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Merge pull request #55 from mhvk/multiple-screens-another-typo
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Further index errors.
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mhvk authored Aug 29, 2021
2 parents 34acd8a + 458b430 commit ce47d9b
Showing 1 changed file with 9 additions and 9 deletions.
18 changes: 9 additions & 9 deletions docs/background/multiple_screens.rst
Original file line number Diff line number Diff line change
Expand Up @@ -200,7 +200,7 @@ writing :math:`s_{ji}=1-d_{j}/d_{i}` (where all :math:`s_{ti}=1`), one finds,

.. math::
\varsigma_{t}\hat{u}_{t} - \varsigma_{i}\hat{u}_{i} - \sum_{j=0}^{i-1} \alpha_{j}s_{ji}\hat{r}_{j} = \rho_{i}\hat{r}_{i} - \rho_{ti}\hat{r}_{t}
\varsigma_{t}\hat{u}_{t} - \varsigma_{i}\hat{u}_{i} - \sum_{j=0}^{i-1} \alpha_{j}s_{ji}\hat{r}_{j} = \rho_{i}\hat{r}_{i} - \rho_{t}\hat{r}_{t}
Instead of taking inner products with :math:`\hat{r}_{1}` and :math:`\hat{u}_{1}`, it
seems easier to allow one to chose particular :math:`x` and :math:`y` directions and
Expand Down Expand Up @@ -234,15 +234,15 @@ then define angles :math:`\phi_{i}` such that :math:`\hat{r}_{i}=\cos \phi_{i} \
\alpha_{n}
\end{matrix}\right) =
\left(\begin{matrix}
\rho_{1}\cos \phi_{1} - \rho_{t1}\cos \phi_{t}\\
\rho_{1}\sin \phi_{1} - \rho_{t1}\sin \phi_{t}\\
\rho_{2}\cos \phi_{2} - \rho_{t2}\cos \phi_{t}\\
\rho_{2}\sin \phi_{2} - \rho_{t2}\sin \phi_{t}\\
\rho_{1}\cos \phi_{1} - \rho_{t}\cos \phi_{t}\\
\rho_{1}\sin \phi_{1} - \rho_{t}\sin \phi_{t}\\
\rho_{2}\cos \phi_{2} - \rho_{t}\cos \phi_{t}\\
\rho_{2}\sin \phi_{2} - \rho_{t}\sin \phi_{t}\\
\vdots\\
\rho_{n}\cos \phi_{n} - \rho_{tn}\cos \phi_{t}\\
\rho_{n}\sin \phi_{n} - \rho_{tn}\sin \phi_{t}\\
\rho_{p}\cos \phi_{p} - \rho_{tp}\cos \phi_{t}\\
\rho_{p}\sin \phi_{p} - \rho_{tp}\sin \phi_{t}
\rho_{n}\cos \phi_{n} - \rho_{t}\cos \phi_{t}\\
\rho_{n}\sin \phi_{n} - \rho_{t}\sin \phi_{t}\\
\rho_{p}\cos \phi_{p} - \rho_{t}\cos \phi_{t}\\
\rho_{p}\sin \phi_{p} - \rho_{t}\sin \phi_{t}
\end{matrix}\right).
These can be solved by by inverting the matrix :math:`A`. Recognizing that
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