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FixLatex
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HansOlsson committed Aug 30, 2022
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2 changes: 1 addition & 1 deletion chapters/operatorsandexpressions.tex
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Expand Up @@ -439,7 +439,7 @@ \subsection{Numeric Functions and Conversion Functions}\label{numeric-functions-
A typical case requiring the event-free semantics is a flow equation of the form \lstinline!abs(x) * x = y!.
With event generation, the equation would switch between the two forms \lstinline!x^2 = y! and \lstinline!-x^2 = y! at the events, where the events would not be coinciding exactly with the sign changes of \lstinline!y!.
When \lstinline!y! passes through zero, neither form of the equation would have a solution in an open neighborhood of \lstinline!y! $= 0$, and hence solving the equation would have to fail at some point sufficiently close to \lstinline!y! $= 0$.
Without event generation, on the other hand, the equation can be solved easily for \lstinline!x!, also as \lstlinline!y! passes through zero.
Without event generation, on the other hand, the equation can be solved easily for \lstinline!x!, also as \lstinline!y! passes through zero.
Note that without event generation the derivative of \lstinline!abs(x) * x! never changes discontinuously, despite \lstinline!abs(x)! having a discontinuous derivative.

In inverted form this equation is \lstinline!x = sign(y) * sqrt(abs(y))!.
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