/**
* Similar to the previous apply_transformation().
* Each row of the result corresponds to one of the rows of @p D_X transformed
- * by @p grad_F, equivalent to $\text{D\_X} \, \text{grad\_F}^T$ in matrix notation.
+ * by @p grad_F, equivalent to $\mathrm{D\_X} \, \mathrm{grad\_F}^T$ in matrix
+ * notation.
*
* @relatesalso DerivativeForm
* @author Sebastian Pauletti, 2011, Reza Rastak, 2019
/**
* A class that represents a subset of indices among a larger set. For
* example, it can be used to denote the set of degrees of freedom within the
- * range $[0,\text{dof\_handler.n\_dofs})$ that belongs to a particular
+ * range $[0,\mathrm{dof\_handler.n\_dofs()})$ that belongs to a particular
* subdomain, or those among all degrees of freedom that are stored on a
* particular processor in a distributed parallel computation.
*
*
* @f[
* \text{result}_{i_1,..,i_{r1},j_1,..,j_{r2}}
- * = \sum_{k_1,..,k_{\text{no\_contr}}}
- * \text{left}_{i_1,..,i_{r1},k_1,..,k_{\text{no\_contr}}}
- * \text{right}_{j_1,..,j_{r2},k_1,..,k_{\text{no\_contr}}}
+ * = \sum_{k_1,..,k_{\mathrm{no\_contr}}}
+ * \mathrm{left}_{i_1,..,i_{r1},k_1,..,k_{\mathrm{no\_contr}}}
+ * \mathrm{right}_{j_1,..,j_{r2},k_1,..,k_{\mathrm{no\_contr}}}
* @f]
*
* Calling this function is equivalent of writing the following low level
* radius of the $k$th shell is given by
*
* @f[
- * r = r_{\text{inner}} + (r_\text{outer} - r_\text{inner})
- * \frac{1 - \tanh(\text{skewness}(1 - k/\text{n\_shells}))}
- * {\tanh(\text{skewness})}
+ * r = r_{\mathrm{inner}} + (r_\mathrm{outer} - r_\mathrm{inner})
+ * \frac{1 - \tanh(\mathrm{skewness}(1 - k/\mathrm{n\_shells}))}
+ * {\tanh(\mathrm{skewness})}
* @f]
*
* where @p skewness is a parameter controlling the shell spacing in the
/**
* Access the real parts of solutions for a solved eigenvector problem,
* pair index solutions, $\text{index}\,\in\,0\dots
- * \text{n\_converged}-1$.
+ * \mathrm{n\_converged}-1$.
*/
void
get_eigenpair(const unsigned int index,
/**
* Access the real and imaginary parts of solutions for a solved
* eigenvector problem, pair index solutions, $\text{index}\,\in\,0\dots
- * \text{n\_converged}-1$.
+ * \mathrm{n\_converged}-1$.
*/
void
get_eigenpair(const unsigned int index,
* \dealcoloneq \{ \bullet \} - \frac{1}{\textrm{dim}}
* \left[ \{ \bullet \} : \mathbf{I} \right]\mathbf{I}
* = \mathcal{P}^{T} : \{ \bullet \}
- * = \texttt{dev\_P} \left( \{ \bullet \} \right)
+ * = \mathtt{dev\_P} \left( \{ \bullet \} \right)
* @f]
* and, therefore,
* @f[
- * \texttt{dev\_P} \left( \{ \bullet \} \right) : \mathbf{I}
- * = \textrm{trace}(\texttt{dev\_P} \left( \{ \bullet \} \right)) = 0 \,
+ * \mathtt{dev\_P} \left( \{ \bullet \} \right) : \mathbf{I}
+ * = \mathrm{trace}(\mathtt{dev\_P} \left( \{ \bullet \} \right)) = 0 \,
* .
* @f]
*
* \{ \bullet \} : \hat{\mathcal{P}}
* \dealcoloneq J^{-2/\textrm{dim}} \left[ \{ \bullet \} -
* \frac{1}{\textrm{dim}}\left[\mathbf{C} : \{ \bullet \}\right]
- * \mathbf{C}^{-1} \right] = \texttt{Dev\_P} \left( \{ \bullet \} \right)
+ * \mathbf{C}^{-1} \right] = \mathtt{Dev\_P} \left( \{ \bullet \} \right)
* \, .
* @f]
* It can therefore be readily shown that
* @f[
- * \texttt{Dev\_P} \left( \{ \bullet \} \right) : \mathbf{C} = 0 \, .
+ * \mathtt{Dev\_P} \left( \{ \bullet \} \right) : \mathbf{C} = 0 \, .
* @f]
*
* @note It may be observed that we have defined the tensor as the
* \hat{\mathcal{P}}^{T} : \{ \bullet \}
* = J^{-2/\textrm{dim}} \left[ \{ \bullet \} - \frac{1}{\textrm{dim}}
* \left[\mathbf{C}^{-1} : \{ \bullet \}\right] \mathbf{C} \right] =
- * \texttt{Dev\_P\_T} \{ \bullet \}
+ * \mathtt{Dev\_P\_T} \{ \bullet \}
* @f]
*/
template <typename Number>