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Adjust non-normative description of smoothOrder
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henrikt-ma committed Sep 6, 2022
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6 changes: 4 additions & 2 deletions chapters/functions.tex
Expand Up @@ -1228,8 +1228,10 @@ \section{Derivatives and Inverses of Functions}\label{derivatives-and-inverses-o

\begin{nonnormative}
This means that the function is at least C\textsuperscript{smoothOrder}.
{\lstinline!smoothOrder = 1!} means that the function can be differentiated at least once in order that all output arguments are still continuous, provided the input arguments are continuous.
If a tool needs the derivative of a function, e.g.\ for index reduction or to compute an analytic Jacobian, the function can be differentiated analytically at least {\lstinline!smoothOrder!} times.

When a tool computes the derivative of a function, e.g., for index reduction or to compute an analytic Jacobian, each differentiation of a function reduces the \lstinline!smoothOrder! by 1.
The \lstinline!smoothOrder! information can then be used to infer continuity of the resulting differentiated function calls.
This is a conservative check, however, meaning that a tool may be able to establish continuity of a function call even though the \lstinline!smoothOrder! has been reduced to less than 0.
\end{nonnormative}

The optional argument {\lstinline!normallyConstant!} of {\lstinline!smoothOrder!} defines that the function argument {\lstinline!IDENT!} is usually constant.
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