1 files changed, 559 insertions, 0 deletions

diff --git a/epare/formulas.ipynb b/epare/formulas.ipynb
new file mode 100644
index 0000000..e63d295
--- /dev/null
+++ b/epare/formulas.ipynb
@@ -0,0 +1,559 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "672213e3-f426-4113-b5b6-304002474ce3",
+   "metadata": {},
+   "source": [
+    "# Formula analysis"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "09d92ba3-ede4-40c3-a061-a9c328e26fb5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import io\n",
+    "import json\n",
+    "\n",
+    "from pprint import pprint\n",
+    "import tabulate\n",
+    "from IPython.display import HTML, display\n",
+    "\n",
+    "from pyecsca.ec.params import load_params_ecgen\n",
+    "from pyecsca.ec.coordinates import AffineCoordinateModel\n",
+    "from pyecsca.ec.model import ShortWeierstrassModel\n",
+    "from pyecsca.ec.point import Point\n",
+    "from pyecsca.ec.mod import mod\n",
+    "from pyecsca.ec.error import UnsatisfiedAssumptionError\n",
+    "from pyecsca.misc.cfg import TemporaryConfig"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "5155a3ab-fd65-4add-ac3d-413de337c849",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "model = ShortWeierstrassModel()\n",
+    "affine_coords = AffineCoordinateModel(model)\n",
+    "\n",
+    "curve_data = b\"\"\"[{\n",
+    "    \"field\": {\n",
+    "        \"p\": \"0x57880ae612d14d33afd0c965938ac1ba44824036cea5d4a1699a9f44000fb273\"\n",
+    "    },\n",
+    "    \"a\": \"0x55d376d1fbcc919da841bb13352d4e419ac85a100fb806014bed884db5916399\",\n",
+    "    \"b\": \"0x21e27f7a065039ee59fd6b12c33d96709642aa6ac3738bd4f66fc663c79a19f8\",\n",
+    "    \"order\": \"0x57880ae612d14d33afd0c965938ac1b91f16808ee875095bafed41e136ca7bfe\",\n",
+    "    \"subgroups\": [\n",
+    "        {\n",
+    "            \"x\": \"0x407d5c52d9ad6f25bd7ff25f07804b4e4ebd4f5c992eafeb8c92e33f81e73b85\",\n",
+    "            \"y\": \"0x4b92eefcfa7c5e295c7e649801b83649156974064a8649f9a94f915754bd2183\",\n",
+    "            \"order\": \"0x57880ae612d14d33afd0c965938ac1b91f16808ee875095bafed41e136ca7bfe\",\n",
+    "            \"cofactor\": \"0x1\",\n",
+    "            \"points\": [\n",
+    "                {\n",
+    "                    \"x\": \"0x2571326cc99fe050bfe1a6a02ea635c56504e49d122152fd281761748a0501d9\",\n",
+    "                    \"y\": \"0x0000000000000000000000000000000000000000000000000000000000000000\",\n",
+    "                    \"order\": \"0x2\"\n",
+    "                },\n",
+    "                {\n",
+    "                    \"x\": \"0x266a5c5927e4f6feec30a9f3e2acb535657f365e1a24c1bb0b0d9158a7668639\",\n",
+    "                    \"y\": \"0x49c431e2a2704efb4b193e0fa26c60f815eaf195f712befd53b7bafb72b98488\",\n",
+    "                    \"order\": \"0x2bc405730968a699d7e864b2c9c560dc8f8b4047743a84add7f6a0f09b653dff\"\n",
+    "                }\n",
+    "            ]\n",
+    "        }\n",
+    "    ]\n",
+    "}]\"\"\"\n",
+    "curve_json = json.loads(curve_data)[0]\n",
+    "p = int(curve_json[\"field\"][\"p\"], 16)\n",
+    "order2_aff = Point(affine_coords,\n",
+    "                   x=mod(int(curve_json[\"subgroups\"][0][\"points\"][0][\"x\"], 16), p),\n",
+    "                   y=mod(int(curve_json[\"subgroups\"][0][\"points\"][0][\"y\"], 16), p))\n",
+    "orderbig_aff = Point(affine_coords,\n",
+    "                     x=mod(int(curve_json[\"subgroups\"][0][\"points\"][1][\"x\"], 16), p),\n",
+    "                     y=mod(int(curve_json[\"subgroups\"][0][\"points\"][1][\"y\"], 16), p))\n",
+    "\n",
+    "def allzero(pt):\n",
+    "    return all(value == 0 for value in pt.coords.values())\n",
+    "\n",
+    "def affine(pt):\n",
+    "    try:\n",
+    "        pt.to_affine()\n",
+    "    except Exception:\n",
+    "        return False\n",
+    "    return True\n",
+    "\n",
+    "def on_curve(curve, pt):\n",
+    "    try:\n",
+    "        return curve.is_on_curve(pt)\n",
+    "    except Exception:\n",
+    "        return False\n",
+    "\n",
+    "def eval_test(expected, out, curve):\n",
+    "    return (expected.equals_homog(out) if expected is not None else \"Undefined\", allzero(out), affine(out), on_curve(curve, out), out)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "e045a4cf-97db-4a2f-a191-582987f6473d",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Skipping jacobian-3, unsatisfied assumption\n",
+      "Skipping jacobian-0, unsatisfied assumption\n",
+      "Skipping projective-1, unsatisfied assumption\n",
+      "Skipping projective-3, unsatisfied assumption\n",
+      "Skipping w12-0, unsatisfied assumption\n",
+      "Skipping xyzz-3, unsatisfied assumption\n"
+     ]
+    }
+   ],
+   "source": [
+    "results_add = {}\n",
+    "results_dbl = {}\n",
+    "\n",
+    "with TemporaryConfig() as cfg:\n",
+    "    cfg.ec.unsatisfied_formula_assumption_action = \"ignore\"\n",
+    "    for coords_name, coords in model.coordinates.items():\n",
+    "        try:\n",
+    "            params = load_params_ecgen(io.BytesIO(curve_data), coords_name, infty=False)\n",
+    "        except UnsatisfiedAssumptionError:\n",
+    "            print(f\"Skipping {coords_name}, unsatisfied assumption\")\n",
+    "            continue\n",
+    "        results_add[coords_name] = {}\n",
+    "        results_dbl[coords_name] = {}\n",
+    "        infty = params.curve.neutral\n",
+    "        order2 = order2_aff.to_model(coords, params.curve)\n",
+    "        orderbig = orderbig_aff.to_model(coords, params.curve)\n",
+    "        orderbig_neg = params.curve.affine_negate(orderbig_aff).to_model(coords, params.curve)\n",
+    "        orderbig2 = params.curve.affine_double(orderbig_aff).to_model(coords, params.curve)\n",
+    "        zeros = Point(coords, **{var: mod(0, p) for var in coords.variables})\n",
+    "\n",
