@al-faraj The commands solve and eval are very different---nearly the opposite of each other. If you have an expression with x and you want to change (or substitute) the x with 17, then the command to use is eval. If you have an expression with x and you want to rearrange it so that the x is isolated on the left side of the equal sign, then the command to use is solve.

Why I say that they are nearly opposite: with solve Maple can tell you that x = 17; with eval you can tell Maple that x= 17.

By the way, I didn't ask for an explanation of what you were doing; I asked to see your code. I understand what power regression is.

@testht06 Please proofread your Replies carefully. Okay, I understand the encoding scheme now. Are you sure that that coefficient is 213? I have checked many different ways, and I get 231 every time. If this is because of a different version of Maple, it will be important to investigate what causes the difference. And note that you misentered the field extension above as x^8+y^4+y^3+1.

And you still have not explained what 256^256 = 487 means.

@ 

I am a committed user of the 1D input. But I do disagree with you about .mws versus .mw. The dichotomy is better known as Classic GUI versus Standard GUI. Yes, Standard is a little slower, and yes, Standard uses a lot more RAM. But there are many features, especially many plotting features, that are only available in Standard. One notable feature of Standard is Code Edit Regions. This is a much easier way to manage a code of a few hundred lines than is a Classic worksheet.

While Standard does use significantly more RAM, so do almost all modern programs. The amount that it uses is usually insignificant on my 16GB system.

Like I said before, the only coefficients in the field GF(2^8) are 0 and 1. So what do your 27, 16, 37, 217, 213, and 30 mean? Is that some way of encoding the 256 polynomial members of the field? For example, does your 16 represent alpha^4 where alpha is root of x^8+x^4+x^3+1?

You wrote,

The factors of this polynomial are: (x + 37)(x + 217)(x^2 + 213x +30) (in maple)

Can you show the Maple command that gave you this?

Furthermore, x^8+x^4+x^3+1 can be factored mod 2, so it doesn't define a valid field extension! My guess is that you mistyped that when you posted and that you meant x^8+x^4+x^3+x+1.

If I make the above correction and use the natural binary encoding scheme, then I get that the factors are (x+37)(x+217)(x^2+231x+30). Note that my coefficients are slightly different from yours: I have 231 instead of 213.

Finally, what does 256^256 = 487 mean? I can't wrap my head around that in any encoding scheme.

@khoirun 

Like the error message says, your system probably does have a singularity at .73473335. If so, that's a mathematical limitation---not a Maple limitation---and there's no way around it. If you believe that the error message is incorrect---that there actually is no singularity---then post your code and someone here will look at it and give you an opinion. It would be best if you posted the code as a new Question rather than appending it to this thread.

I can't see anything wrong with your code as posted. There may be an extraneous invisible character in your worksheet. I am suspicious about the superfluous parentheses around the 2 in -(2). Please upload your worksheet.

Or, just retype the command on a new line. Like I said, I don't see anything wrong with your command. Explicitly retype it---don't cut and paste.

@khoirun You misspelled the command name. It is DEplot3d, not ODEplot3d. Since it is in the package DEtools, you need to either issue the command with(DEtools), or refer to the command as DEtools[DEplot3d].

@Kitonum 

This is an aside, just a coding tip for Kitonum: When you use option remember, there's no need to explicitly assign entries in the remember table. They are assigned automatically. So, your code could be

M:= proc(k::nonnegint, n::nonnegint)
option remember;
     if k*n = 0 then 0
     elif k = 1 then n
     elif n = 1 then 1
     else M(k,n-1)+M(k-1,n-1)+M(k-2,n-2)
     end if
end proc:

Or, looked at another way, your code would do the same thing without option remember because you explicitly assign the remember table entries.

@jan123 Is there any software that tackles the problem of multivariate recurrences? The complexity of the problem compared to univariate recurrences is akin to PDEs compared to ODEs.

Your differential order is two in both independent variables. So, you need another layer of boundary/initial conditions.

Suppose we try to compute M(2,2) from your definitions above. We get

M(2,2) = M(2,1) + M(1,1) + M(0,0) = 1 + 1 + ???

@testht06 The only coefficients in the field GF(2^8) are 0 and 1. Yet you show coefficients 27, 37, 217, 213, 30. Are you talking about the ring Z(2^8) = Z(256)? And I don't know what 256^256 = 487 means even if you are talking about rings.

You should ask this as a separate Question.

@testht06 Ah, you must be using an older version of Maple. I retrofitted the code in the Answer at the head of this subthread, and it should now work in current and older Maple. Please download the new code and let me know if it works (I don't have the older Maple to test it myself).

@In-Jee Jeong 

You need to post a worksheet showing exactly what commands you're using and showing the error message.

@testht06 

Like I showed above, your x needs to be a field extension represented as a root of an irreducible polynomial. This is done with alias and RootOf like this:

alias(x= RootOf(y^8+y^4+y^3+y+1)):

Do this before entering the matrix.

@testht06 

That would be a lot of work, if it is possible at all. The procedure GFM seems to me to be a crude and minimal implementation of matrix algebra over finite fields. The machinery provided by mod (see all the subcommands listed at ?mod) seems much more complete. In particular, my two procedures depend on the commands Roots and Linsolve in the mod package. Please try to convert your application to use mod.