I'd suggest a more difficult conjecture for the next project: any odd number can be written as the difference of a prime number and twice a perfect square.

@Carl Love I think that OP would prefer

eq_arrangement:= (k::posint) -> [k, seq('k+i,k-i', i=1..k-1)];

(maybe also  a local i).

@Hullzie16 The command discont gives the set of discontinuity points. I took the three points (say a,b,c) in the interval 0..5.
The functions were plotted in the intervals  e .. a-e,  a+e .. b-e,  b+e .. c-e,  c+e .. 5-e  (e=0.001) and then displayed together.

@Hullzie16 I took the real parts of the functions. If you want the gaps (to see where the functions have complex values), just remove Re.

@oggsait The equality you want is true only for alpha=1.

@oggsait After expand(simplify(%));  ==>

Download fdiff.mw

@dharr It depends on conventions. E,g. in complex analysis, z > 7 means: Im(z) = 0 and Re(z)>7,  but z > 2+3i is not accepted (nonsense).

@nm  Excellent, thanks!

@Anthrazit Almost. I saw your post and I wanted to answer there, but later I decided to make a separate one, including some code. (Actually I think that your post should have been a question.)

@Carl Love Thank you. Yes, sprintf is definitely easier to read, I should have used it.

- You have alias(f=f(w)) and then D(f)(w). 

- D@@4  is not the same as D^4

- You must be sure that the exprssion you want to substitute appears as a subexpression (e.g. a*b is not subexpression in a*b*c).

@student_1 

int((f_exact(x,t)-f_numeric(x,t))^2, [x=0..2,t=0..2], numeric)^(1/2);

You may want to divide by sqrt(Area) (=2 in this case).

@Federiko On my old computer:

xx:=CodeTools:-Usage(LinearSolve(AA, bb)):
memory used=411.13MiB, alloc change=70.00MiB, cpu time=3.53s, real time=3.43s, gc time=1.22s

(For symbolic computations using floats is usually not a good idea).