## 4867 Reputation

6 years, 363 days

## For information...

Maple 2015  returns the closed form of this integral whatever the input mode (which both behave the same way)

int_warning_1D_2015.mw

int_warning_2D_2015.mw

## @Carl Love Thanks!I use the combina...

Thanks!
I use the combinat package on regular basis but randcom never caught my eye.

## @dharr I didn't know about ...

I didn't know about _EnvUseHeavisideAsUnitStep, whose role is nevertheless clearly stated in Heavside's help page.

It indeed can be a usefull way to remove isolated points where the expression is undefined, but don't you think it's quite dangerous is used blindly?

Here is an example which describes the Coulomb's static friction model.
The piecewise function represents a physically correct model  (while extremely notional) of the variation of the friction coefficient c according to the relative slipping velocity at the contact point of two bodies.

```f := piecewise(v < 0, -c, v=0, 0, v > 0, c)
piecewise(v < 0, -c, v = 0, 0, 0 < v, c)

_EnvUseHeavisideAsUnitStep := false;
convert(f, Heaviside);
eval(%, v=0);
false
2 c Heaviside(v) - c
c undefined - c

_EnvUseHeavisideAsUnitStep := true;
convert(f, Heaviside);
eval(%, v=0);
true
2 c Heaviside(v) - c
c

```

I do prefer the default _EnvUseHeavisideAsUnitStep := false which warns me that there will probablity face later some difficulties, than  _EnvUseHeavisideAsUnitStep := true which seems to say that there will be no problem at all and provides a wrong value at v=0.

For information the numerical treatment of problems invoking this Coulomb's model generally regularize the expression f by writting instead f := c*tanh(v/eps) where eps is a "small" positive number.

For the OP problem I believe that the first thing do do before removing the isolated points where the onverse Laplace transform i undefined, is to check if the left and rightlimites are equal (which happily happens to be the case here).

```restart;
expr:=(s+exp(-Pi*s)-exp(-2*Pi*s))/(s*(s^2+2*s+2)):
y := inttrans:-invlaplace(expr,s,t):

limit(y, t=Pi, left), limit(y, t=Pi, right);
0, 0

limit(y, t=2*Pi, left), limit(y, t=2*Pi, right);
1 + exp(Pi)  1 + exp(Pi)
-----------, -----------
2 exp(Pi)    2 exp(Pi)
```

I nevertheless vote up: for the simplicity of the trtick, even if I'm not convinced of its lack of toxicity

## @tomleslie It's difficult to ad...

It's difficult to admit that Statistics:-AutoCorrelation and Statistics:-CrossCorrelation don't have consistent definitions (the former operates on a mean-shifted vector while the latter works with raw vectors) given that CrossCorr(V, V= = AutoCor(V) by definition.

I keep considering this inconsistency as an error of the same order than a confusion between moments and non centered moments.
But you are free to think otherwise.

## @tomleslie Ypu wrongly onterpreted ...

@tomleslie

You wrongly interpreted what you read here https://en.wikipedia.org/wiki/Autocorrelation.
You confused autocorrelation function and autocovariance function.

## @Elisha Here is your file corrected...

Please look to the parameters q__E (and not q[E]) and sv0 (shich appears as s__v*0 in 1D input).

in dsolve the option parameters requires a list of names, but in the "instanciation" of the solution (solparameters requires a list of values.
An alternative which avoids using the option parameters during the "instanciation"  is given  at the end of my reply.

Covid19_Simulation2-2_mmcdara.mw

## @Carl Love  Thank you Carl for thi...

@Carl Love

Thank you Carl for this extremely interesting (ordered) set of explanations.

The --setsort entry contains a lot of useful informations.
In particular the example s := {bb, aaaaaaaa} whose displayed order ("internal memory order " too?) is based on the length of the elements.
The --setsort option seems to be only avaliable through the Maple command mode, am I right?
Unlesswritting sort(convert(s, list), lexorder), would have been a way to impose the lex order on the set s?

