@DarkMath Yes, the ability of solve and assuming or assume to work with each other is awkward at best. This is described a few places in solve's help. In particular, assumptions on the bound variables (the variables being solved for), including general number-class assumptions like real, either don't work at all or work weirdly. 

To use options explicit and allsolutions together, do

solve({sin(x), -3/2*Pi < x, x < 3/2*Pi}, x, real, explicit, allsolutions);

@tomleslie wrote:

• [T]his site probably(?) isn't the place to receive tuition on basic Maple coding/syntax.

I vehemently disagree. While these issues may be particularly frustrating for those of us who write answers here, the attempts to do so are quite beneficial to our own progress as educators.

If there existed another online forum where basic Maple coding and syntax were discussed, I'd be more inclined to agree with you.

This phenomenon doesn't happen in Maple 2020. Nonetheless, try adding the option optionsopen= [color= "Nautical 1"]. This is because the region being plotted is topologically open (defined by strict inequalities).

You're using both x1, y1, z1 (2nd character is numeral 1) and xl, yl, zl (2nd character is lowercase "ell") as subscripts. Is that what you intend? It's very difficult to read in 2D input; I needed to zoom to 200% to discern them. If you want to use the letter, please make it uppercase L.

@mthkvv My guess is that you'd be hard pressed to beat the speed of modp1 computations, even using compiled code. But I guess that you intend to do a large number of these computations, lest 4 seconds wouldn't be a problem. Perhaps efficiencies can be found by avoiding some repetition? For example, the ConvertIn only needs to be done once for each polynomial.

I think that you attached the wrong worksheet. The one that you attached has no alpha and no Explore.

This section of the Wikipedia article "Ellipse" has explicit (and simple) formulas for all 6 coefficients of the equation of any ellipse in the xy-plane, parameterized by the center, the rotation angle, and the axes' lengths.

If the ellipse is not centered at the origin, then the formula is not quite as simple as you suggest, but neither is it significantly more complicated.

@vv Both the original computations done with modpol and your computations done with modp1 are being done with polynomials whose coefficients come from the ring Z[2^N], not from the field GF(2,N).

@mthkvv  If that's what you (the OP) wants, fine. But that's not what was originally asked. And my limited knowledge of elliptic curves says that they're usually defined over fields, not over non-field rings.

Pourquoi tout ce que vous publiez est-il si bâclé? Il n'y a jamais de sauts de ligne ou d'indentation. Votre code ne peut même pas être copié et collé car un # commentaire doit être suivi d'un saut de ligne.

Why is everything that you post so sloppy? There's never line breaks or indentation. Your code can't even be copied and pasted because a # comment must be followed by a line  break (aka newline or \n).

@acer Sorry about my poorly worded first sentence. My parenthetical comment "(in 2d Input)" was only intended to modify its immediately preceding phrase "with no space after the e." I didn't intend for a reader to infer that juxtaposition with or without space would not be interpretted as a function in 1D input. Had that been my intention, I would've begun the whole sentence "In 2d Input, ...."

@mthkvv Thanks. Your example is as I specified. Now please put that polynomial into a file so that I can use the read command for it. It's very difficult to work with such a huge expression in 2D-Input. Even scrolling the worksheet is brutal.

The OP rudely deleted the equation from the Question. The equation is:

y(x) = c1*exp(x) + c2*exp(2*x) + c3*exp(3*x)

@serge17 Slightly different, yes. When the left operand of || is a name, it is used unevaluated. But this works:

"" || mypath || "foo.m"

@mthkvv Please construct and post an example problem that is still large but that is much smaller than the current example. An example where the modpol command takes approximately 0.1 seconds would be ideal.

There is no attached worksheet.