From 5018f7a89a182ae4b8391eae708c76b417c584d3 Mon Sep 17 00:00:00 2001
From: Luke Naylor <l.naylor@sms.ed.ac.uk>
Date: Fri, 5 Jan 2024 23:03:51 +0000
Subject: [PATCH] Add to notebook for irrational beta_minus case

---
 other_P_choice.ipynb | 408 ++++++++++++++++++++++++++++++-------------
 1 file changed, 291 insertions(+), 117 deletions(-)

diff --git a/other_P_choice.ipynb b/other_P_choice.ipynb
index 217762d..3a2d430 100644
--- a/other_P_choice.ipynb
+++ b/other_P_choice.ipynb
@@ -45,7 +45,7 @@
        "$\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = R \\\\ \\mathrm{ch}_{1} = C \\ell^{1} \\\\ \\mathrm{ch}_{2} = D \\ell^{2} \\end{array}$"
       ],
       "text/plain": [
-       "<pseudowalls.chern_character.Chern_Char object at 0x7f73433b6ad0>"
+       "<pseudowalls.chern_character.Chern_Char object at 0x7f489c75e350>"
       ]
      },
      "execution_count": 3,
@@ -73,7 +73,7 @@
        "$\\displaystyle \\text{ Twisted Chern Character for $\\beta={ B }$ } \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = R \\\\ \\mathrm{ch}_{1} = {\\mathrm{ch}_1^B(v)} \\ell^{1} \\\\ \\mathrm{ch}_{2} = {\\mathrm{ch}_2^B(v)} \\ell^{2} \\end{array}$"
       ],
       "text/plain": [
-       "<pseudowalls.chern_character.Twisted_Chern_Char object at 0x7f733b798820>"
+       "<pseudowalls.chern_character.Twisted_Chern_Char object at 0x7f48926ec4d0>"
       ]
      },
      "execution_count": 4,
@@ -93,6 +93,16 @@
   {
    "cell_type": "code",
    "execution_count": 5,
+   "id": "c21754aa",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "assume(twisted_v2 > 0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
    "id": "6fced6d0",
    "metadata": {},
    "outputs": [
@@ -105,10 +115,10 @@
        "$\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = r \\\\ \\mathrm{ch}_{1} = c \\ell^{1} \\\\ \\mathrm{ch}_{2} = d \\ell^{2} \\end{array}$"
       ],
       "text/plain": [
-       "<pseudowalls.chern_character.Chern_Char object at 0x7f733b7987f0>"
+       "<pseudowalls.chern_character.Chern_Char object at 0x7f4892882f90>"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -120,7 +130,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
    "id": "711e4205",
    "metadata": {},
    "outputs": [
@@ -133,10 +143,10 @@
        "$\\displaystyle \\text{ Twisted Chern Character for $\\beta={ B }$ } \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = r \\\\ \\mathrm{ch}_{1} = {\\mathrm{ch}_1^B(u)} \\ell^{1} \\\\ \\mathrm{ch}_{2} = {\\mathrm{ch}_2^B(u)} \\ell^{2} \\end{array}$"
       ],
       "text/plain": [
-       "<pseudowalls.chern_character.Twisted_Chern_Char object at 0x7f733b799f30>"
+       "<pseudowalls.chern_character.Twisted_Chern_Char object at 0x7f48926ef990>"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 7,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -168,7 +178,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 8,
    "id": "17c390cd",
    "metadata": {},
    "outputs": [
@@ -184,7 +194,7 @@
        "A^2 == 2*twisted_v2/R"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -207,7 +217,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 9,
    "id": "47b34ed7",
    "metadata": {},
    "outputs": [
@@ -223,7 +233,7 @@
        "-1/2*A^2*r + twisted_u2 > 0"
       ]
