Reorganize extended examples and minor updates

.gitignore

@@ -7,4 +7,11 @@ dist
 *.egg-info
 *.pgf
 .ipynb_checkpoints
-src/hilbert_modgroup/version.py
+src/hilbert_modgroup/version.py
+.idea/
+.cache/
+.tox/
+.sage/
+.local/
+__pycache__/
+*.DISABLED

examples_extended/Example_coset.ipynb

@@ -0,0 +1,305 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "3b221a5e-d6b4-4421-aad7-988f124ea38d",
+   "metadata": {},
+   "source": [
+    "# Computing Right Coset Representatives.  \n",
+    "##  $K = \\mathbb{Q}(\\sqrt{10})$,  $\\widehat{\\Gamma}(\\mathcal{O}_K\\oplus \\mathfrak{a}, \\mathfrak{n})$, where $\\mathfrak{a} = (2, \\sqrt{10})$, $\\mathfrak{n} = (3, 1+\\sqrt{10})$.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "bc9054af-7a36-4e67-91fe-24a552bcd632",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from hilbert_modgroup.extended.all import ExtendedHilbertModularGroup, ExtendedHilbertPullback, NFCusp_wrt_lattice_ideal\n",
+    "K.<a> = QuadraticField(10)\n",
+    "lattice_ideal = K.fractional_ideal(2, a)\n",
+    "level_ideal = K.fractional_ideal(3, 1+a)\n",
+    "H1 = ExtendedHilbertModularGroup(K,  lattice_ideal, level_ideal = level_ideal, tp_units = True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "b2796116-be7f-4415-ae86-3ff9881feef6",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[\n",
+       "[        1 3/2*a - 3]  [         1 -1/2*a + 2]\n",
+       "[   -a - 2        -8], [    -a - 2     -a + 2],\n",
+       "\n",
+       "[       a + 6 -17/2*a + 17]  [1 0]\n",
+       "[      -a - 2    -2*a + 12], [0 1]\n",
+       "]"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "right_coset = H1.coset_matrices()\n",
+    "right_coset"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1e81e4eb-145d-44db-b35d-f697a3d0b63c",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7cf87439-7353-4862-b3b3-cff09b6d226f",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "61707006-487f-4d7f-acc3-4d50400415ec",
+   "metadata": {},
+   "source": [
+    "## Algorithm Steps: "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "151deb13-bcc8-449e-b5ee-c4ec748ee873",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Fractional ideal (1), Fractional ideal (3, a + 1)]"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Div = divisors(level_ideal)  #Finding divisors\n",
+    "Div"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "a60413df-428a-4d3d-94c3-19de66beab31",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "delta = Div[0]               #Fixing one divisor"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "645dcb4c-adaf-46bc-a56c-fabb6f8eb78b",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Fractional ideal (3, a + 2)"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "it = K.primes_of_degree_one_iter()         #Finding delta'\n",
+    "deltap = next(it)\n",
+    "while not deltap.is_coprime(level_ideal) or not (deltap * delta * lattice_ideal).is_principal():\n",
+    "    deltap = next(it)\n",
+    "c = (delta * lattice_ideal * deltap).gens_reduced()[0]\n",
+    "deltap                                     "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "id": "19dd1229-64d6-4645-be38-cbfe430b8a2c",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "-a - 2"
+      ]
+     },
+     "execution_count": 29,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "c                                          # Finding c"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "d3895fc8-c902-4f87-b438-0063767cf785",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Fractional ideal (1)"
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "I = delta + level_ideal/delta              # Value of I for this delta\n",
+    "I"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "id": "308468c1-3ffd-4d2a-8bfa-1b093ae9c66c",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[-a, 0, a]"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "D = []                                  # Finding residues of O_k/(n/delta)\n",
+    "for r in (level_ideal/delta).residues():\n",
+    "    D.append(r)\n",
+    "D"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "2c4a950e-a3b4-46c5-a51d-81116de0b976",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[\n",
+       "[        1 3/2*a - 3]  [         1 -1/2*a + 2]\n",
+       "[   -a - 2        -8], [    -a - 2     -a + 2],\n",
+       "\n",
+       "[       a + 6 -17/2*a + 17]\n",
+       "[      -a - 2    -2*a + 12]\n",
+       "]"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "L = []                                  # Finding all coset representative correspoding to fixed delta\n",
+    "for r in (level_ideal / delta).residues():\n",
+    "    if I.is_coprime(r):\n",
+    "        M = delta.prime_to_idealM_part(level_ideal / delta)\n",
+    "        u = (deltap * M).element_1_mod(level_ideal / delta)\n",
+    "        d = u * r + (1 - u)\n",
+    "        if d.is_zero():\n",
+    "            L.append(H1.ambient_group().create_element(1, -1 / c, c, d))\n",
+    "        else:\n",
+    "            B = K.fractional_ideal(c * lattice_ideal.inverse()).element_1_mod(K.fractional_ideal(d))\n",
+    "            b = -B / c\n",
+    "            a = (1 - B) / d\n",
+    "            L.append(H1.ambient_group().create_element(a, b, c, d))\n",
+    "L"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "53e850d1-608e-421c-b554-51ae349cca64",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "92f4ed0f-9b92-4f09-bdba-dcfc02aec635",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c30248ed-5888-49b9-aab3-fbce6d35a234",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b7e620a4-8839-4f85-b50a-a96d8822a738",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "20d520d9-772a-482b-bb06-e938d3dd9d78",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "passagemath 10.8.2",
+   "language": "sage",
+   "name": "sagemath"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}