"What are the equivalent command for FromCharactersCode and ToCharactersCode ?" - see Char and Ord in the StringTools package. In the same package find Chop, which removes the last character. I don't have Mathematica, so these are just guesses.

@Christian Wolinski I don't know if that denom is the problem. IntegerLinearSolve allows for method selection, but I don't know how to get the calling routines to change that choice.

@Christian Wolinski Nice tracing. So as the help for LinearAlgebra:-Modular:-IntegerLinearSolve says "The default method is to solve the system modulo a machine-sized prime and construct rational solutions using p-adic lifting. For large linear systems or systems with large solutions this is the fastest method." That seems indeed to be what it is doing.

Not sure specifically what else you are asking.

"Any ideas why or how to prevent it?" - well it's a bug so you should report it. As for why, without further details we can only speculate.

I'm guessing that solving a linear system with integer/rational coefficients can lead to manipulation of very large integers. To make such problems tractable, one can solve them modulo some primes and then reconstruct the solution from that - see ?iratrecon

I use Maple 2026 (and used 2025)  frequently using a VPN and frequently without a VPN without any issues. The only settings I can think of that might be relevant are file->options->network->enable MapleCloud connection, which I leave unchecked, and I am not logged in to my Maple account.

Maple in installed locally on my machine and the licence file is also local.

As far as I know, the only Maple tools for functional equations are in the LinearFunctionalSystems package, but this is only for systems with one independent variable. Perhaps your example can be coerced into this form, or into a system of differential equations, but how to do that isn't immediately obvious to me.

@vv I didn't really expect to get an answer with the OPs example; it was more about how to use gfun. But I was lucky. Your example can be done with a bit more work.

Download gfun2.mw

@acer Thanks. I had tried forget(evalf), forget(`evalf/int`) and gc(). By commenting out, it seems the key one is forget(..,nm), which I would never have guessed.

Actually, I realized I want t as a local in the module, which then means I need H( f, 10000, F:-t ); with kernelopts(opaquemodules = false). Inelegant but it works.

@Alfred_F If you want more, you can use a range. QuadraticIsolve(P, 0 .. 15) gives 62 solutions.

@salim-barzani 

@salim-barzani I updated the answer to include the fsolve commands, using search ranges based on the plot. Each case with different numerical parameters will be different. There are two examples. The solutions are at the intersections of the red and blue curves.

I don't know why it was deleted, but in the past I have deleted ones that are duplicates and instead of telling the person that it was deleted because it was a duplicate they get told it was spam, which is clearly a problem with the system.

At least in Windows, the alt key shows menu shortcuts, e.g., F pops up above the file menu, then alt-F opens the file menu and shows, e.g., O for open and FO for file open. This is common Windows behaviour, but is an alternative to the ctrl- shortcuts.

@MAXR There is a difference between the dots. Anyway, I am currently traveling so perhaps someone else can help you.

@MAXR Please upload your revised version.