9 years, 93 days

## @Preben Alsholm Given the definitio...

Given the definition of the integration over an infinite domain (simply definition in the sequel):

`int(C, x=0..+infinity) = limit(int(C, x=0..a), a=+infinity);`

one gets

```limit(int(C, x=0..a), a=+infinity);
eval(%, C=0)
signum(C) infinity
undefined
```

In the other way

```limit(int(0, x=0..a), a=+infinity);
0
```

Does this difference comes from the way eval acts?
---------------------------------------------------------------------------------------------------
Now consider this

```int(0, y=0..1, x=0..+infinity);
undefined
```

But, applying the definition:

```int(limit(int(0, x=0..a), a=+infinity), y=0..1);
limit(int(int(0, y=0..1), x=0..a), a=+infinity);
limit(int(0, y=0..1, x=0..a), a=+infinity);
0
0
0
```

So, do we have to consider that Maple doesn't apply the definition when it directly computes the integral?

## Agree!...

Even if the result is very pretty, it xwould have be nice to knowm how this (extremely complex) eqyation has beeen derived.

To @vv : give a look to this site
https://www.researchgate.net/publication/368438992_CREATING_3D_GRAPH_EQUATION_by_DHIMAS_MAHARDIKA
it contains a few other amazing images but the full article is not free.

To @Mahardika Mathematics : do you have a free paper about your work?

## @Thiago_Rangel7 If you prefer the w...

If you prefer the way MMA simplifies expressions, why don't you use MMA instead of Maple?

I wonder if I'm not going to some Mapleprimes-like forum about MMA and ask
"Why doesn't MMA simplify it to (e + r)/cot(alpha/2)?", just to have an idea of what the answers will be.

## That's impossible...

The only"properties one can define for a NewDistribution those ones  List_of_properties.mw

It took me a lot of time to find where this information, and as some others about random variables, where hidden in the Statistics package.
I guess that the properties Parameters and ParentName, that any KnownDistribution has, are used elsewhere for some internal purpose.

## @MaPal93  Sorry for this late ...

Sorry for this late reply but I won't have much time to spend with you from now on as I have just returned to work.

Concerning your not that naive question: "by hand" simplification often involve non explicit knowledge (for instance a variance is a strictly positive quantity, a correlation coefficient rho verifies abs(rho) <= 1, and so on).
If you want Maple to simplfy an expression must set explicitely all the assumtions which seems implicit to you.

Here is your file with simplified expression for the lambdas.
(NOTE that I didn't run your code for I don't have time: I just copy-paste some expresssions into a variable Z ans simplified Z).

Analytical_SOL.mw

## @RezaZanjirani    ...

 > restart
 > Z := (beta__c*y__c^2 + beta__m*y__c*y__n + beta__n*y__n^2)/(2*h*(-r__c*y__c - r__n*y__n + h)) + (beta__c*(1 - y__c)^2 + beta__m*(1 - y__c)*(1 - y__n) + beta__n*(1 - y__n)^2)/(2*h*(h - (1 - y__c)*r__c - (1 - y__n)*r__n)):
 > sys := {diff(Z, y__c) = 0, diff(Z, y__n) = 0}:
 > solve(sys, [y__c, y__n]);
 (1)
 > infolevel[solve]:=100: solve(sys, [y__c, y__n])
 Main: Entering solver with 2 equations in 2 variables Main: attempting to solve as a linear system Main: attempting to solve as a polynomial system Main: Polynomial solver successful. Exiting solver returning 1 solution
 (2)
 > SolveTools:-PolynomialSystem(sys, {y__c, y__n});
 Main: polynomial system split into 1 parts under preprocessing Main: trying resultant methods PseudoResultant: normalize equations, length= 4401 PseudoResultant: 15047473 [1 7000392304 y__c] 2 2 4401 2 107 0 PseudoResultant: factoring all equations length = 4401 PseudoResultant: factoring done length = 4401 PseudoResultant: normalize equations, length= 5467 PseudoResultant: 3917948 [1 4033335347 y__n 1] 2 2 5467 2 107 0 PseudoResultant: normalize equations, length= 4898 PseudoResultant: normalize equations, length= 5452 PseudoResultant: 592024 [1 100005376 y__n] 2 2 4898 2 107 1 PseudoResultant: normalize equations, length= 1300 PseudoResultant: 408832 [1 200169041 y__c] 1 1 1276 2 78 1 PseudoResultant: normalize equations, length= 3 PseudoResultant: -10 [] 0 0 3 0 3 1 PseudoResultant: 4229639 [1 4233342435 y__n 2] 2 2 5452 3 123 0 PseudoResultant: normalize equations, length= 5060 PseudoResultant: normalize equations, length= 5271 PseudoResultant: 1672501 [1 700025440 y__n] 2 2 5060 3 123 1 PseudoResultant: normalize equations, length= 8883 PseudoResultant: 1953068 [1 700028504 y__n] 2 2 5271 4 301 1 PseudoResultant: normalize equations, length= 15387 PseudoResultant: 2065476 [1 700026140 y__n] 2 2 8883 3 123 1 PseudoResultant: normalize equations, length= 8228 PseudoResultant: 2918733 [1 700042247 y__n] 2 2 15387 4 301 0 PseudoResultant: normalize equations, length= 14354 PseudoResultant: 1 solutions found, now doing backsubstitution PseudoResultant: backsubstitution of y__c PseudoResultant: backsubstitution of y__n
 (3)
 >

