@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.

The copy-and-pasted form that you show is equivalent syntax. The operator =~ has been placed in prefix form. If you copy-and-paste Maple Input (aka 1D input), then you get exactly what you typed. However, when you copy-and-paste 2D Input, various transformations occur that make the result not so easy to read. That's one reason why I don't use 2D Input.

@billyp245 Even if you were to add the simplest possible constraint, such as a=b or b=1, these equations would still be way beyond anything that's possible to solve.

If operator `*%` is defined by

a *% b = q*b *% a+1

then we need intial conditions, or else there'd be an infinite loop. You also have to specify the precedence (or binding strength) of the operator: q*b *% a+1 could be interpretted as (q*b) *% (a+1) or q * (b *% a) + 1 or (q* (b *% a)) + 1, etc.

Break up your code into execution groups. Then stop at the first error. The first error that I get is at the first call to dsolve: Error, (in dsolve/numeric/bvp/convertsys) too many boundary conditions: expected 2, got 6. I hope that the meaning of this error message is obvious.

@testht06 I don't know how to solve this problem.