@adel-00 You skipped one line of Doug's code:

spin:= Spin(3);

which you'll want to change to

spin:= Spin(N);

@spalinowy To do multiple equations, simply include all the equations and all the initial conditions in the curly braces that delimit the first argument to dsolve. No other changes are needed. The order doesn't matter.

I just computed the fourth root of your second matrix (from your first Reply above):

M:= <x^3+x^4+x^6+x^7+x, 1+x^2+x^4+x^5+x^6, 1+x+x^2+x^3, x^7+x^6+x^5+x^4;
x^7+x^5+x^4+x^3, x^6+x^4+x^2+1, x^3+x^4+x^6+x^7+x^2+x+1, 1+x^2+x^3+x^4+x^5;
x^7+x^5+x^2, x^7+x^5+x^3+x^2+1, x+x^2+x^6, x^2+x^3+x^5;
x^3+x^4+x^6+1, 1+x^2+x^3+x^4, x^6+x^5+x^4+x^3, x^7+x^3 >;

over GF(2) / (x^8+x^5+x^3+x+1). In this case, the characteristic polynomial is irreducible, so the splitting field has degree 32. The computations are nearly instantaneous, so the Groebner:-Basis technique is much, much better than the Primfield technique.

@Doug Meade A Matrix expression such as

< spin[.., -1] | spin[.., 1..-2] >

can be shortened to

spin[.., [-1, 1..-2]]

I don't know about the relative efficiency or about how ArrayTools:-CircularShift compares.

@Zihan You need to freeze the diff first, or else it will turn to 0 when you freeze the x(t).

@Doug Meade Your technique assumes that once fsolve fails for a particular value of T that it'll fail for any smaller T. Although that seems likely to be true, I don't think that it's a wise policy to assume it.

@Christian Wolinski 

If I make the call

Groebner[Basis]([L], plex(X,Q), characteristic= 2);

then I get results identical to yours:

[Q^24+Q^23+Q^22+Q^21+Q^19+Q^16+Q^14+Q^13+Q^12+Q^10+Q^9+Q^8+Q^6+Q^5+Q^3+Q+1, Q^22+Q^21+Q^19+Q^17+Q^16+Q^15+Q^14+Q^9+Q^7+Q^6+Q^5+Q^2+Q+X]

I wasn't aware that the term order could change the final result. I thought that it only affected the speed with which the result was obtained.

@Markiyan Hirnyk 

Your methods work on a polynomial, but not on more complicated expressions such as

sin(1+eps+eps^2+eps^3)

@Christian Wolinski The share library no longer exists. Does your version of Maple have package Groebner? Let's see if we can get the same results with that. The results that you show above would be useful for this problem because the first polynomial can be easily solved for X. If I try to do the same thing with Groebner[Basis], I get

Groebner[Basis]([L], plex, characteristic= 2);

[Q^2*X^4+Q*X^5+Q^3*X^2+X^5+Q^3+Q^2*X+Q*X^2+Q^2+Q*X+X^2+Q+1,       Q^4*X^2+Q^3*X^3+Q*X^5+X^6+Q^5+Q^3*X^2+Q^2*X^3+Q^4+Q^2*X^2+Q^2+Q, Q^5*X+Q^3*X^3+Q^3*X^2+Q*X^4+X^5+Q^3*X+Q^2*X^2+Q*X^3+X^4+Q^2+Q*X+Q+X, Q^6+Q^3*X^2+Q^2*X^3+Q^3*X+X^4+Q^3+Q^2*X+X^3+Q*X+X^2+X+1, X^7+Q*X^5+X^6+X^5+Q^4+Q^3+Q^2*X+Q*X+Q+X+1, Q*X^6+Q^4*X+Q^3*X+Q^2*X^2+Q*X^2+Q*X+X^2+1]

This result isn't useful to me because I can't solve any of those polynomials for X.

@Christian Wolinski What is "GB"? I can't find it in my Maple. Is it a Groebner Basis? Can you present an executed worksheet that implements this?

I can confirm that this user has a legitimate corrupted worksheet. Here is the file:

Download Projekt_3_-_Copy_(2).mw

I don't know how to fix this, but there are a few other users here who are expert at extracting the bad characters and repairing the worksheet. Hopefully one of them will help you with this.

@abcd I modified the code in the Answer again. I'd forgotten that `^` is a separate type from `*`. Please test again on E(TY^2).

@abhilashun Are you looking for symbolic or numeric solutions? For symbolic solution, try eliminate or solve. For numeric solution, try fsolve or the free third-party add-on package DirectSearch (available at the Maple Application Center) using guesstimates provided by implicitplot as the initial values. If the equation is polynomial, then there are more options. But from what you've said already, I'm guessing that it isn't polynomial.

I'm not saying that 2-D implicitplot is not numeric. It's mostly numeric with some small symbolic features depending on the options that you specify.

@abcd I added expand to the code in the original Answer. Let me know if this does the trick.

Regarding clicking the Thumbs-up, it's like Axel said: You sometimes need to wait several seconds for the click to register. If you get impatient and give a second click, then it negates the first click.

I know of no book on advanced Maple programming other than the Maple Programming Guide. This book is no longer published in hardcopy form, but it is available through Maple's on-board help system (see ?ProgrammingGuide).

You should be able to vote up at this point. You have 15 reputation points. If you can't vote up, it's a bug that should be reported. It doesn't require any reputation points to select an Answer as the Best Answer (the trophy-cup icon near the thumbs-up icon).

I'm not sure that my E and RV cover every possibility, and I would've preferred not to use expand in E.