diff --git a/main.tex b/main.tex index 9eb8b66c9ffacdd672aba32f138f56b76f1db984..e9850dceccfd50c1c26e0a8f078f79e8e9208071 100644 --- a/main.tex +++ b/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}