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17 years, 66 days
PhD in Numerical Optimization.

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These are questions asked by Konstantin@

Here is a toy example

L:=<<1 | 2 | 3>; <4 | 5 | 6>>; 
(L[1,2], L[2,3]):=(0 $ 2):

As expected, L now equals <<1 | 0 | 3>; <4 | 5 | 0>>

Now I want to make a bulk assigment with the use of seq operator

(seq('L'[q,  q+1] , q=1..2)) := (0 $ 2);

but it fails. Nevertheless

seq('L'[q,  q+1] , q=1..2)

works as needed and returns unevaluated L[1,2], L[2,3]

Maple has powerful tools to manager styles of its documents. Similar to word processors, it is possible to set up font and paragraph options. Unfortunately, the styles of Help System, as I understand, are completely unchangeable. Meanwhile, it makes sense to improve the view of Help pages. Say, Help’s hyperlinks are pale and unpleasant  for eyes. Maybe, are there some hidden options for changing Help styles?

Earlier smoothly working generation of normal distribution in v. 2019 unexpectedly shows the error:

RandV  := Statistics[RandomVariable](Normal(0, 1));
Statistics[Sample](RandV, 10);

Error, (in p) unable to convert Float(undefined) to an integer


The issue concerns calculation of 2nd derivative of the numerical solution of 2nd order BVP for an ordinal DE.

Lets consider a test problem:


y(0)=0.2, y(1)=1

 Numerical solution was obtained by

dsolve([-diff(F(x), x$2)+F(x)= x*sin(5*x), F(0)=0.2, F(1)=1], [F(x)], type = numeric, 'output' = Array([seq(k/5, k=0..5)]));


dsolve returns the values of the solution and its 1st derivative (for the test example, a solution can be obtained analytically, but for general case I require numerical solution)..

It is needed to calculate the 2nd derivative of the solution.

I tried to use the Bessel method, when the solution’s 2nd derivative is calculated as the 2nd derivative of 5th degree polynomial having in consequent points t1, t2, t3 the values y(t1), y(t2), y(t3) and 1st derivatives y’(t1), y’(t2), y’(t3), all obtained from the numerical solution. Later I use Hermit piecewise-polynomial interpolation, based on values of the solution and its 1st and 2nd derivatives (polynomial of 5th degree).

Unfortunately, 2nd derivative of such interpolation has a large non-smoothness.

Here, we see the solution. It is smooth.

Here, 1st derivative. Still smooth enough.

Here, 2nd derivative. Typical view with large and sharp teeth.



Maybe, there exists a simple method for calculation of more smooth 2nd derivative?

Also. it is desirable that it would be embedded in Maple.

Dear friends,

I noticed that the function numbcomb from the package combinat fails to calculate a value properly.

Let's try to calculate the example from the function's help page:

combinat[numbcomb](7, 3);
combinat[numbcomb](5, 4);

returns 35, 5 correspondingly, whereas should be 15 and 4.

Please, check this in your systems. Maybe, this is a bag in my installation?


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