7.14 PF Operator

pf(\(\langle \)exp\(\rangle \),\(\langle \)var\(\rangle \)) transforms the expression \(\langle \)exp\(\rangle \) into a list of partial fractions with respect to the main variable, \(\langle \)var\(\rangle \). pf does a complete partial fraction decomposition, and as the algorithms used are fairly unsophisticated (factorization and the extended Euclidean algorithm), the code may be unacceptably slow in complicated cases.

Example: Given 2/((x+1)^2*(x+2)) in the workspace, pf(ws,x); gives the result

            2      - 2         2
        {-------,-------,--------------} .
          x + 2   x + 1    2
                          x  + 2*x + 1

If you want the denominators in factored form, set the switch exp to off. Thus, with 2/((x+1)^2*(x+2)) in the workspace, the input off exp; pf(ws,x); gives the result

            2      - 2       2
        {-------,-------,----------} .
          x + 2   x + 1          2
                          (x + 1)

To recombine the terms, for each… sum can be used. So with the above list in the workspace, for each j in ws sum j; returns the result

             2
     ------------------
                     2
      (x + 2)*(x + 1)

Alternatively, one can use the operations on lists to extract any desired term.

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