PF Operator
Date: 2020-10-07 18:10:00

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### 7.14 PF Operator

PF(⟨exp⟩,⟨var⟩) transforms the expression ⟨exp⟩ into a list of partial fractions with respect to the main variable, ⟨var⟩. 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, use off exp;. Thus, with 2/((x+1)^2*(x+2)) in the workspace, the commands off exp; pf(ws,x); give 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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