@tazatel I think that your main problem is that decimal numbers need to be entered with a decimal point rather than a comma. In other words, what you have entered as 0,0215 must be entered as 0.0215 or .0215 or 2.15e-2, etc.

I need a clarification of the problem statement. What does "exactly two points lie astride every [one] of these lines" mean? Using the colors in your example, does it mean "exactly two [blue] points lie astride every [one] of these [red] lines"? Still, I don't know what "astride" means. My first guess is that it means that if we form the six line segments determined by the blue points, then each of the red lines is intersected by exactly one of these line segments. However, that isn't true for the example diagram. A second guess is that each of the eight red rays and eight red line segments is intersected by exactly one of the line segments determined by the blue points. In that case, we need to deal with the complication that there are some triple intersections.

@Markiyan Hirnyk I base my comments just on careful observation of MaplePrimes over the past three years. Jon Mcloone has made no post in the past three years. If he had, I certainly would've upvoted it. I read everything on MaplePrimes, so I certainly would've seen it. I've seen Comments by Mcloone, but not Posts.

Some Comments by Mcloone can be found in the thread http://www.mapleprimes.com/posts/201237-Comparisons

His Users' page is http://www.mapleprimes.com/users/JonMcloone

@Markiyan Hirnyk I inverted the relationship between n and N from the original formulation. Thus I treat n rather than N as the symbolic variable, and I solve for it. This is handled by the lines

SolN:= [solve(b/c=n, N)]:
N:= SolN[1]:

I do this because it's easier to solve for an integer variable.

Your application depends on a code file, knot.txt, which hasn't been supplied.

@want to be a permanent vegan As we discussed earlier, that if-then-else clause needs to replaced by piecewise!

Can you find on the Web an example of the type of plot that you are talking about?

@Muhammad Usman You were very eager (to the point of being repetitive) to get an Answer, and now you've been silent for two days. So, does my most recently posted code work for you?

@want to be a permanent vegan I read your updated code, and I don't understand why odeplot is not satisfactory for you. Yes, you can use the output= Array(L) option to dsolve to pass in a list L of any number of independent-variable values. You'll receive as dsolve's return value an Array with the corresponding dependent-variables values (and some other stuff). Yes, you can make the spacing of the independent-variable values as fine as you want (for some extremely fine spacings you may need to adjust dsolve's error-control options). And yes, you can use these values to make a plot. But all these things can be handled better by odeplot, especially if you use its numpoints option.

@want to be a permanent vegan 

Please don't mix the MaplePrimes threads. That thread is about your if/piecewise problem. Please repost your latest Reply from that thread here, in this thread.

Neither the command-line interface (CLI) nor the print command is needed to realize this bug. Apparently, the bug is in the kernel. Any theories about how this arises? It seems that there's two distinct copies of t23.

@Muhammad Usman 

(vv: Thanks for explaining the raising to the 1/p power.)

Muhammad:

Please try this corrected translation of your algorithm. Note that it is divided into two procedures.

`mod/ReduceExponents`:= (f::polynom, p::posint)->
     #This procedure should only be used when all exponents of f are multiples of p.
     evalindets(f, `^`, t-> op(1,t)^iquo(op(2,t), p))
:

`mod/SFF`:= proc(f::polynom, p::posint)
local R:= 1, x:= indets(f, name)[], i, c, w, g, y, z;
     if x=NULL then return f mod p end if; #f is degree 0.
     g:= diff(f,x);
     if g=0 then return thisproc(ReduceExponents(f) mod p, p)^p end if;
     c:= Gcd(f,g) mod p;
     w:= Quo(f,c,x) mod p;
     for i while w <> 1 do
          y:= Gcd(w,c) mod p;
          z:= Quo(w,y,x) mod p;
          R:= R*z^i;
          w:= y;
          c:= Quo(c,y,x) mod p
     end do;
     R*thisproc(ReduceExponents(c) mod p, p)^p #returns R if c=1
end proc:

f:= x^11 + 2*x^9 + 2*x^8 + x^6 + x^5 + 2*x^3 + 2*x^2 + 1:
SFF(f) mod 3;

@Muhammad Usman 

Ah, yes, I didn't include the f^(1/p) and c^(1/p) steps. I don't know how to handle that. How can this be done without fully factoring the polynomial? I see that in the case you mention, you can just replace x^3 with x, but what about the general case?

@Just_Some_Guy 

In your worksheet, you have a vector of independent-variable values, X, which doesn't appear in your original Question. Also, what you called E---the independent variable in the original---has become dependent variable f in the above. Which is correct?

@Maple4evergr8 Before upgrading, you may want to confirm that that bug has indeed been fixed. I'm not sure. I'm sure that someone else reading this who has Maple 2015 can answer that question.