fix style

neps/nep-0488.md

@@ -87,26 +87,26 @@ $$
 y^2 \equiv x^3 + Ax + B \mod p
 $$
 
-together with an imaginary point at infinity $\mathcal{O}$, where: $A, B \in F_p$, p is prime > 3, and $4A^3 + 27B^2 \not \equiv 0 \mod p$
+together with an imaginary point at infinity $\mathcal{O}$, where: $A, B \in F_p$, $p$ is a prime $> 3$, and $4A^3 + 27B^2 \not \equiv 0 \mod p$
 
-In the case of BLS12-381 equation is $y^2 \equiv x^3 + 4 \mod p$[^15],[^51],[^14],[^11]
+In the case of BLS12-381 the equation is $y^2 \equiv x^3 + 4 \mod p$[^15],[^51],[^14],[^11]
 
 **Parameters for our case:**
 
 - $A = 0$
 - $B = 4$
 - $p = \mathtt{0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab}$
 
-Let $P \in E(F_q)$ have coordinates (x, y), define **$-P$**  as a point on a curve with coordinates (x, -y).
+Let $P \in E(F_q)$ have coordinates $(x, y)$, define **$-P$** as a point on a curve with coordinates $(x, -y)$.
 
-**The addition operation for Elliptic Curve** is a function $+\colon E(F_p) \times E(F_p) \rightarrow E(F_p)$ defined with following rules: let P and Q $\in E(F_p)$
+**The addition operation for Elliptic Curve** is a function $+\colon E(F_p) \times E(F_p) \rightarrow E(F_p)$ defined with following rules: let $P$ and $Q \in E(F_p)$
 
 - if  $P \ne Q$ and $P \ne -Q$
-  - draw a line passing through P and Q. This line intersects the curve at a third point R
-  - reflect the point R across the x-axis by changing the sign of the y-coordinate. The resulting point is P+Q.
+  - draw a line passing through $P$ and $Q$. This line intersects the curve at a third point $R$.
+  - reflect the point $R$ across the $x$-axis by changing the sign of the $y$-coordinate. The resulting point is $P+Q$.
 - if $P=Q$
-  - draw a tangent line throw P for an elliptic curve. The line will intersect the curve at the second point R.
-  - reflect the point R across the x-axis the same way to get point 2P
+  - draw a tangent line through $P$ for an elliptic curve. The line will intersect the curve at the second point $R$.
+  - reflect the point $R$ across the $x$-axis the same way to get point $2P$
 - $P = -Q$
   - $P + Q = P + (-P) = \mathcal{O}$ — the point on infinity
 - $Q = \mathcal{O}$
@@ -552,7 +552,7 @@ This section aims to validate the correctness of point inversion:
 Edge cases:
 
 - Point not from $G_1$
-- -$\mathcal{O}$
+- $-\mathcal{O}$
 
 <ins>Tests for incorrect data</ins>