Use GitHub math fences for display equations

README.md

@@ -20,19 +20,19 @@ This repository studies a Boolean-indexed polynomial basis in which every basis
 Let $N = 2^m$, let $F$ be an arbitrary field, and index Boolean vectors by
 $y=(y_0,\ldots,y_{m-1}) \in \{0,1\}^m$. Define
 
-$$
+```math
 K_y(X)=\prod_{i=0}^{m-1}\left(X^{2^i}+y_i\right).
-$$
+```
 
 The paper proves three structural facts.
 
 ### 1. Boolean kernel basis
 
 The family
 
-$$
+```math
 \{K_y : y\in\{0,1\}^m\}
-$$
+```
 
 is a basis of $F[X]_{<N}$, even though every $K_y$ has degree exactly $N-1$.
 
@@ -42,15 +42,15 @@ This is deliberately unlike a degree-graded basis: low degree cannot be read off
 
 For
 
-$$
+```math
 U(X)=\sum_y \lambda_y K_y(X)=\sum_a u_a X^{|a|_2},
-$$
+```
 
 the monomial coefficients satisfy
 
-$$
+```math
 u_a=\sum_{y\ge \bar a}\lambda_y.
-$$
+```
 
 Thus kernel coordinates and monomial coordinates are related by a Boolean zeta transform composed with the complement permutation. The inverse is Boolean Möbius inversion. Both admit $O(N\log N)$ butterfly algorithms.
 
@@ -59,21 +59,21 @@ Thus kernel coordinates and monomial coordinates are related by a Boolean zeta t
 Split a kernel index as $y=(x,h)$, where $x\in\{0,1\}^k$ and
 $h\in\{0,1\}^{q}$ with $q=m-k$. Then
 
-$$
+```math
 \deg U < 2^k
 \quad\Longleftrightarrow\quad
 \lambda_{(x,h)}
 =
 (-1)^{q-\operatorname{wt}(h)}\mu_x
-$$
+```
 
 for a unique function $\mu:\{0,1\}^k\to F$.
 
 In characteristic two, $-1=1$, so this becomes constancy across each high-coordinate fiber:
 
-$$
+```math
 \lambda_{(x,h)}=\mu_x.
-$$
+```
 
 ## Why this artifact exists