Implementation

<< RCF.m

Examples

Example 1

r1[n_] := 
      n (n + 2)/((n - 3) (n - 2)^2 (n + 6) (n + 
                  12))

PNF[r1[n], n]

RNF[r1[n], n]

RCF1[r1[n], n]

RCF2[r1[n], n]

RCF3[r1[n], n]

RCF4[r1[n], n]

Example 2

r2[n_] := (n - 4 + Sqrt[2]) (n - 3 + Sqrt[2]) (n + 2 + 
            Sqrt[2]) (n + 11 + 
              Sqrt[2])/((n - 1 + Sqrt[2]) (n + 1 + 
                  Sqrt[2]))

PNF[r2[n], n]

RNF[r2[n], n]

RCF1[r2[n], n]

RCF2[r2[n], n]

RCF3[r2[n], n]

RCF4[r2[n], n]

Example 3

r[n_] := r1[n] r2[n]

PNF[r[n], n]

RCF1[r[n], n]

RCF2[r[n], n]

RCF3[r[n], n]

RCF4[r[n], n]

Example 4

RCF3[(2  n + 1)^3 (2  n + 17)^2/(2  n + 13)^3, 
      n]

%[[1]] (%[[2]] /. n -> n + 1)/%[[2]] // 
      Factor

RCF4[(2  n + 1)^3 (2  n + 17)^2/(2  n + 13)^3, 
      n]

%[[1]] (%[[2]] /. n -> n + 1)/%[[2]] // 
      Factor