diff --git a/exact_quantum_factoring_v2.txt b/exact_quantum_factoring_v2.txt
index 8f354d0..e6997fc 100644
--- a/exact_quantum_factoring_v2.txt
+++ b/exact_quantum_factoring_v2.txt
@@ -14,7 +14,7 @@ quantum circuits with the following properties.
   - Gate count and qubit count are bounded by a fixed polynomial in
     $n = n(N)$, roughly the bit length of $N$.
   - Every circuit uses only the fixed finite gate set $G$: NOT, CNOT,
-    Toffoli, Hadamard, $S = \mathrm{diag}(1,i)$, their inverses, and
+    Toffoli, Hadamard, $S = diag(1,i)$, their inverses, and
     their singly controlled versions.
 
 "Polynomial-time uniform" means that some single deterministic classical
@@ -162,8 +162,8 @@ success probability exactly 1/4.
 ./pdf/ozols-roetteler-roland-2012-quantum-rejection-sampling.pdf
 
 As a first computation, take $N = 15$ and $a = 2$, a unit mod 15. The
-powers of 2 mod 15 are $2, 4, 8, 1, 2, \ldots$, so
-$\operatorname{ord}_{15}(2) = 4$. Since $r = 4$ is even,
+powers of 2 mod 15 are $2, 4, 8, 1, 2, ...$, so
+$ord_{15}(2) = 4$. Since $r = 4$ is even,
 $\gcd(2^{r/2} - 1, 15) = \gcd(3, 15) = 3$, splitting $15 = 3 \times 5$.
 Every factoring run reduces to this. The remaining work is
 exact-probability engineering that makes $r$ (a multiple of the true