000000" or "111111" is about 80%, but a humain brain tends to avoid such "simulations".

My Question: what (if any) statistical test can be used in Maple for an answer?
(I have tried ChiSquareSuitableModelTest but both lists were accepted).

 

restart;
plot([sin(x), sin(x), x=0..420]);

The matrix A := op([1,1], %)  has equal columns, so the bug is in the PLOT engine.
plot(A) generates the same plot.
See also the "circle":
plot([cos(x), sin(x), x=0..5000*Pi]);

 

combine(2^n*4, icombine);

2^(2+n)

(1)

combine(2^n*4);

4*2^n

(2)

combine(2^n/4, icombine); # BUG

Error, (in compat) invalid input: igcd received undefined, which is not valid for its 2nd argument

 

combine(2^n/4);

(1/4)*2^n

(3)

combine(2^n/2^m, icombine); # BUG

Error, (in compat) invalid input: igcd received undefined, which is not valid for its 2nd argument

 

combine(2^n*2^(-m), icombine);

2^(n-m)

(4)

combine(2^n/2^m);

2^(n-m)

(5)

is(2^n/4 = 2^(n-2)); # ???

false

(6)

 


Download bug-icombine-is.mw

The  plots help page contains an entry for ternaryplot. But it is empty (Maple 2018&2019) and there is no such command.
Does somebody know about it?

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