Skip to content

Commit

Permalink
Update README.md
Browse files Browse the repository at this point in the history
Signed-off-by: Rui Campos <mail@ruicampos.org>
  • Loading branch information
RuiFilipeCampos authored Mar 23, 2024
1 parent 8c550fd commit 8dda430
Showing 1 changed file with 0 additions and 8 deletions.
8 changes: 0 additions & 8 deletions README.md
Original file line number Diff line number Diff line change
Expand Up @@ -60,14 +60,6 @@ $$\rho^{bnul} = \delta^{f(u)g(u)} p^{bnf(u)f(l)} p^{bnf(u)g(l)} + 2 \tilde \del

Substituting this back, while attending to the relevant substitution on the first term of the original expression,


$$q^{bnul} _ {l} = \delta^{f(l)g(l)} \bar M^n_{l} \left [ \delta^{f(u)g(u)} p^{bnf(u)f(l)} p^{bnf(u)f(l)} + 2 \tilde \delta^{f(u)g(u)} p^{bnf(u)f(l)} p^{bng(u)f(l)} \right ] + 2 \tilde \delta^{f(l)g(l)} \bar M^n_l \left [ \delta^{f(u)g(u)} p^{bnf(u)f(l)} p^{bnf(u)g(l)} + 2 \tilde \delta^{f(u)g(u)} p^{bnf(u)f(l)} p^{bng(u)g(l)} \right ]$$

which we'll now group according to the $\delta$'s

$$q^{bnul} _ {l} = \bar M^n _ {l} p^{bnf(u)f(l)} p^{bnf(u)f(l)} \delta^{f(l)g(l)} \delta^{f(u)g(u)} + 2 \bar M^n_{l} p^{bnf(u)f(l)} p^{bng(u)f(l)} \delta^{f(l)g(l)} \tilde \delta^{f(u)g(u)} + 2 \bar M^n_l p^{bnf(u)f(l)} p^{bnf(u)g(l)} \delta^{f(u)g(u)} \tilde \delta^{f(l)g(l)} + 4 \bar M^n_l p^{bnf(u)f(l)} p^{bng(u)g(l)} \tilde \delta^{f(u)g(u)} \tilde \delta^{f(l)g(l)}$$


$$
\begin{aligned}
q^{bnul} _ {l} &= \delta^{f(l)g(l)} \bar M^n_{l} \left [ \delta^{f(u)g(u)} p^{bnf(u)f(l)} p^{bnf(u)f(l)} + 2 \tilde \delta^{f(u)g(u)} p^{bnf(u)f(l)} p^{bng(u)f(l)} \right ] \\
Expand Down

0 comments on commit 8dda430

Please sign in to comment.