@@ -122,7 +122,7 @@ Where latexmath:[e^{-:\!H\!: s}] is the Lie expansion.
=== Implementaion of map tracking
For the derivative of the Hamiltonian, a Differential Algebra (DA) was used, in particular the Truncated Power Series Algebra (TPSA).
This algebra uses the Taylor expansion as the equivalent function, which also is responsible for its name by creating truncated power series.
Just form the definition of the Taylor expansion, it can be seen that a finite expansion is an approximaion of the acutal function, due to the error term latexmath:[\mathcal{O}\left( \vec{v}_{\left( \Delta s\right)}^{\,\Omega +1}\right) ].
Just form the definition of the Taylor expansion, it can be seen that a finite, to the order latexmath:[\Omega], expansion is an approximaion of the acutal function, due to the error term latexmath:[\mathcal{O}\left( \vec{v}_{\left( \Delta s\right)}^{\,\Omega +1}\right) ].
[latexmath]
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@@ -131,7 +131,10 @@ Just form the definition of the Taylor expansion, it can be seen that a finite e
\end{aligned}
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In _OPAL-map_ the Hamiltonian gets Taylor expanded and its map derived (`link:opalmap#sec.opalmap.creationOfMap[Creation of Map]`) in the TPSA using the _OPAL-DA_ package. The truncation length gets definded in `TRACK` setting the `MAP_ORDER` attribute.
