Rewrite "Lagrange multiplier", various improvements

1 files changed, 5 insertions, 4 deletions

diff --git a/source/know/concept/shors-algorithm/index.md b/source/know/concept/shors-algorithm/index.md
index a47151a..5ae5077 100644
--- a/source/know/concept/shors-algorithm/index.md
+++ b/source/know/concept/shors-algorithm/index.md
@@ -33,9 +33,10 @@ Shor's algorithm can solve practically every such problem.
 
 ## Integer factorization
 
-Originally, Shor's algorithm was designed to factorize an integer $$N$$,
-in which case the goal is to find the period $$s$$ of
-the modular exponentiation function $$f$$ (for reasons explained later):
+Originally, Shor's algorithm was designed to factorize an integer $$N$$.
+For reasons explained later,
+this means our goal is to find the period $$s$$ of
+the modular exponentiation function $$f$$:
 
 $$\begin{aligned}
     f(x)
@@ -79,7 +80,7 @@ $$\begin{aligned}
     \frac{1}{\sqrt{Q}} \sum_{x = 0}^{Q - 1} \Ket{x} \Ket{f(x)}
 \end{aligned}$$
 
-Then we measure $$f(x)$$, causing it collapse as follows,
+Then we measure $$f(x)$$, causing it collapse as follows
 for an unknown arbitrary value of $$x_0$$:
 
 $$\begin{aligned}