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.

If your code works at all, then your usage of modpol is not supported by its help page. It says that the 4th argument should be prime and that the command works with polynomials over fields of prime order (rather than prime-power order).

Using a much smaller example, please verify that your usage of modpol works.

Does a folder "namef" (with a properly qualified name) appear listed in your global variable libname?

@vs140580 And here's an iterator for combinations:

Combos:= proc(S::set, k::nonnegint)
description `Iterator for k-combinations of S`;
option 
    `Reference: Donald Knuth, _The Art of Computer Programming_`,
        `section 7.2.1.3, Algorithm L`
;
local c:= Array([$1..k, nops(S)+1, 1]);
    proc()
    local j, R:= S[[seq](c[..k])];
        for j while c[j]+1 = c[j+1] do c[j]:= j od;
        c[j]++;
        R
    end proc
end proc
:
Get:= Combos({a,b,c,d,e,f}, 3):
'Get'() $ binomial(6,3);
{a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}, {a, b, e}, {a, c, e}, {b, c, e},
{a, d, e}, {b, d, e}, {c, d, e}, {a, b, f}, {a, c, f}, {b, c, f}, {a, d, f}, 
{b, d, f}, {c, d, f}, {a, e, f}, {b, e, f}, {c, e, f}, {d, e, f}

binomial(6,3)=nops({%});
                            20 = 20

@vv Yes, I noticed. That's why I multiplied by the local `1` (which converts to 1 at the finish).

@ThU The solutions do not approach infinity as k (or C) approaches 0. And, if you use my method, the solutions can be directly evauated at C=0 to get the obvious limiting value 2*Pi.