      },
-     "execution_count": 8,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -234,7 +244,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 10,
    "id": "d8abf566",
    "metadata": {},
    "outputs": [
@@ -250,7 +260,7 @@
        "R*twisted_u2 - r*twisted_v2 > 0"
       ]
      },
-     "execution_count": 9,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -266,7 +276,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 11,
    "id": "194e313d",
    "metadata": {},
    "outputs": [
@@ -282,7 +292,7 @@
        "d > 1/2*B^2*r + B*q + r*twisted_v2/R"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -311,7 +321,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 12,
    "id": "f09514cb",
    "metadata": {},
    "outputs": [],
@@ -321,7 +331,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 13,
    "id": "73e90e13",
    "metadata": {},
    "outputs": [
@@ -337,7 +347,7 @@
        "1/2*beta^2*r + beta*q + 1/2*q^2/r"
       ]
      },
-     "execution_count": 40,
+     "execution_count": 13,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -358,23 +368,23 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 61,
+   "execution_count": 14,
    "id": "a686d2da",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<html>\\(\\displaystyle \\frac{1}{2} \\, B^{2} r + B q - \\frac{{\\left(q - {\\mathrm{ch}_1^B(v)}\\right)}^{2}}{2 \\, {\\left(R - r\\right)}} + {\\mathrm{ch}_2^B(v)}\\)</html>"
+       "<html>\\(\\displaystyle \\frac{1}{2} \\, \\beta^{2} r + \\beta q - \\frac{{\\left({\\operatorname{ch}_1^{\\beta}(v)} - q\\right)}^{2}}{2 \\, {\\left(R - r\\right)}} + {\\operatorname{ch}_2^{\\beta}(v)}\\)</html>"
       ],
       "text/latex": [
-       "$\\displaystyle \\frac{1}{2} \\, B^{2} r + B q - \\frac{{\\left(q - {\\mathrm{ch}_1^B(v)}\\right)}^{2}}{2 \\, {\\left(R - r\\right)}} + {\\mathrm{ch}_2^B(v)}$"
+       "$\\displaystyle \\frac{1}{2} \\, \\beta^{2} r + \\beta q - \\frac{{\\left({\\operatorname{ch}_1^{\\beta}(v)} - q\\right)}^{2}}{2 \\, {\\left(R - r\\right)}} + {\\operatorname{ch}_2^{\\beta}(v)}$"
       ],
       "text/plain": [
-       "1/2*B^2*r + B*q - 1/2*(q - twisted_v1)^2/(R - r) + twisted_v2"
+       "1/2*beta^2*r + beta*q - 1/2*(ch1bv - q)^2/(R - r) + ch2bv"
       ]
      },
-     "execution_count": 61,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -397,27 +407,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 15,
    "id": "3f3b7d88",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<html>\\(\\displaystyle \\frac{1}{2} \\, \\beta^{2} r + \\beta q - \\frac{{\\left({\\operatorname{ch}_1^{\\beta}(v)} - q\\right)}^{2}}{2 \\, {\\left(R - r\\right)}} + {\\operatorname{ch}_2^{\\beta}(v)}\\)</html>"
-      ],
-      "text/latex": [
-       "$\\displaystyle \\frac{1}{2} \\, \\beta^{2} r + \\beta q - \\frac{{\\left({\\operatorname{ch}_1^{\\beta}(v)} - q\\right)}^{2}}{2 \\, {\\left(R - r\\right)}} + {\\operatorname{ch}_2^{\\beta}(v)}$"
-      ],
-      "text/plain": [
-       "1/2*beta^2*r + beta*q - 1/2*(ch1bv - q)^2/(R - r) + ch2bv"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# substitutions to replace beta -> B in relevant equations to specialize to problem 1\n",
     "beta_substitutions = [beta==B, ch1bv==twisted_v.ch[1], ch2bv==twisted_v.ch[2]]"
