Regenerate notebook

qualtran/bloqs/gf_arithmetic/gf2_inverse.ipynb

@@ -58,8 +58,10 @@
     "    a^{-1} = a^{2^m - 2}\n",
     "$$\n",
     "\n",
-    "The exponential $a^{2^m - 2}$ using $\\mathcal{O}(m)$ squaring and $\\mathcal{O}(\\log_2(m))$\n",
-    "multiplications via Itoh-Tsujii inversion. See Ref[1, 2] for more details.\n",
+    "The exponential $a^{2^m - 2}$ is computed using $\\mathcal{O}(m)$ squaring and\n",
+    "$\\mathcal{O}(\\log_2(m))$ multiplications via Itoh-Tsujii inversion. The algorithm is described on\n",
+    "page 4 and 5 of Ref[1] and resembles binary exponentiation. The inverse is computed as $B_{n-1}^2$,\n",
+    "where $B_1 = x$ and $B_{i+j} = B_i B_j^{2^i}$.\n",
     "\n",
     "#### Parameters\n",
     " - `bitsize`: The degree $m$ of the galois field $GF(2^m)$. Also corresponds to the number of qubits in the input register whose inverse should be calculated. \n",
@@ -70,8 +72,8 @@
     " - `junk`: Output RIGHT register of size $m$ and shape ($m - 2$) that stores results from intermediate multiplications. \n",
     "\n",
     "#### References\n",
-    " - [Efficient quantum circuits for binary elliptic curve arithmetic:     reducing T -gate complexity](https://arxiv.org/abs/1209.6348). \n",
-    " - [Structure of parallel multipliers for a class of fields     GF(2^m)](https://doi.org/10.1016/0890-5401(89)90045-X)\n"
+    " - [Efficient quantum circuits for binary elliptic curve arithmetic: reducing T -gate complexity](https://arxiv.org/abs/1209.6348). Section 2.3\n",
+    " - [Structure of parallel multipliers for a class of fields GF(2^m)](https://doi.org/10.1016/0890-5401(89)90045-X)\n"
    ]
   },
   {