dbtilde doesn't exist in sphinx and was not compiling well

Author: vschutze-alt

doc/sphinx/source/n3fit/methodology.rst

@@ -374,26 +374,26 @@ Next, we move to the basis in which :math:`\rho` is diagonal. Writing :math:`\rh
     \chi^2 &= \tilde{\epsilon}^T \rho^{-1} \tilde{\epsilon} \\
            &= \tilde{\epsilon}^T (\tilde{U}^T \tilde{\Lambda} \tilde{U})^{-1} \tilde{\epsilon} \\
            &= \tilde{\epsilon}^T \tilde{U}^T \tilde{\Lambda}^{-1} \tilde{U} \tilde{\epsilon} \\
-           &\equiv \dbtilde{\epsilon}^T \tilde{\Lambda}^{-1} \dbtilde{\epsilon} \, ,
+           &\equiv \tilde{\tilde{\epsilon}}^T \tilde{\Lambda}^{-1} \tilde{\tilde{\epsilon}} \, ,
 
 where on the last line we have defined
 
 .. math::
 
-    \dbtilde{\epsilon} \equiv \tilde{U}\tilde{\epsilon} = \tilde{U}R^{-1}(D-T).
+    \tilde{\tilde{\epsilon}} \equiv \tilde{U}\tilde{\epsilon} = \tilde{U}R^{-1}(D-T).
 
 In index notation, this reads
 
 .. math::
 
-    \dbtilde{\epsilon_i} = \tilde{U}_{ij} \frac{(D-T)_j}{\sqrt{C_{0, jj}}}
+    \tilde{\tilde{\epsilon_i}} = \tilde{U}_{ij} \frac{(D-T)_j}{\sqrt{C_{0, jj}}}
 
-The transformed data :math:`\dbtilde{\epsilon}` is statistically independent in the diagonal basis of the correlation matrix :math:`\rho`.
-Computing the covariance of :math:`\dbtilde{\epsilon}`,
+The transformed data :math:`\tilde{\tilde{\epsilon}}` is statistically independent in the diagonal basis of the correlation matrix :math:`\rho`.
+Computing the covariance of :math:`\tilde{\tilde{\epsilon}}`,
 
 .. math::
 
-    \mathbb{E}[\dbtilde{\epsilon}\dbtilde{\epsilon}^T]
+    \mathbb{E}[\tilde{\tilde{\epsilon}}\tilde{\tilde{\epsilon}}^T]
       &= \mathbb{E} \big[ (\tilde{U} R^{-1}(D-T)) (\tilde{U} R^{-1}(D-T))^T \big] \\
       &= \tilde{U} R^{-1} \mathbb{E}[(D-T)(D-T)^T] R^{-1} \tilde{U}^T \\
       &= \tilde{U} \rho \tilde{U}^T \\