@@ -425,7 +418,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 118,
+   "execution_count": 16,
    "id": "ed6fbc1d",
    "metadata": {},
    "outputs": [],
@@ -439,7 +432,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": 17,
    "id": "d006ea59",
    "metadata": {},
    "outputs": [
@@ -455,7 +448,7 @@
        "1/2*B^2*r"
       ]
      },
-     "execution_count": 43,
+     "execution_count": 17,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -466,7 +459,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 18,
    "id": "c1ec0dec",
    "metadata": {},
    "outputs": [
@@ -482,7 +475,7 @@
        "1/2*B^2*r"
       ]
      },
-     "execution_count": 44,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -491,14 +484,6 @@
     "bgmlv2_d_upperbound_terms.linear"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "e124ab6f",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
   {
    "cell_type": "markdown",
    "id": "ae775c5e",
@@ -509,7 +494,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
+   "execution_count": 19,
    "id": "3eab094d",
    "metadata": {},
    "outputs": [
@@ -522,10 +507,10 @@
        "$\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 3 \\\\ \\mathrm{ch}_{1} = 2 \\ell^{1} \\\\ \\mathrm{ch}_{2} = -2 \\ell^{2} \\end{array}$"
       ],
       "text/plain": [
-       "<pseudowalls.chern_character.Chern_Char object at 0x7f733b799300>"
+       "<pseudowalls.chern_character.Chern_Char object at 0x7f489c831fd0>"
       ]
      },
-     "execution_count": 48,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -537,7 +522,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 88,
+   "execution_count": 20,
    "id": "b4f4f892",
    "metadata": {},
    "outputs": [],
@@ -547,7 +532,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 89,
+   "execution_count": 21,
    "id": "8756764b",
    "metadata": {
     "scrolled": true
@@ -562,10 +547,10 @@
        "$\\displaystyle \\text{ Twisted Chern Character for $\\beta={ -\\frac{67}{99} }$ } \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 3 \\\\ \\mathrm{ch}_{1} = \\frac{133}{33} \\ell^{1} \\\\ \\mathrm{ch}_{2} = \\frac{265}{6534} \\ell^{2} \\end{array}$"
       ],
       "text/plain": [
-       "<pseudowalls.chern_character.Twisted_Chern_Char object at 0x7f7332a27ee0>"
+       "<pseudowalls.chern_character.Twisted_Chern_Char object at 0x7f48926f1250>"
       ]
      },
-     "execution_count": 89,
+     "execution_count": 21,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -577,7 +562,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 110,
+   "execution_count": 22,
    "id": "16dce8ed",
    "metadata": {},
    "outputs": [],
@@ -587,7 +572,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 111,
+   "execution_count": 23,
    "id": "bf3b7639",
    "metadata": {},
    "outputs": [],
@@ -603,7 +588,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 112,
+   "execution_count": 24,
    "id": "db9f2513",
    "metadata": {},
    "outputs": [
@@ -619,7 +604,7 @@
        "4489/19602*r + 4489/2178/(r - 3) - 8579/6534"
       ]
      },
-     "execution_count": 112,
+     "execution_count": 24,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -633,7 +618,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 113,