I do remember sets ordered in a different way from one session to another. I even think this "nuisance" lasted a little bit longer than Maple 8.

I agreee.

The problem I submitted comes from the transformation of a system of ODEs of arbitrary orders into a system of first order ODEs alone.
The selection of the dependent functions (F) and the derivatives through which they intervene (DF) is descibed below (the system comes from a recent question on this site).
My algorithm to transform this system into a first order ODE system starts from the rightmost element of each set in DF an ends to the leftmost one, inrtoducing intermediate functions at each move.
But it didn't work due to the different "true" orders (by opposition to the "displaying orders") of each of these sets.
(I did otherwise meanwhile)

 > restart:
 > odeSys := {diff(Theta(x), x, x)+Pr*(R*(diff(Theta(x), x))*f(x)+Nb*(diff(Theta(x), x))*(diff(Phi(x), x))+Nt*(diff(Theta(x), x))^2), N2*(diff(G(x), x, x))-N1*(2*G(x)+diff(f(x), x, x))-N3*R*((diff(f(x), x))*G(x)-f(x)*(diff(G(x), x))), diff(Phi(x), x, x)+R*Sc*f(x)*(diff(Phi(x), x))+Nt*(diff(Theta(x), x, x))/Nb, (1+N1)*(diff(g(x), x, x))+R*((diff(g(x), x))*f(x)-g(x)*(diff(f(x), x)))-M*g(x)+2*Kr*(diff(f(x), x)), (1+N1)*(diff(f(x), x, x, x, x))-R*((diff(f(x), x))*(diff(f(x), x, x))-f(x)*(diff(f(x), x, x, x)))+N1*(diff(G(x), x, x))-M*(diff(f(x), x, x))-2*Kr*(diff(g(x), x))}:
 > # print~(odeSys):
 > DF0, F := selectremove(has, indets(odeSys, function), diff): F; print(): DF     := convert(map(u -> select(has, DF0, u), F), list): print~(DF):       (1)
 >

@Carl Love

Thank you Carl.

## @vs140580 The reason is probably th...

The reason is probably the word "+" in the file name, try this one and let me know.
PLS_PCR_Linnerund.mw

## I advise you to start by searching for t...

I advise you to start by searching for the word homotopy on this site.
You will probably find some interesting things.

I think if you want someone to help you, you should provide a Maple code instead of an excerpt from a PDF file that nobody here is willing to code themselves.

## @Kitonum Both @tomleslie and I...

Both @tomleslie and I have already answered the same thing to a previous question
https://www.mapleprimes.com/questions/235674-Chevrons-Lemma.
It seems that @JAMET ​ does not read the answers it's been provided.

@JAMET

I also notice, as @tomleslie pointed out recently, that yours questions never provide any worksheet, a remark that obviously did not change your attitude..
I find this latter contemptuous and would personally make it a point to never respond to you again.

## @vs140580  By the way, it happens ...

@vs140580

By the way, it happens that one of the best book ever (IMO) on data mining, inference and prediction is freely avaliable:
https://hastie.su.domains/Papers/ESLII.pdf

In my paper version Chapter 13 is entirely devoted to Nearest-Neighbors methods.
Several algorithms (sometimes in pseudo code are provided too).

PCR is described in pp 79-80, PLS in pp 80-82 and, more generaly, regression methods in Chapter 3.

## @Carl Love  Yeah, it was indeed cl...

@Carl Love

Yeah, it was indeed clustering.
I don't remember exactly what you did but KNN is just a particular type of clustering.
Maybe this could help @vs140580

## @Delali Accolley  I consider that ...

@Delali Accolley

I consider that I have spent enough time trying to explain to you why your problem is not correctly set.
You have obviously paid no attention to my arguments and keep getting the same error again and again.
Please consider me finished with you.
I hope you find a more conciliatory ear than mine.

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