@vv 

thanks,. I did not know about Basis. I was using the book definition of ColumnSpace. 

 I paste it into MathType, could not get the required equation

The Maple latex generated is valid. Compiled OK using TexLive on Linux and using MikTex on windows.

Therefore, I suggest contacting Microsoft  or MathType customer support asking them why it did not work in their software. This is not an issue with Maple that I could see.

you could check this post 

https://math.stackexchange.com/questions/345922/algorithm-to-check-if-a-matrix-is-elementary

and tanslate the code to Maple

why not give an small example of an input matrix, this way one does not have to make one up and guess wrong?

You could map type/numeric.

https://www.maplesoft.com/support/help/Maple/view.aspx?path=type%2Fnumeric 

"check for an object of type numeric"

@tomleslie 

Thanks for the observation. I used list for unknowns, to make the the order match the order of the ode's given which is also in a list and not a set. I do this all the time actually, I did not think this would make a difference. 

It is not a big problem, since both answers are correct, but it would be nice if same solutions came out the same.

looking at help page for Dynamic systems, there is no equivalent command in Maple for imp2ss. At least I could not find it looking at all the commands there.

This is a system identification problem (or system realization). Given an impulse response, estimate what the system that could have generated this would be.

@acer 

When making the pattern, it is ofcourse up to the person to decide when the pattern is valid or not.

The only difference between using the pattern and using Maple's other commands, is that the assumption in the later case is explicit.

For example

restart;
expr:=sqrt(A)*sqrt(B);
combine(expr,radical) assuming B>0

vs.

unassign('a,b');
patmatch(expr,sqrt(a::anything)*sqrt(b::anything),'la'):
assign(la);
sqrt(a*b);

In production code, one would add comments next to pattern so that to make it clear when it is valid, or add extra logic to check. But it is up to the programmer who made the pattern to know when the transformation is valid or not.  

@janhardo 

These are textbooks we used at school, I found them good:

Elementary Differential Equations and Boundary Value Problems, 10th Edition. William E. Boyce,200e Richard C. DiPrima

and

Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 5th ed. Richard Haberman

For Fourier Series background, this was the textbook we used

Fourier Series and Boundary Value Problems, 8th edition by Brown

Just like learning anything in math, solving as many problems as you can by hand, and then using the computer to check your answers is a good way to improve ones skills.

 wish to assign the values 1 and 7 to x

  How could a variable have 2 different values at the same time? Or do you want x to be the list [1,7] or set {1,7} ?

@vv 

sure, thanks. I know I could do this. But It seems to me copy folder should be part of FileTools along with the many other commands there (which could also be done using system calls if needed). The whole idea is that FileTools puts a generic layer between system specific calls and Maple so the code works on any platform.

@Carl Love 

This unfortunately does not always work. As Maple can return free variables such as _t2[3] and _t0[5] and _t[7] and so on. Each time it is called, it is different.

in math, you can not take derivative with respect to a sum. So

            diff( f(a,b), a+b) 

makes no sense. (At least at school the teacher never mentioned such a case)

The argument to diff needs to be a symbol.  

@Carl Love 

"Thus, it's safer to use x__1."

This is good to know. This is what I ended up using. I also found that x__(t) is a little easier to read in the editor than x[1](t)

@Carl Love 

"

• There is an algorithm to generate another (linearly independent) eigenvector from this same eigenvalue called the defective eigenvalue method.

The algorithm that you speak of does not generate (true) eigenvectors; rather, it generates generalized eigenvectors. Given the matrix A and vector v__2 from your example, you can easily check that A.v__2 <> 3*v__2, and thus v__2 is not an eigenvector."

Yes, they are called generalized eigenvectors and this is what our textbook uses. So I am following it.

I was asking if Maple implements this algorithm. i.e. I give it v1, and the number of missing eigevectors needed, or giving it A, and the defective eigenvalue, and it will generate all the eigenvectors associated.

I know how to do it by hand, (solved many problems like this) but I wanted to automate/program it.

I have to use this algorithm and not Jordan form method since this is what our text uses. It is not hard to code it. I just wanted to know if Maple has a package that allready does it.

Reference: Differential equations and linear algebra. 4th edition. Edwards,Penney, Calvis.

@ecterrab 

Thanks, I did not know about "PDEtools/max_C". That is a good function.

"suppose you know the differential order of the equations you are handling"

I do not know for sure. These ode's are read from different textbooks by a program I wrote. In general, these will be low order ODE's, since the books I use are for undergraduate.  Also, there are systems of linear ode's, and not just one single ODE. The A matrix for the system of linear ode's can be large.

So I thought it will be better to be general on the largest number for _Cn.  I do not like to hardcode numbers inside a program if I can avoid it.