+   "execution_count": 25,
    "id": "71f8d1ef",
    "metadata": {},
    "outputs": [
@@ -649,7 +634,7 @@
        "4489/19602*r + 2/r - 134/99"
       ]
      },
-     "execution_count": 113,
+     "execution_count": 25,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -663,7 +648,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 114,
+   "execution_count": 26,
    "id": "bd3a5e35",
    "metadata": {},
    "outputs": [
@@ -679,7 +664,7 @@
        "2377/9801*r - 134/99"
       ]
      },
-     "execution_count": 114,
+     "execution_count": 26,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -691,32 +676,33 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 115,
+   "execution_count": 27,
    "id": "ec13b9b8",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": "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\n",
+      "image/png": "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\n",
       "text/plain": [
        "Graphics object consisting of 3 graphics primitives"
       ]
      },
-     "execution_count": 115,
+     "execution_count": 27,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "r_range = r,0,17\n",
+    "r_range = r,0,18\n",
     "\n",
     "example_plot = (\n",
-    "    plot(example_upperbound_1, (r,3,17))\n",
-    "    + plot(example_upperbound_2, (r,0,17))\n",
+    "    plot(example_upperbound_1, (r,3,18), rgbcolor=\"purple\")\n",
+    "    + plot(example_upperbound_2, r_range)\n",
     "    + plot(example_lowerbound_1, r_range, rgbcolor=\"red\")\n",
     ")\n",
     "example_plot.ymin(-1.5)\n",
     "example_plot.ymax(3)\n",
+    "example_plot.axes_labels([r\"$r$\", r\"$d$\"])\n",
     "example_plot"
    ]
   },
@@ -728,101 +714,293 @@
     "# Finding intersection points"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "d0f2a900",
+   "metadata": {},
+   "source": [
+    "Find intersection of lower bound with upper bound from bgmlv2:"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 132,
-   "id": "c36db5ce",
+   "execution_count": 28,
+   "id": "ec524a1e",
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<html>\\(\\displaystyle \\left[\\left(-\\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^B(v)}}}, 1\\right), \\left(\\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^B(v)}}}, 1\\right)\\right]\\)</html>"
+      ],
+      "text/latex": [
+       "$\\displaystyle \\left[\\left(-\\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^B(v)}}}, 1\\right), \\left(\\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^B(v)}}}, 1\\right)\\right]$"
+      ],
+      "text/plain": [
+       "[(-sqrt(1/2)*q*sqrt(R/twisted_v2), 1), (sqrt(1/2)*q*sqrt(R/twisted_v2), 1)]"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "var(\"epsilon\", latex_name=r\"\\varepsilon\")\n",
+    "( intersections_bgmlv2 :=\n",
+    "    ( bgmlv2_d_upperbound_terms.all - radius_condition_d_bound.rhs() )\n",
+    "      .roots(r)\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "id": "13ffe85d",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<html>\\(\\displaystyle \\frac{R q^{2}}{2 \\, {\\mathrm{ch}_2^B(v)}} = r^{2}\\)</html>"
+       "<html>\\(\\displaystyle \\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^B(v)}}}\\)</html>"
