Kitonum

18909 Reputation

26 Badges

14 years, 34 days

MaplePrimes Activity


These are replies submitted by Kitonum

@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);

@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.

@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.

@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.

@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.).

@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

simplify(add(cos(2*Pi*k/214748364), k=0..214748363));
     Error, Maple was unable to allocate enough memory to complete this computation.  Please see ?alloc
 

 

@acer    @vv  Thanks for the helpful comments.

 @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

@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!

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

@Markiyan Hirnyk 

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  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]]:   
m:=add(L[i,1], i=1..nops(L))/3;  
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]

 

                              

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

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." ?

@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. 

First 43 44 45 46 47 48 49 Last Page 45 of 124