@Preben Alsholm "For i from i do" means "resume i". Initially I reused that loop to get the result I wanted. Now I've simply copied it twice.

@Carl Love I just saw this: PolynomialTools, Split. Thats what it is.

@Preben Alsholm Maple V, Release 4 (1996).


It looks like a coding slip up, easy fixed.

@Carl Love `evala/toprof` given a parameter containing RootOfs chooses one RootOf in the expression, not used in parameter of any other RootOfs or functions in the expression.

@Markiyan Hirnyk Oh, I see now, residue introduces radicals. That should not be. Can you keep it in RootOf notation, for example using series and coeff?

Still I do not know what has caused the divergence. Also, I seem to have somehow omitted an important element regarding use of RootOfs. I added seq((evala@Expand)(Y*Z^i), i = 0 .. d - 1).

returns:

C0 := 2^(1/4)*(-1)^(3/8)
P := z^2/(z^4+2*z^2+2)^2
Pf := z^2/(z-beta)^2/(z+alpha)^2/(z+beta)^2/(z-alpha)^2
Pfs := [alpha, -beta, -alpha, beta]

Residue   alpha   -3/32*alpha^3-1/16*alpha
Degree   alpha   4
Basis   alpha-k   alpha^2-alpha*k   alpha^3-alpha^2*k   -2*alpha^2-2-alpha^3*k
Ordering   alpha
Simplified   -1/32*k*(2+3*k^2)
Result   (1/32-3/32*I)*2^(1/4)*(-1)^(3/8)
Residue   -beta   -3/32*alpha^2*beta-1/8*beta
Degree   beta   2
Degree   alpha   4
Basis   -beta-k   alpha^2+2-beta*k   alpha^2+2+k^2   alpha^3+2*alpha+alpha*k^2
  -2+alpha^2*k^2   -2*alpha+alpha^3*k^2
Ordering   beta   alpha
Simplified   -1/32*k*(2+3*k^2)
Result   (1/32-3/32*I)*2^(1/4)*(-1)^(3/8)
Residue   -alpha   3/32*alpha^3+1/16*alpha
Degree   alpha   4
Basis   -alpha-k   -alpha^2-alpha*k   -alpha^3-alpha^2*k   2*alpha^2+2-alpha^3
*k
Ordering   alpha
Simplified   -1/32*k*(2+3*k^2)
Result   (1/32-3/32*I)*2^(1/4)*(-1)^(3/8)
Residue   beta   3/32*alpha^2*beta+1/8*beta
Degree   beta   2
Degree   alpha   4
Basis   beta-k   -alpha^2-2-beta*k   alpha^2+2+k^2   alpha^3+2*alpha+alpha*k^2
  -2+alpha^2*k^2   -2*alpha+alpha^3*k^2
Ordering   beta   alpha
Simplified   -1/32*k*(2+3*k^2)
Result   (1/32-3/32*I)*2^(1/4)*(-1)^(3/8)
ANS := {(1/32-3/32*I)*2^(1/4)*(-1)^(3/8)}
Residue   alpha   -3/32*alpha^3-1/16*alpha
Degree   alpha   4
Basis   alpha-k   alpha^2-alpha*k   alpha^3-alpha^2*k   -2*alpha^2-2-alpha^3*k
Ordering   alpha
Simplified   -1/32*k*(2+3*k^2)
Result   -1/32*k*(2+3*k^2)
Residue   -beta   -3/32*alpha^2*beta-1/8*beta
Degree   beta   2
Degree   alpha   4
Basis   -beta-k   alpha^2+2-beta*k   alpha^2+2+k^2   alpha^3+2*alpha+alpha*k^2
  -2+alpha^2*k^2   -2*alpha+alpha^3*k^2
Ordering   beta   alpha
Simplified   -1/32*k*(2+3*k^2)
Result   -1/32*k*(2+3*k^2)
Residue   -alpha   3/32*alpha^3+1/16*alpha
Degree   alpha   4
Basis   -alpha-k   -alpha^2-alpha*k   -alpha^3-alpha^2*k   2*alpha^2+2-alpha^3
*k
Ordering   alpha
Simplified   -1/32*k*(2+3*k^2)
Result   -1/32*k*(2+3*k^2)
Residue   beta   3/32*alpha^2*beta+1/8*beta
Degree   beta   2
Degree   alpha   4
Basis   beta-k   -alpha^2-2-beta*k   alpha^2+2+k^2   alpha^3+2*alpha+alpha*k^2
  -2+alpha^2*k^2   -2*alpha+alpha^3*k^2
Ordering   beta   alpha
Simplified   -1/32*k*(2+3*k^2)
Result   -1/32*k*(2+3*k^2)
ANS2 := {-1/32*k*(2+3*k^2)}, k = 2^(1/4)*(-1)^(3/8)

@Carl Love What does `evala/toprof`(Pf); `evala/toprof`(indets(Pf,RootOf)); return? ANS2 should contain variable k. If it does not then what would explain this? Also I added a print command.

I am editing too much. The codes work flawlessly in Maple V R4. I wonder in which version the discontinuity occurs.

@Markiyan Hirnyk It appears _EnvExplicit:=true; is being used, converting all RootOfs into radicals. Lets see if _EnvExplicit:=false; would change that.

@Carl Love roots or evala@Roots or another? Which is better?

@Carl Love Thank you for your help. It appears roots command does not succeed. I'll change it to evala@Roots.

I ask, what command would you use to obtain roots of a factored polynomial?

@Carl Love I suppose split is the same thing as evala@AFactor. I tested it. It seems to work. I already edited my original answer.

@Dave L If you do that you should state the author of the statement you edit.

@Carl Love I have forgotten about this option completely, my apology. Unfortunately I have no access to the Groebner package. I can only suggest using method=buchberger and plex(X,Q). Quote from the help file for GB:

- GB is an implementation of Buchberger's algorithm for computing Grobner bases
  over Zp(a,b,...)[x1, ..., xn].
      
- GB(F,X,termorder) computes the reduced, minimal Grobner basis of the
  polynomials F with respect to the indeterminates X and the given term order-
  ing.      

No help otherwise.

..Also the basis you quoted is identical to tdeg basis.

@testht06 

Your definitions for x and q are:

so the monic for Q is what you seek and it is obtained with:

@roman_pearce Thank You, that is precisely the function I needed. But also I was wondering if there is any support for this from side of Maple (even though the solution is so simple).