       ],
       "text/latex": [
-       "$\\displaystyle \\frac{R q^{2}}{2 \\, {\\mathrm{ch}_2^B(v)}} = r^{2}$"
+       "$\\displaystyle \\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^B(v)}}}$"
       ],
       "text/plain": [
-       "1/2*R*q^2/twisted_v2 == r^2"
+       "sqrt(1/2)*q*sqrt(R/twisted_v2)"
       ]
      },
-     "execution_count": 132,
+     "execution_count": 29,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "(\n",
-    "    ( bgmlv2_d_upperbound_terms.all == radius_condition_d_bound.rhs() )\n",
-    "    .subtract_from_both_sides(B^2*r/2 + B*q)\n",
-    "    .multiply_both_sides(r * R)\n",
-    "    .divide_both_sides(twisted_v.ch[2])\n",
+    "( positive_intersection_bgmlv2 :=\n",
+    "    intersections_bgmlv2[1][0]\n",
     ")"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "e56b41cc",
+   "metadata": {},
+   "source": [
+    "Quickly verify this is indeed a root:"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 137,
-   "id": "f712c5fd",
+   "execution_count": 30,
+   "id": "fc553cfa",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<html>\\(\\displaystyle r_{\\mathit{alt}}\\)</html>"
+       "<html>\\(\\displaystyle 0\\)</html>"
       ],
       "text/latex": [
-       "$\\displaystyle r_{\\mathit{alt}}$"
+       "$\\displaystyle 0$"
       ],
       "text/plain": [
-       "r_alt"
+       "0"
       ]
      },
-     "execution_count": 137,
+     "execution_count": 30,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "var(\"r_alt\")"
+    "(\n",
+    "    ( bgmlv2_d_upperbound_terms.all - radius_condition_d_bound.rhs() )\n",
+    "    .subs(r==positive_intersection_bgmlv2)\n",
+    ").factor()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "33d05050",
+   "metadata": {},
+   "source": [
+    "Find intersection of lower bound with upper bound from bgmlv2:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 166,
-   "id": "829e36f9",
+   "execution_count": 31,
+   "id": "05ba80db",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<html>\\(\\displaystyle \\left[\\left(\\frac{q^{2} - 2 \\, q {\\mathrm{ch}_1^B(v)} + {\\mathrm{ch}_1^B(v)}^{2} + 4 \\, r {\\mathrm{ch}_2^B(v)} + \\sqrt{q^{2} - 2 \\, q {\\mathrm{ch}_1^B(v)} + {\\mathrm{ch}_1^B(v)}^{2} + 8 \\, r {\\mathrm{ch}_2^B(v)}} {\\left(q - {\\mathrm{ch}_1^B(v)}\\right)}}{4 \\, {\\mathrm{ch}_2^B(v)}}, 1\\right), \\left(\\frac{q^{2} - 2 \\, q {\\mathrm{ch}_1^B(v)} + {\\mathrm{ch}_1^B(v)}^{2} + 4 \\, r {\\mathrm{ch}_2^B(v)} - \\sqrt{q^{2} - 2 \\, q {\\mathrm{ch}_1^B(v)} + {\\mathrm{ch}_1^B(v)}^{2} + 8 \\, r {\\mathrm{ch}_2^B(v)}} {\\left(q - {\\mathrm{ch}_1^B(v)}\\right)}}{4 \\, {\\mathrm{ch}_2^B(v)}}, 1\\right)\\right]\\)</html>"
+       "<html>\\(\\displaystyle \\left[\\left(\\frac{\\sqrt{2} \\sqrt{R {\\mathrm{ch}_2^B(v)}} {\\left(q - {\\mathrm{ch}_1^B(v)}\\right)} + 2 \\, R {\\mathrm{ch}_2^B(v)}}{2 \\, {\\mathrm{ch}_2^B(v)}}, 1\\right), \\left(-\\frac{\\sqrt{2} \\sqrt{R {\\mathrm{ch}_2^B(v)}} {\\left(q - {\\mathrm{ch}_1^B(v)}\\right)} - 2 \\, R {\\mathrm{ch}_2^B(v)}}{2 \\, {\\mathrm{ch}_2^B(v)}}, 1\\right)\\right]\\)</html>"
       ],
       "text/latex": [
