close(filename);
readbytes(filename,18);

  [70, 105, 108, 101, 84, 111, 111, 108, 115, 32, 101, 120, 97, 109,

        112, 108, 101, 13]

Alec

Standard deviations should be enough. After a and c are found, we have only one variable left for each column - b for x and d for y, so they can be found using one equation (with one variable) for each - and standard deviation seems to be a good choice.

Alec

Standard deviations should be enough. After a and c are found, we have only one variable left for each column - b for x and d for y, so they can be found using one equation (with one variable) for each - and standard deviation seems to be a good choice.

Alec

I didn't mean the simulation. I meant that the mean of the distribution seems to be (x,y)=(a,c). So a and c can be chosen as the mean values of the sample columns (or rows), corresponding to x and y. Similarly, b and d could be, probably found from the standard deviations of the columns (or rows).

Alec

I didn't mean the simulation. I meant that the mean of the distribution seems to be (x,y)=(a,c). So a and c can be chosen as the mean values of the sample columns (or rows), corresponding to x and y. Similarly, b and d could be, probably found from the standard deviations of the columns (or rows).

Alec

I just tried more simple example, ln(y)/ln(y-1)=ln(3)/ln(2), without square roots, and none of the combinations of solve, expand, convert, simplify, collect, assuming etc, that I tried, worked.

Alec

I just tried more simple example, ln(y)/ln(y-1)=ln(3)/ln(2), without square roots, and none of the combinations of solve, expand, convert, simplify, collect, assuming etc, that I tried, worked.

Alec

Solving f(y)=f(A) assuming that f is monotonic (or, more general, 1-1), should give an answer y=A.

That doesn't work in Maple in general, or in this example with

f:=t->ln(t)/ln(t-1)

Alec

Solving f(y)=f(A) assuming that f is monotonic (or, more general, 1-1), should give an answer y=A.

That doesn't work in Maple in general, or in this example with

f:=t->ln(t)/ln(t-1)

Alec

Using attributes is an interesting idea. I think, Joe Riel used attributes for sorting lists in one of the postings on this site (a long time ago), and I might use them after that for a similar purpose (but I don't remeber exactly what for.) Otherwise, they appear quite rarely on this site.

Developing packages for Maple is an interesting idea as well. However, putting them in the Application Center doesn't attract me personally as much as including them in the share library (distributed with Maple) would.

What was the reason for the excluding the share library from the distribution?

Alec

Frankly, I don't understand what you want. If you can't write that in Maple language - can you write that in traditional mathematical form?

Alec

PS Perhaps, you need help with Mathematica and not with Maple? -Alec

Frankly, I don't understand what you want. If you can't write that in Maple language - can you write that in traditional mathematical form?

Alec

PS Perhaps, you need help with Mathematica and not with Maple? -Alec

Something similar can be drawn using the deprecated networks package, with f instead of e,

with(networks):
g:=graph({a,b,c,d,f},
    {{a,b},{a,d},{b,d},{b,f},{c,d},{c,f}}):
plots:-display(
    plottools:-rotate(
        draw(Linear([a, b, c], [d, f]), g), 
        -(1/2)*Pi), 
    symbol = solidcircle, 
    symbolsize = 18, 
    font = [roman, italic, 18]);

A closer picture can be produced using the plots package,

with(plots);
display(
    pointplot([[0, 0], [0, 1], [1, 0], [1, 1], [2, 1]], 
        symbol = solidcircle, symbolsize = 18), 
    textplot([[0, 1.1, a], [1, 1.1, b], [2, 1.1, c], 
        [0, -.1, d], [1, -.1, e]]), 
    pointplot([[0, 0], [0, 1], [1, 1], [1, 0], [2, 1], 
        [0, 0], [1, 1]], connect), 
    scaling = constrained, 
    axes = none, 
    font = [roman, italic, 18]);

Alec

Something similar can be drawn using the deprecated networks package, with f instead of e,

with(networks):
g:=graph({a,b,c,d,f},
    {{a,b},{a,d},{b,d},{b,f},{c,d},{c,f}}):
plots:-display(
    plottools:-rotate(
        draw(Linear([a, b, c], [d, f]), g), 
        -(1/2)*Pi), 
    symbol = solidcircle, 
    symbolsize = 18, 
    font = [roman, italic, 18]);

A closer picture can be produced using the plots package,

with(plots);
display(
    pointplot([[0, 0], [0, 1], [1, 0], [1, 1], [2, 1]], 
        symbol = solidcircle, symbolsize = 18), 
    textplot([[0, 1.1, a], [1, 1.1, b], [2, 1.1, c], 
        [0, -.1, d], [1, -.1, e]]), 
    pointplot([[0, 0], [0, 1], [1, 1], [1, 0], [2, 1], 
        [0, 0], [1, 1]], connect), 
    scaling = constrained, 
    axes = none, 
    font = [roman, italic, 18]);

Alec

The following works,

f:=Int(Int(sin(t*y*x^n)/exp(x),x=0..1),y=0..1):

series(f,t);

      exp(-1/2) WhittakerM(n/2, n/2 + 1/2, 1)
  1/2 --------------------------------------- t -
                       1 + n

                                  3 n  3 n
             exp(-1/2) WhittakerM(---, --- + 1/2, 1)
                                   2    2             3
        1/24 --------------------------------------- t  +
                             1 + 3 n

                                   5 n  5 n
              exp(-1/2) WhittakerM(---, --- + 1/2, 1)
                                    2    2             5      6
        1/720 --------------------------------------- t  + O(t )
                              5 n + 1

Using integral in the new (shortened) form

f:=Int(sin(t*y*x^n)/exp(x),[x=0..1,y=0..1]);

gives an error in series,

series(f,t);
Error, (in series/int) invalid arguments

which may be a bug.

Alec