Rename inappropriately name sage var 'beta_min' to 'beta'

main.tex

@@ -167,10 +167,10 @@ $\chern(F)$, and so we can write:
 
 \begin{sagesilent}
 ts = stability.Tilt
-beta_min = var("beta", domain="real")
+beta = var("beta", domain="real")
 
 c_lower_bound = -(
-	ts(beta=beta_min).rank(u)
+	ts(beta=beta).rank(u)
 	/ts().alpha
 ).expand() + c
 
@@ -275,10 +275,10 @@ assert bgmlv1_d_lowerbound_const_term == (
 		bgmlv1_d_lowerbound_const_term_alt :=
 		(
 			chbv/2
-			+ beta_min*q
+			+ beta*q
 		)
 	)
-	.subs(chbv == v.twist(beta_min).ch[2])
+	.subs(chbv == v.twist(beta).ch[2])
 	.expand()
 )
 
@@ -288,12 +288,12 @@ assert bgmlv1_d_lowerbound_exp_term == (
 		bgmlv1_d_lowerbound_exp_term_alt :=
 		(
 			- R*chbv/2
-			- R*beta_min*q
+			- R*beta*q
 			+ C*q
 			- q^2
 		)/(R-2*r)
 	)
-	.subs(chbv == v.twist(beta_min).ch[2])
+	.subs(chbv == v.twist(beta).ch[2])
 	.expand()
 )
 \end{sagesilent}
@@ -502,10 +502,10 @@ assert bgmlv3_d_upperbound_const_term == (
 		# keep hold of this alternative expression:
 		bgmlv3_d_upperbound_const_term_alt := (
 			chbv
-			+ beta_min*q
+			+ beta*q
 		)
 	)
-	.subs(chbv == v.twist(beta_min).ch[2]) # subs real val of ch_1^\beta(v)
+	.subs(chbv == v.twist(beta).ch[2]) # subs real val of ch_1^\beta(v)
 	.expand()
 )
 
@@ -516,11 +516,11 @@ assert bgmlv3_d_upperbound_exp_term == (
 		(
 			R*chbv
 			+ (C - q)^2/2
-			+ R*beta_min*q
+			+ R*beta*q
 			- D*R
 		)/(r-R)
 	)
-	.subs(chbv == v.twist(beta_min).ch[2]) # subs real val of ch_1^\beta(v)
+	.subs(chbv == v.twist(beta).ch[2]) # subs real val of ch_1^\beta(v)
 	.expand()
 )
 \end{sagesilent}