diff --git a/main.tex b/main.tex index db5b4c1f82e8a510ad3b90cc454f75285ff7992e..c560ce7c6545100a27f8cf5299667fb3385cf17e 100644 --- a/main.tex +++ b/main.tex @@ -211,9 +211,13 @@ This can be rearranged to express a bound on $d$ as follows: \begin{sagesilent} var("r_alt",domain="real") # r_alt = r - R/2 temporary substitution + bgmlv1_with_q_reparam = (bgmlv1_with_q.subs(r == r_alt + R/2)/r_alt).expand() - bgmlv1_d_ineq = ((0 > -bgmlv1_with_q_reparam) + 4*d)/4 # Rearrange for d - bgmlv1_d_ineq = bgmlv1_d_ineq.subs(r_alt == r - R/2).expand() # Resubstitute r back in + bgmlv1_d_ineq = ( + ((0 >= -bgmlv1_with_q_reparam)/4 + d) # Rearrange for d + .subs(r_alt == r - R/2) # Resubstitute r back in + .expand() + ) bgmlv1_d_lowerbound = bgmlv1_d_ineq.rhs() # Keep hold of lower bound for d \end{sagesilent}