--- /home/rubey/axiom--main--1--patch-40/src/algebra/fr.spad.pamphlet	2005-07-14 11:35:23.000000000 +0200
+++ fr.spad.pamphlet	2005-07-14 15:47:13.000000000 +0200
@@ -412,10 +412,39 @@
       unitNormalize mkFF(1, [[fl, r, i]$FF])
 
     differentiate(u:%, deriv: R -> R) ==
+      ans := deriv(unit u) * ((u exquo unit(u)::%)::%)
+      ans + (_+/[fact.xpnt * deriv(fact.fctr) *
+       ((u exquo nilFactor(fact.fctr, 1))::%) for fact in factorList u])
+
+@
+
+This operation provides an implementation of [[differentiate]] from the
+category [[DifferentialExtension]]. It uses the formula 
+
+$$\frac{d}{dx} f(x) = \sum_{i=1}^n \frac{f(x)}{f_i(x)}\frac{d}{dx}f_i(x),$$
+
+where 
+
+$$f(x)=\prod_{i=1}^n f_i(x).$$
+
+Note that up to [[patch--40]] the following wrong definition was used:
+
+\begin{verbatim}
+    differentiate(u:%, deriv: R -> R) ==
       ans := deriv(unit u) * ((u exquo (fr := unit(u)::%))::%)
       ans + fr * (_+/[fact.xpnt * deriv(fact.fctr) *
        ((u exquo nilFactor(fact.fctr, 1))::%) for fact in factorList u])
+\end{verbatim}
+
+which causes wrong results as soon as units are involved, for example in 
+
+<<inputfile>>=
+  D(factor (-x), x)
+@
+
+(Issue~\#176)
 
+<<domain FR Factored>>=
     map(fn, u) ==
      fn(unit u) * _*/[irreducibleFactor(fn(f.fctr),f.xpnt) for f in factorList u]