diff --git a/plots_and_expressions.ipynb b/plots_and_expressions.ipynb index 436e57461ef01a74522a27a5bd60e0908147367b..78c6aeff541368856c0623cb541e53403fc09455 100644 --- a/plots_and_expressions.ipynb +++ b/plots_and_expressions.ipynb @@ -28,78 +28,22 @@ "var(\"beta\", domain=\"real\")\n", "\n", "def beta_minus(v):\n", - " beta = stability.Tilt().beta\n", - " solutions = solve(\n", - " stability.Tilt(alpha=0).degree(v)==0,\n", - " beta)\n", - " return min(map(lambda s: s.rhs(), solutions))\n", + " beta = stability.Tilt().beta\n", + " solutions = solve(\n", + " stability.Tilt(alpha=0).degree(v)==0,\n", + " beta)\n", + " return min(map(lambda s: s.rhs(), solutions))\n", "\n", "class Object(object):\n", " pass" ] }, - { - "cell_type": "markdown", - "id": "c9348fd3", - "metadata": {}, - "source": [ - "# SECTION: The Problem: Finding Pseudo-walls" - ] - }, - { - "cell_type": "markdown", - "id": "1f414cfb", - "metadata": {}, - "source": [ - "## SUBSECTION: Problem statements" - ] - }, - { - "cell_type": "markdown", - "id": "1c779178", - "metadata": {}, - "source": [ - "## SUBSECTION: Numerical Formulations of the Problems" - ] - }, - { - "cell_type": "markdown", - "id": "b0b54ece", - "metadata": {}, - "source": [ - "# SECTION: B.Schmidt's Solutions to the Problems" - ] - }, - { - "cell_type": "markdown", - "id": "72e5b556", - "metadata": {}, - "source": [ - "## SUBSECTION: Bound on $\\operatorname{ch}_0(u)$ for Semistabilizers" - ] - }, - { - "cell_type": "markdown", - "id": "4982f084", - "metadata": {}, - "source": [ - "## SUBSECTION: Pseudo-Wall Finding Method" - ] - }, - { - "cell_type": "markdown", - "id": "05d5916c", - "metadata": {}, - "source": [ - "## SUBSECTION: Limitations" - ] - }, { "cell_type": "markdown", "id": "cb9c11e7", "metadata": {}, "source": [ - "# SECTION: Tighter Bounds" + "# Bounds on $\\operatorname{ch}_2(u)=d$" ] }, { @@ -112,10 +56,13 @@ "v = Chern_Char(*var(\"R C D\", domain=\"real\"))\n", "u = Chern_Char(*var(\"r c d\", domain=\"real\"))\n", "\n", + "alpha = ts().alpha\n", + "beta = ts().beta\n", + "\n", "\n", "c_lower_bound = -(\n", " ts(beta=beta).rank(u)\n", - " /ts().alpha\n", + " /alpha\n", ").expand() + c\n", "\n", "var(\"q\", domain=\"real\")\n", @@ -151,10 +98,10 @@ }, { "cell_type": "markdown", - "id": "932838f4", + "id": "900f332b", "metadata": {}, "source": [ - "## SUBSECTION: Numerical Inequalities" + "## $\\Delta(u) \\geq 0$" ] }, { @@ -319,6 +266,14 @@ "bgmlv2_d_upperbound_exp_term" ] }, + { + "cell_type": "markdown", + "id": "024e8c41", + "metadata": {}, + "source": [ + "## $\\Delta(v-u) \\geq 0$" + ] + }, { "cell_type": "code", "execution_count": 10, @@ -663,6 +618,14 @@ "bgmlv3_d_upperbound_exp_term_alt2" ] }, + { + "cell_type": "markdown", + "id": "2997ec1a", + "metadata": {}, + "source": [ + "## Plots for all Bounds on $d$" + ] + }, { "cell_type": "code", "execution_count": 20, @@ -689,63 +652,67 @@ " ymax=5,\n", " ymin=-2,\n", " xmax=20,\n", - " aspect_ratio=None\n", - "):\n", + " aspect_ratio=None):\n", "\n", - " # Equations to plot imminently representing the bounds on d:\n", - " eq2 = (\n", - " bgmlv2_d_upperbound\n", - " .subs(R == v_example.ch[0])\n", - " .subs(C == v_example.ch[1])\n", - " .subs(D == v_example.ch[2])\n", - " .subs(beta = beta_minus(v_example))\n", - " .subs(q == q_example)\n", - " )\n", + " # Equations to plot imminently representing the bounds on d:\n", + " eq2 = (bgmlv2_d_upperbound\n", + " .subs(R == v_example.ch[0])\n", + " .subs(C == v_example.ch[1])\n", + " .subs(D == v_example.ch[2])\n", + " .subs(beta = beta_minus(v_example))\n", + " .subs(q == q_example)\n", + " )\n", "\n", - " eq3 = (\n", - " bgmlv3_d_upperbound\n", - " .subs(R == v_example.ch[0])\n", - " .subs(C == v_example.ch[1])\n", - " .subs(D == v_example.ch[2])\n", - " .subs(beta = beta_minus(v_example))\n", - " .subs(q == q_example)\n", - " )\n", + " eq3 = (bgmlv3_d_upperbound\n", + " .subs(R == v_example.ch[0])\n", + " .subs(C == v_example.ch[1])\n", + " .subs(D == v_example.ch[2])\n", + " .subs(beta = beta_minus(v_example))\n", + " .subs(q == q_example)\n", + " )\n", "\n", - " eq4 = (\n", - " positive_radius_condition.rhs()\n", - " .subs(q == q_example)\n", - " .subs(beta = beta_minus(v_example))\n", - " )\n", + " eq4 = (positive_radius_condition.rhs()\n", + " .subs(q == q_example)\n", + " .subs(beta = beta_minus(v_example))\n", + " )\n", "\n", - " example_bounds_on_d_plot = (\n", - " plot(\n", - " eq3,\n", - " (r,v_example.ch[0],xmax),\n", - " color='green',\n", + " example_bounds_on_d_plot = (\n", + " plot(\n", + " eq3,\n", + " (r,v_example.ch[0],xmax),\n", + " color='green',\n", " linestyle = \"dashed\",\n", - " legend_label=r\"upper bound: $\\Delta(v-u) \\geq 0$\",\n", - " )\n", - " + plot(\n", - " eq2,\n", - " (r,0,xmax),\n", - " color='blue',\n", + " legend_label=r\"upper bound: $\\Delta(v-u) \\geq 0$\",\n", + " )\n", + " + plot(\n", + " eq2,\n", + " (r,0,xmax),\n", + " color='blue',\n", " linestyle = \"dashed\",\n", - " legend_label=r\"upper bound: $\\Delta(u) \\geq 0$\"\n", - " )\n", - " + plot(\n", - " eq4,\n", - " (r,0,xmax),\n", - " color='orange',\n", + " legend_label=r\"upper bound: $\\Delta(u) \\geq 0$\"\n", + " )\n", + " + plot(\n", + " eq4,\n", + " (r,0,xmax),\n", + " color='orange',\n", " linestyle = \"dotted\",\n", - " legend_label=r\"lower bound: $\\mathrm{ch}_2^{\\beta_{-}}(u)>0$\"\n", - " )\n", + " legend_label=r\"lower bound: $\\mathrm{ch}_2^{\\beta_{-}}(u)>0$\"\n", + " )\n", " )\n", - " example_bounds_on_d_plot.ymin(ymin)\n", - " example_bounds_on_d_plot.ymax(ymax)\n", - " example_bounds_on_d_plot.axes_labels(['$r$', '$d$'])\n", - " if aspect_ratio:\n", - " example_bounds_on_d_plot.set_aspect_ratio(aspect_ratio)\n", - " return example_bounds_on_d_plot" + " example_bounds_on_d_plot.ymin(ymin)\n", + " example_bounds_on_d_plot.ymax(ymax)\n", + " example_bounds_on_d_plot.axes_labels(['$r$', '$d$'])\n", + " if aspect_ratio:\n", + " example_bounds_on_d_plot.set_aspect_ratio(aspect_ratio)\n", + " return example_bounds_on_d_plot" + ] + }, + { + "cell_type": "markdown", + "id": "683ac3f7", + "metadata": {}, + "source": [ + "### Bounds on $d$ with Minimal $q=\\operatorname{ch}^{\\beta}_1(u)$" ] }, { @@ -756,7 +723,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] @@ -771,6 +738,14 @@ "bounds_on_d_qmin" ] }, + { + "cell_type": "markdown", + "id": "24dd62c1", + "metadata": {}, + "source": [ + "### Bounds on $d$ with Maximal $q=\\operatorname{ch}^{\\beta}_1(u)$" + ] + }, { "cell_type": "code", "execution_count": 22, @@ -779,7 +754,7 @@ "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" ] @@ -794,6 +769,14 @@ "bounds_on_d_qmax" ] }, + { + "cell_type": "markdown", + "id": "133ccbe7", + "metadata": {}, + "source": [ + "### Bounds on $d$ with Mid-way $q=\\operatorname{ch}^{\\beta}_1(u)$" + ] + }, { "cell_type": "code", "execution_count": 23, @@ -802,7 +785,7 @@ "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" ] @@ -822,7 +805,7 @@ "id": "1c6f5622", "metadata": {}, "source": [ - "## SUBSECTION: Bounds on Semistabilizer Rank" + "# Bounds on Semistabilizer Rank $r=\\operatorname{ch}_0(u)$" ] }, { @@ -996,12 +979,14 @@ "outputs": [], "source": [ "var(\"Delta nu\", domain=\"real\")\n", + "\n", "q_sol = solve(\n", - " r_upper_bound1.subs(kappa==1).rhs()\n", - " == r_upper_bound2.subs(kappa==1).rhs()\n", - ", q)[0].rhs()\n", - "r_upper_bound_all_q = (\n", - " r_upper_bound1.rhs()\n", + " r_upper_bound1.subs(kappa==1).rhs()\n", + " == r_upper_bound2.subs(kappa==1).rhs()\n", + " , q\n", + ")[0].rhs()\n", + "\n", + "r_upper_bound_all_q = (r_upper_bound1.rhs()\n", " .expand()\n", " .subs(q==q_sol)\n", " .subs(kappa==1)\n", @@ -1179,8 +1164,7 @@ "metadata": {}, "outputs": [], "source": [ - "rhs_numerator = (\n", - " positive_radius_condition\n", + "rhs_numerator = (positive_radius_condition\n", " .rhs()\n", " .subs([q_value_expr,beta_value_expr])\n", " .factor()\n", @@ -1212,7 +1196,9 @@ } ], "source": [ - "positive_radius_condition.subs([q_value_expr,beta_value_expr]).factor()" + "(positive_radius_condition\n", + " .subs([q_value_expr,beta_value_expr])\n", + " .factor())" ] }, {