Import sage expressions from external script

main.tex

@@ -919,6 +919,10 @@ var("q", domain="real")
 c_in_terms_of_q = c_lower_bound + q
 \end{sagesilent}
 
+\begin{sagesilent}
+from plots_and_expressions import c_in_terms_of_q	
+\end{sagesilent}
+
 \begin{equation}
 	\label{eqn-cintermsofm}
 	c=\chern_1(u) = \sage{c_in_terms_of_q}
@@ -987,6 +991,10 @@ bgmlv2_with_q = (
 )
 \end{sagesilent}
 
+\begin{sagesilent}
+from plots_and_expressions import bgmlv2_with_q
+\end{sagesilent}
+
 \begin{equation}
 	\sage{0 <= bgmlv2_with_q}
 \end{equation}
@@ -1008,6 +1016,9 @@ bgmlv2_d_ineq = (
 bgmlv2_d_upperbound = bgmlv2_d_ineq.rhs()
 \end{sagesilent}
 
+\begin{sagesilent}
+from plots_and_expressions import bgmlv2_d_ineq
+\end{sagesilent}
 \begin{equation}
 	\label{eqn-bgmlv2_d_upperbound}
 	\sage{bgmlv2_d_ineq}
@@ -1037,6 +1048,12 @@ bgmlv2_d_upperbound_exp_term = (
 ).expand()
 \end{sagesilent}
 
+\begin{sagesilent}
+from plots_and_expressions import \
+bgmlv2_d_upperbound_const_term, \
+bgmlv2_d_upperbound_linear_term, \
+bgmlv2_d_upperbound_exp_term
+\end{sagesilent}
 Viewing equation \ref{eqn-bgmlv2_d_upperbound} as a lower bound for $d$ in term
 of $r$ again, there is a constant term
 $\sage{bgmlv2_d_upperbound_const_term}$,
@@ -1162,6 +1179,13 @@ assert bgmlv3_d_upperbound_exp_term == (
 )
 \end{sagesilent}
 
+\begin{sagesilent}
+from plots_and_expressions import \
+bgmlv3_d_upperbound_const_term_alt, \
+bgmlv3_d_upperbound_linear_term, \
+bgmlv3_d_upperbound_exp_term_alt2
+\end{sagesilent}
+
 \bgroup
 \def\psi{\chern_1^{\beta}(v)}
 \def\phi{\chern_2^{\beta}(v)}
@@ -1216,6 +1240,9 @@ These give bounds with the same assymptotes when we take $r\to\infty$
 \let\originalbeta\beta
 \renewcommand\beta{{\originalbeta_{-}}}
 
+\begin{sagesilent}
+from plots_and_expressions import phi	
+\end{sagesilent}
 \bgroup
 % redefine \psi in sage expressions (placeholder for ch_1^\beta(F)
 \def\psi{\chern_1^{\beta}(F)}
@@ -1449,6 +1476,12 @@ Substituting the current values of $q$ and $\beta$ into the condition for the
 radius of the pseudo-wall being positive
 (eqn \ref{eqn:radiuscond_d_bound_betamin}) we get:
 
+\begin{sagesilent}
+from plots_and_expressions import \
+positive_radius_condition, \
+q_value_expr, \
+beta_value_expr
+\end{sagesilent}
 \begin{equation}
 \label{eqn:positive_rad_condition_in_terms_of_q_beta}
 	\frac{1}{2}\ZZ
@@ -1482,6 +1515,9 @@ r_upper_bound2 = (
 assert r_upper_bound2.lhs() == r
 \end{sagesilent}
 
+\begin{sagesilent}
+from plots_and_expressions import r_upper_bound1, r_upper_bound2, kappa
+\end{sagesilent}
 \begin{theorem}[Bound on $r$ \#1]
 \label{thm:rmax_with_uniform_eps}
 	Let $v = (R,C\ell,D\ell^2)$ be a fixed Chern character. Then the ranks of the
@@ -1547,6 +1583,10 @@ bounds_too_tight_condition2 = (
 )
 \end{sagesilent}
 
+\begin{sagesilent}
+from plots_and_expressions import bounds_too_tight_condition1, bounds_too_tight_condition2
+\end{sagesilent}
+
 \bgroup
 \def\psi{\chern_1^{\beta}(F)}
 \begin{equation}
@@ -1597,6 +1637,10 @@ r_upper_bound_all_q = (
 )
 \end{sagesilent}
 
+\begin{sagesilent}
+from plots_and_expressions import r_upper_bound_all_q, q_sol
+\end{sagesilent}
+
 \begin{corollary}[Bound on $r$ \#2]
 \label{cor:direct_rmax_with_uniform_eps}
 	Let $v$ be a fixed Chern character and