Exact
float6
Disp "Enter rational function in the form of a/b(x)"
Prompt a,b,x
If x="x" or x="s" or x="t" Then
   q:=a/b // 몫 계산
   r:=a-q*b // 나머지 계산
   If q=0 Then
      Disp "The original polynomial is:"
      Disp r
   Else
      Disp "The quotient is:"
      Disp q
      Disp "The remainder is:"
      Disp r
   EndIf
   roots:=poly_roots(b,x)
   coeffs:=List(0,dim(roots))
   For i,root In roots Do
      If Im(root)=0 Then // 근이 실수인 경우
         coeff:=limit(a/b/(x-root),x,root)
      Else // 근이 복소수인 경우
         Disp "Select PFD level for complex roots of", root
         Menu "PFD Level", ["Real", "Complex"]
         If Ans=1 Then // PFD level: Real
            coeff:=limit(a/b/(x-root),x,root)
         Else // PFD level: Complex
            coeff_real:=limit(a/b/(x-Re(root)),x,Re(root))
            coeff_imag:=limit(a/b/(x-Im(root)),x,Im(root))
            coeff:=Matrix([[coeff_real,coeff_imag],[-coeff_imag,coeff_real]])
         EndIf
      EndIf
      coeffs[i]:=coeff
   EndFor
   If dim(roots)=0 Then
      Disp "No roots found."
   Else
      Disp "Coefficients:"
      Disp coeffs
   EndIf
Else
   Disp "Error: Invalid variable used"
   Stop
EndIf

설명만 입력하고 ti nspire 용으로 만들어 달랬더니 위와 같이 만들어줬습니다. 
대충 ti basic 하고 비슷은 한데, 못쓰는 명령어도 짬뽕되어 있고 그렇네요.