+    "        adds = set(formula for formula in coords.formulas.values() if formula.shortname == \"add\")\n",
+    "        dbls = set(formula for formula in coords.formulas.values() if formula.shortname == \"dbl\")\n",
+    "        for add in adds:\n",
+    "            res = {}\n",
+    "            results_add[coords_name][add.name] = res\n",
+    "            # P + P = ?\n",
+    "            PpP = add(p, orderbig, orderbig, **params.curve.parameters)[0]\n",
+    "            # P + infty = ?\n",
+    "            PpInfty = add(p, orderbig, infty, **params.curve.parameters)[0]\n",
+    "            InftypP = add(p, infty, orderbig, **params.curve.parameters)[0]\n",
+    "            # ord2 + ord2 = ?\n",
+    "            O2pO2 = add(p, order2, order2, **params.curve.parameters)[0]\n",
+    "            # P + Q = infty\n",
+    "            EqInfty1 = add(p, orderbig, orderbig_neg, **params.curve.parameters)[0]\n",
+    "            EqInfty2 = add(p, orderbig_neg, orderbig, **params.curve.parameters)[0]\n",
+    "            # P + zeros = ?\n",
+    "            PpZeros = add(p, orderbig, zeros, **params.curve.parameters)[0]\n",
+    "            ZerospP = add(p, zeros, orderbig, **params.curve.parameters)[0]\n",
+    "            res[\"PpP\"] = eval_test(orderbig2, PpP, params.curve)\n",
+    "            res[\"PpInfty\"] = eval_test(orderbig, PpInfty, params.curve)\n",
+    "            res[\"InftypP\"] = eval_test(orderbig, InftypP, params.curve)\n",
+    "            res[\"O2pO2\"] = eval_test(infty, O2pO2, params.curve)\n",
+    "            res[\"EqInfty1\"] = eval_test(infty, EqInfty1, params.curve)\n",
+    "            res[\"EqInfty2\"] = eval_test(infty, EqInfty2, params.curve)\n",
+    "            res[\"PpZeros\"] = eval_test(None, PpZeros, params.curve)\n",
+    "            res[\"ZerospP\"] = eval_test(None, ZerospP, params.curve)\n",
+    "        for dbl in dbls:\n",
+    "            res = {}\n",
+    "            results_dbl[coords_name][dbl.name] = res\n",
+    "            O2twice = dbl(p, order2, **params.curve.parameters)[0]\n",
+    "            Inftytwice = dbl(p, infty, **params.curve.parameters)[0]\n",
+    "            Zerostwice = dbl(p, zeros, **params.curve.parameters)[0]\n",
+    "            res[\"O2twice\"] = eval_test(infty, O2twice, params.curve)\n",
+    "            res[\"Inftytwice\"] = eval_test(infty, Inftytwice, params.curve)\n",
+    "            res[\"Zerostwice\"] = eval_test(None, Zerostwice, params.curve)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "d0928c16-9688-4d65-a559-5895d1b7c85b",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "<thead>\n",
+       "<tr><th>Formula       </th><th>Test    </th><th>Correct?  </th><th>Zeros?  </th><th>Affine?  </th><th>On curve?  </th></tr>\n",
+       "</thead>\n",
+       "<tbody>\n",
+       "<tr><td>add-2007-bl   </td><td>PpP     </td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>add-2007-bl   </td><td>PpInfty </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2007-bl   </td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2007-bl   </td><td>O2pO2   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-2007-bl   </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-2007-bl   </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-2007-bl   </td><td>PpZeros </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2007-bl   </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2002-bj   </td><td>PpP     </td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>add-2002-bj   </td><td>PpInfty </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2002-bj   </td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2002-bj   </td><td>O2pO2   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-2002-bj   </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-2002-bj   </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-2002-bj   </td><td>PpZeros </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2002-bj   </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2015-rcb  </td><td>PpP     </td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>add-2015-rcb  </td><td>PpInfty </td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>add-2015-rcb  </td><td>InftypP </td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>add-2015-rcb  </td><td>O2pO2   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-2015-rcb  </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-2015-rcb  </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-2015-rcb  </td><td>PpZeros </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2015-rcb  </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-1998-cmo</td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-1998-cmo</td><td>PpInfty </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-1998-cmo</td><td>InftypP </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-1998-cmo</td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-1998-cmo</td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>mmadd-1998-cmo</td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>mmadd-1998-cmo</td><td>PpZeros </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-1998-cmo</td><td>ZerospP </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo  </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo  </td><td>PpInfty </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo  </td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo  </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo  </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-1998-cmo  </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-1998-cmo  </td><td>PpZeros </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo  </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-1998-cmo </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-1998-cmo </td><td>PpInfty </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>madd-1998-cmo </td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-1998-cmo </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-1998-cmo </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>madd-1998-cmo </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>madd-1998-cmo </td><td>PpZeros </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>madd-1998-cmo </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2015-rcb </td><td>PpP     </td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>madd-2015-rcb </td><td>PpInfty </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2015-rcb </td><td>InftypP </td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>madd-2015-rcb </td><td>O2pO2   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>madd-2015-rcb </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>madd-2015-rcb </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>madd-2015-rcb </td><td>PpZeros </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2015-rcb </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>PpInfty </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>PpZeros </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2009-bl </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2009-bl </td><td>PpInfty </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2009-bl </td><td>InftypP </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2009-bl </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2009-bl </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>mmadd-2009-bl </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>mmadd-2009-bl </td><td>PpZeros </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2009-bl </td><td>ZerospP </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>add-2009-bl   </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2009-bl   </td><td>PpInfty </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2009-bl   </td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2009-bl   </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2009-bl   </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-2009-bl   </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-2009-bl   </td><td>PpZeros </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2009-bl   </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2009-bl  </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2009-bl  </td><td>PpInfty </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2009-bl  </td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2009-bl  </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2009-bl  </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>madd-2009-bl  </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>madd-2009-bl  </td><td>PpZeros </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2009-bl  </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>PpInfty </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>PpZeros </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2008-s    </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2008-s    </td><td>PpInfty </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2008-s    </td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2008-s    </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2008-s    </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-2008-s    </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-2008-s    </td><td>PpZeros </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2008-s    </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2008-s   </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2008-s   </td><td>PpInfty </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2008-s   </td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2008-s   </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2008-s   </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>madd-2008-s   </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>madd-2008-s   </td><td>PpZeros </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2008-s   </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2008-s  </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2008-s  </td><td>PpInfty </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2008-s  </td><td>InftypP </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2008-s  </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2008-s  </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>mmadd-2008-s  </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>mmadd-2008-s  </td><td>PpZeros </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2008-s  </td><td>ZerospP </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2007-bl  </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2007-bl  </td><td>PpInfty </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2007-bl  </td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2007-bl  </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2007-bl  </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>madd-2007-bl  </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>madd-2007-bl  </td><td>PpZeros </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2007-bl  </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo  </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo  </td><td>PpInfty </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo  </td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo  </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo  </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-1998-cmo  </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-1998-cmo  </td><td>PpZeros </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo  </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>zadd-2007-m   </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>zadd-2007-m   </td><td>PpInfty </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>zadd-2007-m   </td><td>InftypP </td><td>False     </td><td>False   </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>zadd-2007-m   </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>zadd-2007-m   </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>zadd-2007-m   </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>zadd-2007-m   </td><td>PpZeros </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>zadd-2007-m   </td><td>ZerospP </td><td>Undefined </td><td>False   </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2001-b    </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2001-b    </td><td>PpInfty </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2001-b    </td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2001-b    </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2001-b    </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-2001-b    </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-2001-b    </td><td>PpZeros </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2001-b    </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>PpInfty </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>PpZeros </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-cmo-2</td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1986-cc   </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1986-cc   </td><td>PpInfty </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1986-cc   </td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1986-cc   </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1986-cc   </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-1986-cc   </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-1986-cc   </td><td>PpZeros </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1986-cc   </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2004-hmv </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2004-hmv </td><td>PpInfty </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2004-hmv </td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2004-hmv </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2004-hmv </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>madd-2004-hmv </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>madd-2004-hmv </td><td>PpZeros </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2004-hmv </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2007-bl   </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2007-bl   </td><td>PpInfty </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2007-bl   </td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2007-bl   </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2007-bl   </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-2007-bl   </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-2007-bl   </td><td>PpZeros </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-2007-bl   </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2008-g   </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2008-g   </td><td>PpInfty </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2008-g   </td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2008-g   </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2008-g   </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>madd-2008-g   </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>madd-2008-g   </td><td>PpZeros </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>madd-2008-g   </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2007-bl </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2007-bl </td><td>PpInfty </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2007-bl </td><td>InftypP </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2007-bl </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2007-bl </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>mmadd-2007-bl </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>mmadd-2007-bl </td><td>PpZeros </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>mmadd-2007-bl </td><td>ZerospP </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-hnm  </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-hnm  </td><td>PpInfty </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-hnm  </td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-hnm  </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-hnm  </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-1998-hnm  </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>add-1998-hnm  </td><td>PpZeros </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>add-1998-hnm  </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd          </td><td>PpP     </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd          </td><td>PpInfty </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>madd          </td><td>InftypP </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd          </td><td>O2pO2   </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>madd          </td><td>EqInfty1</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>madd          </td><td>EqInfty2</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>madd          </td><td>PpZeros </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>madd          </td><td>ZerospP </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "</tbody>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "table = [[\"Formula\", \"Test\", \"Correct?\", \"Zeros?\", \"Affine?\", \"On curve?\"]]\n",
+    "test_filter = None\n",
+    "for vals in results_add.values():\n",
+    "    for name, formula in vals.items():\n",
+    "        for k, v in formula.items():\n",
+    "            if test_filter is None or k in test_filter:\n",
+    "                table.append((name, k, v[0], v[1], v[2], v[3]))\n",