-       "$\\displaystyle \\left[\\left(\\frac{q^{2} - 2 \\, q {\\mathrm{ch}_1^B(v)} + {\\mathrm{ch}_1^B(v)}^{2} + 4 \\, r {\\mathrm{ch}_2^B(v)} + \\sqrt{q^{2} - 2 \\, q {\\mathrm{ch}_1^B(v)} + {\\mathrm{ch}_1^B(v)}^{2} + 8 \\, r {\\mathrm{ch}_2^B(v)}} {\\left(q - {\\mathrm{ch}_1^B(v)}\\right)}}{4 \\, {\\mathrm{ch}_2^B(v)}}, 1\\right), \\left(\\frac{q^{2} - 2 \\, q {\\mathrm{ch}_1^B(v)} + {\\mathrm{ch}_1^B(v)}^{2} + 4 \\, r {\\mathrm{ch}_2^B(v)} - \\sqrt{q^{2} - 2 \\, q {\\mathrm{ch}_1^B(v)} + {\\mathrm{ch}_1^B(v)}^{2} + 8 \\, r {\\mathrm{ch}_2^B(v)}} {\\left(q - {\\mathrm{ch}_1^B(v)}\\right)}}{4 \\, {\\mathrm{ch}_2^B(v)}}, 1\\right)\\right]$"
+       "$\\displaystyle \\left[\\left(\\frac{\\sqrt{2} \\sqrt{R {\\mathrm{ch}_2^B(v)}} {\\left(q - {\\mathrm{ch}_1^B(v)}\\right)} + 2 \\, R {\\mathrm{ch}_2^B(v)}}{2 \\, {\\mathrm{ch}_2^B(v)}}, 1\\right), \\left(-\\frac{\\sqrt{2} \\sqrt{R {\\mathrm{ch}_2^B(v)}} {\\left(q - {\\mathrm{ch}_1^B(v)}\\right)} - 2 \\, R {\\mathrm{ch}_2^B(v)}}{2 \\, {\\mathrm{ch}_2^B(v)}}, 1\\right)\\right]$"
       ],
       "text/plain": [
-       "[(1/4*(q^2 - 2*q*twisted_v1 + twisted_v1^2 + 4*r*twisted_v2 + sqrt(q^2 - 2*q*twisted_v1 + twisted_v1^2 + 8*r*twisted_v2)*(q - twisted_v1))/twisted_v2,\n",
+       "[(1/2*(sqrt(2)*sqrt(R*twisted_v2)*(q - twisted_v1) + 2*R*twisted_v2)/twisted_v2,\n",
        "  1),\n",
-       " (1/4*(q^2 - 2*q*twisted_v1 + twisted_v1^2 + 4*r*twisted_v2 - sqrt(q^2 - 2*q*twisted_v1 + twisted_v1^2 + 8*r*twisted_v2)*(q - twisted_v1))/twisted_v2,\n",
+       " (-1/2*(sqrt(2)*sqrt(R*twisted_v2)*(q - twisted_v1) - 2*R*twisted_v2)/twisted_v2,\n",
        "  1)]"
       ]
      },
-     "execution_count": 166,
+     "execution_count": 31,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "var(\"epsilon\", latex_name=r\"\\varepsilon\")\n",
+    "( intersections_bgmlv3 :=\n",
+    "    ( bgmlv3_d_upperbound_terms.all - radius_condition_d_bound.rhs() )\n",
+    "      .roots(r)\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "id": "2da5d4a6",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<html>\\(\\displaystyle -\\frac{\\sqrt{2} \\sqrt{R} q}{2 \\, \\sqrt{{\\mathrm{ch}_2^B(v)}}} + \\frac{\\sqrt{2} \\sqrt{R} {\\mathrm{ch}_1^B(v)}}{2 \\, \\sqrt{{\\mathrm{ch}_2^B(v)}}} + R\\)</html>"
+      ],
+      "text/latex": [
+       "$\\displaystyle -\\frac{\\sqrt{2} \\sqrt{R} q}{2 \\, \\sqrt{{\\mathrm{ch}_2^B(v)}}} + \\frac{\\sqrt{2} \\sqrt{R} {\\mathrm{ch}_1^B(v)}}{2 \\, \\sqrt{{\\mathrm{ch}_2^B(v)}}} + R$"
+      ],
+      "text/plain": [
+       "-1/2*sqrt(2)*sqrt(R)*q/sqrt(twisted_v2) + 1/2*sqrt(2)*sqrt(R)*twisted_v1/sqrt(twisted_v2) + R"
+      ]
+     },
+     "execution_count": 32,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "( positive_intersection_bgmlv3 :=\n",
+    "    intersections_bgmlv3[1][0].expand().simplify()\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "be17bb44",
+   "metadata": {},
+   "source": [
+    "Quickly verify this is indeed a root too:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "id": "e4fb002a",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<html>\\(\\displaystyle 0\\)</html>"
+      ],
+      "text/latex": [
+       "$\\displaystyle 0$"
+      ],
+      "text/plain": [
+       "0"
+      ]
+     },
+     "execution_count": 33,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "(\n",
-    "    ( bgmlv3_d_upperbound_terms.all == radius_condition_d_bound.rhs() )\n",
