## SEEMOUS 2017

by: Maple

Here is a problem from SEEMOUS 2017 (South Eastern European Mathematical Olympiad for University Students)
which Maple can solve (with a little help).

For k a fixed nonnegative integer, compute:

Sum( binomial(i,k) * ( exp(1) - Sum(1/j!, j=0..i) ), i=k..infinity );

(It is the last one, theoretically the most difficult.)

## Print nothing when using a procedure...

**I am trying write a procedure (bit(n,k)) that print all the binary sequences with 2 following conditions:
- Each of the sequences has the length of 'n'. (n elements)
- k bits of n elements have the value 1. (all the remains have the value 0)
Example: bit(3,2) and the result is ((101),(110),(011)).
**My code:
bit := proc (n, k)
local one, index, i, d;
global A;
one := 0;
index := 1;
A := [seq(0, i = 1 .. n)];
d := proc (index)
if one = k or index = n+1 then return NULL; end if;
for i from 0 to 1 do
A[index] := i;
if i = 1 then one := one+1; end if;
if one = k then print(op(A)); end if;
d(index+1);
if i = 1 then one := one-1; A[index] := 0; end if;
end do;
end proc;
d(1);
end proc;
>bit(5,1);
result:
0, 0, 0, 0, 1
That 's not the answer for the excercise. What is the problem?

## How do I solve a simple line integral in Maple?...

Hello there. I have to solve a simple line integral (3*y-x)dL from A(2;1) to B(3;-1). A and B are points in the line described by function y=5-2x. I found a function LineInt. Using paramether Line I wrote LineInt(3*y-x, Line(<2, 1>, <3, -1>)), it doesn't work with error below:

Error, (in Line:-ModuleCopy) invalid input: invalid specification of line

It seems that the problem is with first argument, that is the equation under the integral sign. Or no... How to write it properly? Thanks.

## Simple Integral of Product Gives Wrong Results...

Hello,

I've got the following problem: Sometimes when I let Maple compute an integral it gives a result which is much smaller than it should be. This happens even for rather simple integrals such as the product of a Gauss function and a 1/x-type function. Here's a minimal working example:

restart;
with(plots):
f := x -> exp(-x^2):
g := (x,a) -> 1/(1+abs(x-a)):
plot([f(x),g(x,3)],x=-3..10):
for a from 1 to 100 do
A[a] := int(f(x)*g(x,a),x=-infinity..a-1)
end do:
B:=[seq(A[a],a=1..100)]:
X:=[seq(a,a=1..100)]:
plot(X,B);

The plot it returns looks like this:

which is clearly wrong between around a=35 and a=60...

Does anyone have an idea how this can be repaired?

## How do I connect 3 arms to a single part with revo...

I have created a model for a robot in Solidworks and have imported it into Maplesim using the CAD toolbox. The problem I have is that the robot has 3 arms that are supposed to come together on a central piece pictured below in figure 1, but attempting to simulate the model with all arms connected with a revolute joint as in figure 2 yields an error that says "The system is underdetermined" the location of the error is main.

For the purposes of the image below I only connected one of the arms, this allows Maplesim to run the file successfully.

figure 1 showing the central piece that the 3 arms are supposed to connect to.

Figure 2 showing the problem revolute joints circled in black, the error at the bottom and the setting of the revolute joint on the right.

Essentially my question is how do I get the model to work? I apologise if this problem is not terribly well demonstrated, this is my first post onto this forum so I am not sure of all the standards.

## Maple TA 2016: Lists depopulate in adaptive questi...

I am currently working on an adaptive question in Maple TA 2016 and it seems that there is a bug in the drop - down list functionality:

After I click "Verify" in a section, the answer disappears even though I choose it to be displayed. The window simply goes back to showing (Click for List) instead of keeping the answer, see the screenshot below.

Perhaps I am doing something wrong, though I have used Lists extensively in the previous version and never had that problem ..

Elisabeth

## ODE boundary value problem ...

It is known that ODE boundary value problem is similar to the problem of solving systems of nonlinear equations. Equations are the boundary conditions, and the variables are the values of the initial data.
For example:

y '' = f (x, y, y '), 0 <= x <= 1,

y (0) = Y0, y (1) = Y1;

Where y (1) = Y1 is the equation, and Z0 is variable, (y '(0) = Z0).

solve () and fsolve () are not directly suitable for such tasks. Directly should work the package of optimization in relation to a system of nonlinear equations. (Perhaps it has already been implemented in Maple.)
Personally, I am very small and unprofessional know Maple and cannot do it. Maybe there is someone who would be interested, and it will try to implement this approach to solving ODE boundary value problems?

## Problem with differential operator...

hi.please see attached file below and help me.one problem is apply differential operator on matrix and then caclute 3D integral?

maple2.mw

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