+    "display(HTML(tabulate.tabulate(table, tablefmt=\"html\", headers=\"firstrow\")))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "2d74db05-0606-4e54-87e0-c7fe0cbb5519",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "<thead>\n",
+       "<tr><th>Formula       </th><th>Test      </th><th>Correct?  </th><th>Zeros?  </th><th>Affine?  </th><th>On curve?  </th></tr>\n",
+       "</thead>\n",
+       "<tbody>\n",
+       "<tr><td>mdbl-2007-bl  </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>mdbl-2007-bl  </td><td>Inftytwice</td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>mdbl-2007-bl  </td><td>Zerostwice</td><td>Undefined </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2015-rcb  </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2015-rcb  </td><td>Inftytwice</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2015-rcb  </td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>dbl-1998-cmo  </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-1998-cmo  </td><td>Inftytwice</td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>dbl-1998-cmo  </td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>dbl-2007-bl   </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2007-bl   </td><td>Inftytwice</td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>dbl-2007-bl   </td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>dbl-1998-cmo-2</td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-1998-cmo-2</td><td>Inftytwice</td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>dbl-1998-cmo-2</td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>dbl-2009-bl   </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2009-bl   </td><td>Inftytwice</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2009-bl   </td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>mdbl-2009-bl  </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>mdbl-2009-bl  </td><td>Inftytwice</td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>mdbl-2009-bl  </td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>dbl-1998-cmo-2</td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-1998-cmo-2</td><td>Inftytwice</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-1998-cmo-2</td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>mdbl-2008-s-1 </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>mdbl-2008-s-1 </td><td>Inftytwice</td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>mdbl-2008-s-1 </td><td>Zerostwice</td><td>Undefined </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2008-s-1  </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2008-s-1  </td><td>Inftytwice</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2008-s-1  </td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>dbl-1998-cmo  </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-1998-cmo  </td><td>Inftytwice</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-1998-cmo  </td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>dbl-1986-cc   </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-1986-cc   </td><td>Inftytwice</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-1986-cc   </td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>dbl-2007-bl   </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2007-bl   </td><td>Inftytwice</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2007-bl   </td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>dbl-1998-cmo-2</td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-1998-cmo-2</td><td>Inftytwice</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-1998-cmo-2</td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>dbl-1998-hnm  </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-1998-hnm  </td><td>Inftytwice</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-1998-hnm  </td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>mdbl-2007-bl  </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>mdbl-2007-bl  </td><td>Inftytwice</td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>mdbl-2007-bl  </td><td>Zerostwice</td><td>Undefined </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2002-bj-3 </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2002-bj-3 </td><td>Inftytwice</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2002-bj-3 </td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>dbl-2002-bj   </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2002-bj   </td><td>Inftytwice</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2002-bj   </td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>dbl-2002-it-2 </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2002-it-2 </td><td>Inftytwice</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2002-it-2 </td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>dbl-2002-it   </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2002-it   </td><td>Inftytwice</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2002-it   </td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>dbl-2002-bj-2 </td><td>O2twice   </td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2002-bj-2 </td><td>Inftytwice</td><td>True      </td><td>False   </td><td>False    </td><td>True       </td></tr>\n",
+       "<tr><td>dbl-2002-bj-2 </td><td>Zerostwice</td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "</tbody>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "table = [[\"Formula\", \"Test\", \"Correct?\", \"Zeros?\", \"Affine?\", \"On curve?\"]]\n",
+    "test_filter = None\n",
+    "for vals in results_dbl.values():\n",
+    "    for name, formula in vals.items():\n",
+    "        for k, v in formula.items():\n",
+    "            if test_filter is None or k in test_filter:\n",
+    "                table.append((name, k, v[0], v[1], v[2], v[3]))\n",
+    "display(HTML(tabulate.tabulate(table, tablefmt=\"html\", headers=\"firstrow\")))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9194ed95-4aeb-4aeb-bf8f-b8e0c1f1f987",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}