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+% Copyright The Numerical Algorithms Group Limited 1992-94. All rights reserved.
+% !! DO NOT MODIFY THIS FILE BY HAND !! Created by ht.awk.
+\newcommand{\FactoredFunctionsTwoXmpTitle}{FactoredFunctions2}
+\newcommand{\FactoredFunctionsTwoXmpNumber}{9.23}
+%
+% =====================================================================
+\begin{page}{FactoredFunctionsTwoXmpPage}{9.23 FactoredFunctions2}
+% =====================================================================
+\beginscroll
+
+%%
+%% fr2.htex
+%%
+%% FactoredFunctions2
+%%
+
+The \spadtype{FactoredFunctions2} package implements one operation,
+\spadfunFrom{map}{FactoredFunctions2}, for applying an operation to every
+base in a factored object and to the unit.
+\xtc{
+}{
+\spadpaste{double(x) == x + x \bound{double}}
+}
+\xtc{
+}{
+\spadpaste{f := factor(720) \bound{f}}
+}
+\xtc{
+Actually, the \spadfunFrom{map}{FactoredFunctions2} operation used
+in this example comes from \spadtype{Factored} itself, since
+\userfun{double} takes an integer argument and returns an integer
+result.
+}{
+\spadpaste{map(double,f) \free{f}\free{double}}
+}
+\xtc{
+If we want to use an operation that returns an object that has a type
+different from the operation's argument,
+the \spadfunFrom{map}{FactoredFunctions2} in \spadtype{Factored}
+cannot be used and we use the one in \spadtype{FactoredFunctions2}.
+}{
+\spadpaste{makePoly(b) == x + b \bound{makePoly}}
+}
+\xtc{
+In fact, the ``2'' in the name of the package means that we might
+be using factored objects of two different types.
+}{
+\spadpaste{g := map(makePoly,f) \free{f}\free{makePoly}\bound{g}}
+}
+It is important to note that both versions of \spadfunFrom{map}{FactoredFunctions2}
+destroy any information known about the bases (the fact that they are prime,
+for instance).
+\xtc{
+The flags for each base are set to ``nil'' in the object returned
+by \spadfunFrom{map}{FactoredFunctions2}.
+}{
+\spadpaste{nthFlag(g,1) \free{g}}
+}
+
+For more information about factored objects and their use, see
+\downlink{`Factored'}{FactoredXmpPage}\ignore{Factored} and
+\downlink{``\ugProblemGaloisTitle''}{ugProblemGaloisPage} in Section \ugProblemGaloisNumber\ignore{ugProblemGalois}.
+\endscroll
+\autobuttons
+\end{page}
+%