Something about substitutinn B[i, j] by some expression?
Here is the file this question contained m1.mw

Whatever here is my answer m1_mcdara.mw

PS:
It seems to be a custom for you to delete your own questions, isn't it?
I don't think this attitude is appropriate, even if you've realized in retrospect that these questions are no longer of interest for whatever reason. 
If I regularly protest against deletions by moderators, it's not because I want users to do the same; this will undermine their credibility in the long run.

@FZ 

Does this question have anything in common with Hirota's derivation?
(By the way your comment in red is not clear.)
If this has indeed something to do with the Hirota derivative have a look to these files
Sawada_Kotera_(Hirota_form).mw
Hirota_derivative_KdV_equation.mw
Hirota_derivative_Sawada_Kotera_2.mw
Hirota_derivative_KdV_equation.mw
Hirota_derivative_KdV_equation_2.mw

@acer 

I agree, and if I'm not mistaken Janhardo asked about the same question than me.

@vv 

Strange remark coming from you...
Let's drop it, it's a waste of my time.

@vv 

Maybe I wasnt clear?

For a set of initial positions and velocities there is only one solution, which can be either 4 or 8 depending on those positions and velocities.

In your answer you wrote (so, 2 solutions, AREA=4 and AREA=8).
And I keep saying NO it is AREA=4 or AREA=8 (you can say x^2=1 has 2 solutions x=-1 and x=+1, but the and is not correct in your claim)

Here is an illustration where I use the Heron's formula

animation.mw

@vv 
(copy to @Kitonum)

You wrote "abs is necessary because we want an unoriented area (Area(ABC) = Area(ACB))."

I'm not okay with that.
There are never two solutions as you say: either the solution is area(10)=4 Or (exclusive) it is area(10)=8 .
What makes a solution to be 4 or 8 is the fact that the area becomes 0 somewhere in betwwen 0 and 5, or not.

A correct expression of the solution should be

• If the area is strictly positive in the range t=0..5, then the solution is 4
• If it gets to 0 somewhere in between 9 and 5, then the area is 8.

(I didn't try to verify that if the area is strictly potitive in the range 0..5 then it remains strictly positive in the range 5..10 too.

So, in my opinion, using abs is not correct as it leads to 2 solutions

ABC_area_falls_to_0.mw

I don't know hot to get this piecewise solution with maple (I mean using built-in functions and without writing a procedure)

I use Maple for graphic purpose an for pretty displaus but it is not at all necessary (whas it a challenge to use it).

ABC.mw

Assuming all the velocities have the same sign we get by hand "the area at t=10 is equal to 4" (5 units of time increase the initial area by one then 10 units of time increase it by 2 as the transformation is a dilatation along rhe parallel lines)

Why does @vv code provide then two solutions?
Removing abs in line area := -> ... removes the second solution: is abs necessary?

@nm 

Did you find this by trial and error? Or was it by accident?
IThat's what I've always done, and I'd probably have been very confused if the reverse order hadn't produced the desired result.
In fact the Grid:-Set help page says "The Set command sets variables in remote parallel compute nodes." ... so I guess I found natural to do Grid:-Setup before Grid:-Set in order this latter command knowson which processors it has to set variables or procedures.
But yeah, I was also probably lucky.

Or do you think this is a bug I should report it?
I don't know, it seems to me there is som logic in placing Grid:-Setup before Grid:-Set, but one could also say that Grid:-Set is a kind of statement which tells all the nodes "hey, I'm going to use the function ...ok", and then Grid:-Setup declares the nodeswhich are going to be used.
Maybe it's not a bug, but surely an undocumented feature that should be reported.

@nm 

I did almost the same thing you did and got the same lack of results.
I tried using LibraryTools to display the Grid:-Run function and understand how the printer option works.
And, of course, advanced search is of no help.

Grid:-Run help page says:
The printer option specifies a procedure that will be called with a string every time there is a line of output available from an external computation. The printf command is the default if no custom procedure is supplied.   The printer is called with a single argument, a string, that represents intermediate printed output from each of the nodes.

I've tried unsuccessfuly to figure out how to use this option (no example provided in my 2015 version).

Maybe you will bemore astute than me.

@C_R 

The same feature exists with Maple 2015.
I'm gong to check if it fixes my issue.

Thanks for the tip.

@salim-barzani 

You can change the cokors as you want (things to play with are yellow highlighted in theattached file)

graph-density-adjusted_colors.mw

PLOT3D examples:

@acer 

That is exactly what I wanted.
More: the way you define T by modifying its font will be very useful to me for making more readable a training session about Statistics I'm working on.

PS: Sorry for the poor wording of my initial question.

@acer 

And I wouldn't have mentioned it.

My goal is to define a binary operator (T) .
I looked to the operator, binary help page and saw that &<name> was neutral binary operator neutral, but I git this

`&T`(a, b)
                             a &T b

So I thought 

(1) to use  define and write something like 

define(T, 'binary');

# and hoped to get 
T(a, b);
          a T b

but  'binary' is not a property of define.

(2) use an already existing binary operator, for instance union, and define an alias of it 

restart
alias(T=`union`):
`union`(a, b)
                            T(a, b)    # not a T b

Nevertheless your answer, like @dharr's are probably enough for me.

Thank you both.

@C_R 

Thanks for the encouragement.
I'll think about your suggestion but I think there may be other members here who are more qualified than me on the subject.

I got a master in signal processing about 35 years ago but ketp another route for years now.
So my memory is quite partial on the subject and my skills have slowly become blunt.

But I'll try to think about it

@C_R 

I bought more than 30 years ago an excellent introduction to chaos (in French) by Bergé, Pomeau and Vidal.
Here is the 1987 English edition (oldies but goodies)

Order within Chaos

Berge, Pierre; Pomeau, Yves; Vidal, Christian
Wiley-VCH, 1987
ISBN 10 : 0471849677 / ISBN 13 : 9780471849674

I don't now if a legit pdf version is avaliable for free online, but it is worth to be read, IMO.

"How should it be possible to prove chaos?"

There are basically two tests for chaos detection: the Lyapounov exponent test and the 0-1 test.
For a compared study see Lok.

Here is an excerpt from the conclusion of Lok's work :
Although the 0-1 test is much more general and is suitable for the analysis
of many different dynamical systems, including experimental data, the Lyapunov
Exponent test appears to be more elegant in understanding and in use, and has
some beneficial extra’s, for example it’s ability to show super attractive fixed points.
If a phase space reconstruction is possible, the Lyapunov Exponent test is highly
favorable, but if a phase space reconstruction is not possible, the 0-1 test can be
used

In the sequel I onsider only the 0-1 test for time issues.
A simple code for the Lyapounov exponent test is given in Lok page 12 [only when the derivative of the dynamical system is known, which makes this code useless for time series]; for more details I advice you to read Wolf et al , specifically paragraph 4 An approach to spectral estimation for experimental data [a Fortran code is given in appendix B]).

Basically the 0-1 test answers 0 (or something close) if the system is regular and 1 (or about) if it is chaotic.This test doesn't enable determining the periods of when the system is regular.
A few examples aboout the 0-1 test can be found  here.

 0-1_test_for_chaos_detection.mw  is a fairly elementary code to decide if the logistic map

f := (x, r) -> r*x*(1-x)

has a regular or chaotic regime depending on the value of r.
 

(performances were not of my concern when I wrote the code)