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Specify inverse.
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HansOlsson committed Feb 19, 2021
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7 changes: 3 additions & 4 deletions chapters/functions.tex
Expand Up @@ -1515,10 +1515,9 @@ \section{Declaring Inverses of Functions}\label{declaring-inverses-of-functions}
More than one inverse can be defined within the same \lstinline!inverse! annotation.
Several inverses are separated by commas.

\begin{nonnormative}
The inverse requires that for all valid values of the input arguments of \lstinline!$f_2$($\ldots$, y, $\ldots$)! and $u_k$ being calculated as \lstinline!$u_k$ := $f_2$($\ldots$, y, $\ldots$)! implies
the equality \lstinline!y = $f_1$($\ldots$, $u_k$, $\ldots$)! up to a certain precision.
\end{nonnormative}
The function in the \lstinline!inverse! annotation must be an actual inverse.
This requires that for all valid values of the input arguments of \lstinline!$f_2$($\ldots$, y, $\ldots$)! and $u_k$ being calculated as \lstinline!$u_k$ := $f_2$($\ldots$, y, $\ldots$)! implies
the equality \lstinline!y = $f_1$($\ldots$, $u_k$, $\ldots$)! is satisfied up to a certain precision.

Function $f_1$ can have any number and types of formal parameters with and without default value.
The restriction is that the \emph{number of unknown variables} (see \cref{balanced-models}) in the output formal parameter of both $f_1$ and $f_2$ must be the same and that $f_2$ should have a union of output and formal parameters that is the same or a sub-set of that union for $f_1$, but the order of the formal parameters may be permuted.
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