vv

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MaplePrimes Activity


These are questions asked by vv

Two days ago I have answered a question about using numapprox:-infnorm for functions of several variables. The question is now deleted. Is it possible to find whether it was deleted by the author (even if she/he has used the "best answer" tag)?

The simple test procedure P constructs a large matrix.
Measuring the real time twice  (t1 and t2), t2 was by about 25% larger!
Now, if we remove the comment  before "Start",  t1 increases by 25% and t2 ~ t1.
So, the timing depends on whether some output is already on screen (standard interface).
Can you explain this?

restart;
P := proc(n,A)
  local i, j;
  for i from 1 to n do  for j from 1 to n do
    A[i,j]:=sin(arcsin(1/i-1/j+1/n))-1/i+1/j-1/n+i+j
  od od;
  NULL  #A;
end proc:

# "Start";
n := 300:
s := time[real]():
A:=Matrix(n,datatype=float[8]):
P(n,A):
t1:=time[real]()-s;

s := time[real]():
A:=Matrix(n,datatype=float[8]):
P(n,A):
t2:=time[real]()-s;
t2/t1;  # 1.24   WHY?

(For one of my programs, I found t2/t1 = 1.7)

 

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]);

 

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