-    "    .subtract_from_both_sides(B^2*r/2 + B*q + r*twisted_v.ch[2]/R)\n",
-    "    .subs(r == r_alt + R)\n",
-    "    .multiply_both_sides(R*r_alt) # assumes r>R\n",
-    "    .expand()\n",
-    "    .subs(r_alt == r - R)\n",
-    "    .expand()\n",
-    ").lhs().poly(r).roots()\n"
+    "    ( bgmlv3_d_upperbound_terms.all - radius_condition_d_bound.rhs() )\n",
+    "    .subs(r==positive_intersection_bgmlv3)\n",
+    ").factor()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6acd7233",
+   "metadata": {},
+   "source": [
+    "## Find which q value maximises the minimum of these two quantities"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "id": "09b81707",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<html>\\(\\displaystyle \\frac{1}{2} \\, \\sqrt{2} \\sqrt{R} \\sqrt{{\\mathrm{ch}_2^B(v)}} + \\frac{1}{2} \\, {\\mathrm{ch}_1^B(v)}\\)</html>"
+      ],
+      "text/latex": [
+       "$\\displaystyle \\frac{1}{2} \\, \\sqrt{2} \\sqrt{R} \\sqrt{{\\mathrm{ch}_2^B(v)}} + \\frac{1}{2} \\, {\\mathrm{ch}_1^B(v)}$"
+      ],
+      "text/plain": [
+       "1/2*sqrt(2)*sqrt(R)*sqrt(twisted_v2) + 1/2*twisted_v1"
+      ]
+     },
+     "execution_count": 34,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(maximising_q :=\n",
+    "    (positive_intersection_bgmlv3 - positive_intersection_bgmlv2)\n",
+    "     .roots(q)[0][0]\n",
+    "     .expand()\n",
+    "     .simplify()\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "id": "d9c2f5fc",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<html>\\(\\displaystyle \\frac{\\sqrt{2} \\sqrt{R} {\\mathrm{ch}_1^B(v)}}{4 \\, \\sqrt{{\\mathrm{ch}_2^B(v)}}} + \\frac{1}{2} \\, R\\)</html>"
+      ],
+      "text/latex": [
+       "$\\displaystyle \\frac{\\sqrt{2} \\sqrt{R} {\\mathrm{ch}_1^B(v)}}{4 \\, \\sqrt{{\\mathrm{ch}_2^B(v)}}} + \\frac{1}{2} \\, R$"
+      ],
+      "text/plain": [
+       "1/4*sqrt(2)*sqrt(R)*twisted_v1/sqrt(twisted_v2) + 1/2*R"
+      ]
+     },
+     "execution_count": 35,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "( r_max :=\n",
+    "    positive_intersection_bgmlv2\n",
+    "     .subs(q == maximising_q)\n",
+    "     .expand()\n",
+    "     .simplify()\n",
+    ")"
    ]
   },
   {
@@ -835,7 +1013,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 184,
+   "execution_count": 36,
    "id": "7b6ac93e",
    "metadata": {},
    "outputs": [
@@ -852,7 +1030,7 @@
        " (-1/2*(R*epsilon - sqrt(R^2*epsilon^2 + 2*R*q^2*twisted_v2))/twisted_v2, 1)]"
       ]
      },
-     "execution_count": 184,
+     "execution_count": 36,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -861,18 +1039,14 @@
     "var(\"epsilon\", latex_name=r\"\\varepsilon\")\n",
     "(\n",
     "    ( bgmlv2_d_upperbound_terms.all - radius_condition_d_bound.rhs() - epsilon )\n",
-    "      .__mul__(r * R)\n",
-    "      .expand()\n",
-    "      .poly(r)\n",
     "      .roots(r)\n",
-    "\n",
     ")"
    ]
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "SageMath 9.7",
+   "display_name": "SageMath 10.0",
    "language": "sage",
    "name": "sagemath"
   },
@@ -886,7 +1060,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.8"
+   "version": "3.11.6"
   }
  },
  "nbformat": 4,
-- 
GitLab