## 18909 Reputation

14 years, 34 days

## Re...

@asa12  In Maple 2015 everything works correctly. You have initialized the procedure code. And then probably you forgot to execute the following code:

RotationIn2D(2,1);

## OK...

@das1404  Your calculations are correct, except  hs . For your parameters should be  hs=sqrt(2)/2  rather than  1/2 . In my code first there were 2 errors in the expressions for  st  and  hs  (I took the wrong segments). Now everything is fixed.

## Re...

@asa12  The blue particle is at the origin. The red particle rotates around the blue one. x0, y0 are the initial coordinates of the red particle:

RotationIn2D:=proc(x0, y0)
local A;
uses plots;
A:=t-><cos(t),-sin(t); sin(t),cos(t)>;
animate(plot, [[[convert(A(s).<x0,y0>,list)[],s=0..t], [convert(A(t).<x0,y0>,list)]], style=[line, point], linestyle=3, color=red, symbol=solidcircle, symbolsize=17], t=0..2*Pi, frames=90,background=plot([[0,0]], style=point, symbol=solidcircle, color=blue, symbolsize=17), axes=none, scaling=constrained);
end proc:

Example of use:

RotationIn2D(2,1);

Edit.

## Re...

@Markiyan Hirnyk  Thank you for attention! The reason for the error is that there are just no solutions for these parameters. I made the necessary adjustments to the procedure code. Now it returns an empty list in such cases.

For example
HeronianTriangles(170, 165);

returns the solutions.

## Re...

@acer Thanks. With Maple it can be made easier

restart;
sum(cos(2*Pi*k/n), k=0..n-1);

0

But even easier to prove this identity manually, if we note that the sum of  n unit vectors with the beginning in the origin and whose ends lie at the vertices of the regular n-gon is equal to  0  (this identity is simply the projection of this vector equality on the horizontal axis.).

## Easier manually than with Maple...

@ThU  Similar identities are often much easier to prove manually than with Maple. Here is an example in which the result is also obviously :

simplify(sum(cos(2*Pi*k/214748364), k=0..214748363));
Error, (in SumTools:-DefiniteSum:-ClosedForm) summand is singular in the interval of summation

Error, Maple was unable to allocate enough memory to complete this computation.  Please see ?alloc

## Re...

@vv    `GAMMA/magic`:=100,100,infinity,50;   # I did not understand what that meant. Is it documented somewhere?

## ?...

@mmcdara  Your procedure is contrary to the condition. According to the condition
if x<Mthen Mi*2
else Mi

those elements of the list must be doubled, which is more than a given number  . In your example  x=5

## OK...

@Markiyan Hirnyk  We all know that the analytical skills of Mathematica in a number of areas are unsurpassed. This is not news. So once again, do not spoil the mood of all Maple fans.

Happy New Year!

## Unknown parameters...

What is a[1] , a[3]  and  p[3]  in your diff. equation?

## Re...

I saw your comment after I sent my answer and should note the following:

1. Your answer contains a significant error: for  t-variable the period is equal to  8*Pi  and not  2*Pi.

2. I would not rely on Optimization:-Minimize command, because it reliably finds only local extremes, not global extremes.

3. I consider the most psychologically convincing argument (at least for me personally) a neatly constructed plot. There is almost nothing in your comment regarding graphics.

## @Christopher2222  Unfortunatel...

@Christopher2222  Unfortunately, in another example, less obvious, the procedure does not work correctly.

Digits:=20:
L:=[[116,1], [139,1], [189,1], [208,1], [282,1], [471,1], [724,1], [782,1], [885,1]]:
evalf[5](m);
BinPacking1D(m, L);

3796/3
1265.3
[[208] = 1, [282, 885] = 1, [471, 724] = 1, [116, 139, 189, 782] = 1]

The correct answer is   [[782, 471], [189, 885, 208], [724, 282, 139, 116]]

The sums of the numbers in sub-lists   [1253, 1282, 1261]

## Re...

@n11n11  See the discussion of a similar example in this thread

## Re...

1. You must submit all of this not as an image, but as a text that can be copied to the Maple window and then work with it. I do not think there are people who want to reprint it all.

2. You wrote "how i can introduce this function?". What function do you have in mind?
And how to understand this  "m is power and not derivative, for example m=1 is derivative of order 1." ?

## Re...

@n11n11  The reason is that Maple 2015 does not have a built-in tool for solving elliptic equations with boundary conditions. Therefore, you must either use the newer versions of Maple, or you can solve it partially manually, using known methods.

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