@Scot Gould

Thank you Scot

## @ecterrab My apologies for being so...

It lifts the veil on this mysterious (for me at least) package.

Great thanks

## @tjxkdcl There is no such things in...

There is no such things in Maple (Ridge, LASSO, LARS, ...).
I've written my own code for Ridge regression (which is the simplest method, just look to the formula in my first reply).

Simple Ridge regression algorithms generally proceed this way:

1. Define a range D of prior values for lambda.
2. Take a value of from D.
1. For this value of lambda compute the minimizer w(lambda) according to the formula I sent you.
2. Assess the "quality" of this lambda (see below).

Assessing the "quality" of lambda:
This is usually done by using some resampling method (often cross-validation or Leave-k-out) which, all take the following form:

1. Split, randomly or not, your data base in two disjoint sub-bases (let's say L and T).
2. Using subase L: compute w(lambda) for a given value of lambda (alg. above) (previous algorithm).
3. Compute the prediction error w(lambda) gives on sub-base T.

This pseudo-code is to be executed a large number of times to reduce the splitting effect,
(note that the w's you get at point (2) are all different, thus are the prediction errors you get: but they all are a realization of the prediction error associated to the particular value of lambda you used).

So, to be clear, if you take 100 lambda values within the domain D and assess the prediction error through 100 (L, T)-splitings, you have to run 10^4 computations.
The best lambda is the one which minimizes some criterion, for instance the mean of all the replicates of the prediction error.

Let me know if you need more help.
(I'm going to sleep right now).

## @ecterrab Thank you Edgardo for thi...

Thank you Edgardo for this detailed answer.

I really feel that Physics is a world within Maple.
For instance, why are there so many updates and why are they not synchronized with the version changes of Maple?
Why is Physics such a special package?

@C_R

Maybe I didn't explain myself correctly but your example is not relevent.

• Physics, example
• Second section Mechanics
• First subsection Static: reactions of planes and tensions on cables
• "and the solution is eq 2.1.17
`{abs(R[A]) = cos(alpha)*abs(w)*sin(beta)/(2*sin(alpha)), abs(R[B]) = abs(w), abs(T[A]) = cos(alpha)*abs(w)*cos(beta)/(2*sin(alpha)), abs(T[B]) = cos(alpha)*abs(w)/(2*sin(alpha))}`
• Obviously abs(T[A]) is not necessarily positive (take beta=0 and alpha=3*Pi/4 for instance).
Then: what does abs(...) mean in the Physics package notation?

## @Carl Love Thanks Carl, sorry for t...

Thanks Carl, sorry for the inconvenience

## @permanoon123 Still a lot of errors...

@permanoon123

Still a lot of errors:

• As you perform an integration over x, C is a function of t alone.

• You missed many " * " symbols (a common error for people using 2D input mode).
For instance tou wrote `n &pi;x` instead n*Pi*x (copy paste your expression into a 1D input mode worksheet).

• It's quite simple to see (after having corrected the previous error) that the value of the integral is
`3250 * f(t) * exp(-lambda^2*t)`

(just put the terms containing t out of the integral and even out of the Sum])
Thus C, which is an infinite sum of this value is infinite too.

HINT: You probably wanted to write

`sin(n*Pi*x/L)*sin(m*Pi*x/L)`

? But even in this case

`sum(int(sin(n*Pi*x/L)*sin(m*Pi*x/L), x=0..L), m=1..+infinity) = 3250  # whatever the value of n`

I can't do anything more for you;
Correct your own equations and come back if you still have a problem.

## None of what you are looking for (PLS, P...

None of what you are looking for (PLS, PCR, KNN [see your previous question]) is avaliable in Maple.

Concerning KNN: if I'm not mistaken I think @Carl Love posted an implementation of it, let's say less than a year ago.
Try and search this within the "Posts".

Concerning PLS and PCR I will provide you two codes in a few hours (I need to extract them from a larger project I'm working on and make them work in an autonomous way... so it takes time).
See you soon.

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