5 years, 1 days

## Psi(rational) ...

Maple

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:

 (1)
 > (simplify@value)(eval(%, [n=0, p=1, q=12]));
 (2)
 > evalf(%);
 (3)

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

## A probability riddle...

Maple

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).

## An unexpected PLOT bug...

Maple
```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.
plot([cos(x), sin(x), x=0..5000*Pi]);

## Trying to icombine; is too...

Maple
 > combine(2^n*4, icombine);
 (1)
 > combine(2^n*4);
 (2)
 > combine(2^n/4, icombine); # BUG
 > combine(2^n/4);
 (3)
 > combine(2^n/2^m, icombine); # BUG
 > combine(2^n*2^(-m), icombine);
 (4)
 > combine(2^n/2^m);
 (5)
 > is(2^n/4 = 2^(n-2)); # ???
 (6)
 >

## ternaryplot in plots...

Maple

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