@acer 

f is the procedure simplify built-in Maple 

@acer 

debuger.mw 

In this worksheet, I have the same example but another possible choice of the decomposition.

The calculation needs a lot of time, so I stop it after 3 hours.

The real problem is that in the literature this method of decomposition (minimal basis decomposition:http://www3.risc.jku.at/publications/download/risc_3455/jacobson_form-middeke08.pdf ) is fast, and in this example I have maximum degree two. I wonder if I have a much higher degree, this toolbox can't decompose the matrix because of simplify.

Do you think that if we replace the cos and sin by other expressions, we could reduce the computation time and have more space in the memory?

@acer 

Hello, I use Maple 2017.3.

Thank you for these suggestions, I will try them. I attach two worksheets with and whithout simplify:

with_using_simplify.mw 

whithout_using_simplify.mw 

@acer Hello, 

I've provided an example to show the difference "Simplify" does.

First, if I use simplify I get the correct answer in the end of the procedure but I need a lot of memory and time, and if I don't use simplify I get a wrong answer, so it is mandatory to simplify in order to obtain a correct result.

Next, simplify is used in a for loop, so I asked maple to show me the result (with and without simplify) on each iteration to understand the difference that "simplify" makes and the type of simplification we need. 

On the left-hand side of the equation above, we have the expression returned by maple without any simplification, while the right-hand side is the expression after using Simplify and which we need to obtain the correct result.

Same for these examples below:

Do you know any alternative method to simplify that would yield results much faster ?

@acer @Carl Love

 I'm using and trying to further develop the toolbox under the permission of the thesis director of its developer and I have an email message proving it. But if you already know it perhaps you can help me find the "glitch" in skewSimplify that makes it computationally expensive.

I didn't intend to breach the copyrights of the toolbox I only posted a small snippet of code that I found to be problematic for me in order to ask for your kind assistance.

I explain again the problem without posting the code:

The profiling procedure has found a problem in the skewSimplifier(a procedure designed by the developper) and more precisely in the Maple built-in Simplify function. It is taking too much memory and time due to the fact that the entries in the polynomial matrix being simplified are huge. Do you know any other more efficient method that would replace "simplify" in the case of skew polynomial and skew matrices ? I join a photo of a part of one coefficient of a skew polynomial:

Thank you.

@Joe Riel 

In fact, the designer of this toolbox develloped a procedure called skewSimplifer to simplify skew polynomials and skew matrices and he used the command simplify : [moderator note: unattributed procedure source deleted]

@Joe Riel 

Hello,

I rerun the script after removing simplify but the yielded answer in not correct. I explain you what I do:

The input of the procedure is a 1*3 polynomial matrix to be decoposed using a method called Smith decomposition. 

I divided the procedure into steps, but after a few steps I found that the matrix of the Smith decomposition is very large. It is a 3*3 matrix but each entry contains a polynomial of degree 2 maximum with larg coefficients. I join a photo of a part of one coefficient: 

the notation x1D0 is to say that it is the variable x1 and x1D1 for the first derivative of x1 with respect to time..

Thank you in advance

@Joe Riel In the procedure, we add two skewPolynomial or two skewMatrix, and we want to simplify the result so we use "simplify" procedure. Do you know any other more efficient way to do so? 

@Joe Riel Yes, this line calls a procedure which I profiled repeatedly and found out that the built-in Maple function "simplify" is taking  a lot of time to execute properly. What do you think that problem might be?

Thank you in advance. 

@Joe Riel 

Hello, I tried this and on the line 117 of my procedure I have these outputs:  

Can you help me to interpret this please?

@Joe Riel Thank you, I will try it 

@bmartin 

Thank you for your kind reply.

My problem is that I have Mathematical operations involving high-dimensional matrices that require a lot of memory to compute efficiently and I'm using an already developed toolbox.

But it doesn't seem to be using multithreading or multiprocessing and it's taking forever for the operations to terminate.

Is there a way I can enable the toolbox to do multithreading without having to recode its functions and packages from scratch ? Thanks for your help.

@acer Ohh Thank you, this was helpful.

@Carl Love Thank you Carl. This was helpful.

@Joe Riel  Thank you Joe. I created it using a module with option: packages and then I saved it in a my own library using savelib. Do you think there is another method to do this?