diff --git a/examples.ipynb b/examples.ipynb
index 6d16ae9beb806b0ac93463b91a5581fc91e94beb..5204573080aa52bd46cf3c80582c715b0217c9d5 100644
--- a/examples.ipynb
+++ b/examples.ipynb
@@ -69,7 +69,7 @@
"$\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 3 \\\\ \\mathrm{ch}_{1} = 2 \\ell^{1} \\\\ \\mathrm{ch}_{2} = -2 \\ell^{2} \\end{array}$"
],
"text/plain": [
- "<pseudowalls.chern_character.Chern_Char object at 0x7f679c692150>"
+ "<pseudowalls.chern_character.Chern_Char object at 0x7f25db3a9990>"
]
},
"execution_count": 2,
@@ -100,7 +100,7 @@
"$\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 29 \\\\ \\mathrm{ch}_{1} = 13 \\ell^{1} \\\\ \\mathrm{ch}_{2} = -\\frac{3}{2} \\ell^{2} \\end{array}$"
],
"text/plain": [
- "<pseudowalls.chern_character.Chern_Char object at 0x7f67924d6810>"
+ "<pseudowalls.chern_character.Chern_Char object at 0x7f25d1953e20>"
]
},
"execution_count": 3,
@@ -256,59 +256,59 @@
]
},
{
- "cell_type": "code",
- "execution_count": 8,
- "id": "712b7324",
+ "cell_type": "markdown",
+ "id": "8de156d1",
"metadata": {},
- "outputs": [],
"source": [
- "from plots_and_expressions import \\\n",
- "r_upper_bound_all_q, Delta, nu, n, R\n",
- "# Delta: symbol for Δ(v)\n",
- "# n: symbol for denominator for β_(v)\n",
- "# R : symbol for chern_0(v)\n",
- "# nu : ..."
+ "$\\renewcommand\\nu\\ell$\n",
+ "Redefine \\nu to $\\nu$ in latex\n",
+ "$\\let\\originalDelta\\Delta$\n",
+ "$\\renewcommand\\Delta{\\originalDelta(v)}$\n",
+ "Redefine \\Delta in latex to be $\\Delta$"
]
},
{
"cell_type": "code",
- "execution_count": 9,
- "id": "5814dd1d",
- "metadata": {
- "scrolled": true
- },
+ "execution_count": 8,
+ "id": "712b7324",
+ "metadata": {},
"outputs": [
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle \\frac{{\\left(R + \\frac{\\Delta n^{2}}{\\nu^{2}}\\right)}^{2} \\nu^{2}}{4 \\, \\Delta n^{2}}\\)</html>"
+ "<html>\\(\\displaystyle \\frac{1}{2} \\, R + \\frac{\\Delta n^{2}}{4 \\, \\nu^{2}} + \\frac{R^{2} \\nu^{2}}{4 \\, \\Delta n^{2}}\\)</html>"
],
"text/latex": [
- "$\\displaystyle \\frac{{\\left(R + \\frac{\\Delta n^{2}}{\\nu^{2}}\\right)}^{2} \\nu^{2}}{4 \\, \\Delta n^{2}}$"
+ "$\\displaystyle \\frac{1}{2} \\, R + \\frac{\\Delta n^{2}}{4 \\, \\nu^{2}} + \\frac{R^{2} \\nu^{2}}{4 \\, \\Delta n^{2}}$"
],
"text/plain": [
- "1/4*(R + Delta*n^2/nu^2)^2*nu^2/(Delta*n^2)"
+ "1/2*R + 1/4*Delta*n^2/nu^2 + 1/4*R^2*nu^2/(Delta*n^2)"
]
},
- "execution_count": 9,
+ "execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "r_upper_bound_all_q"
+ "from plots_and_expressions import main_theorem1, Delta, nu, R, n\n",
+ "# Delta: symbol for Δ(v)\n",
+ "# n: symbol for denominator for β_(v)\n",
+ "# R : symbol for chern_0(v)\n",
+ "# nu : ...\n",
+ "main_theorem1.corollary_r_bound"
]
},
{
"cell_type": "code",
- "execution_count": 10,
+ "execution_count": 9,
"id": "43aa5f56",
"metadata": {},
"outputs": [],
"source": [
"def corrolary_bound(example):\n",
" return (\n",
- " r_upper_bound_all_q.expand()\n",
+ " main_theorem1.corollary_r_bound\n",
" .subs(Delta==example.bgmlv)\n",
" .subs(nu==1)\n",
" .subs(R==example.chern.ch[0])\n",
@@ -322,7 +322,7 @@
},
{
"cell_type": "code",
- "execution_count": 11,
+ "execution_count": 10,
"id": "5baed51c",
"metadata": {},
"outputs": [
@@ -338,7 +338,7 @@
"53838.5009765625"
]
},
- "execution_count": 11,
+ "execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
@@ -349,7 +349,7 @@
},
{
"cell_type": "code",
- "execution_count": 12,
+ "execution_count": 11,
"id": "fcc15f60",
"metadata": {},
"outputs": [
@@ -365,7 +365,7 @@
"37.515625"
]
},
- "execution_count": 12,
+ "execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
@@ -384,7 +384,7 @@
},
{
"cell_type": "code",
- "execution_count": 13,
+ "execution_count": 12,
"id": "ef8f09ff",
"metadata": {},
"outputs": [],
@@ -436,7 +436,7 @@
},
{
"cell_type": "code",
- "execution_count": 14,
+ "execution_count": 13,
"id": "9cd102ac",
"metadata": {},
"outputs": [
@@ -462,7 +462,7 @@
" [0, 0, 4, 3, 8, 25, 12, 15, 19, 6, 5, 4, 3]], dtype=object)"
]
},
- "execution_count": 14,
+ "execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
@@ -474,7 +474,7 @@
],
"metadata": {
"kernelspec": {
- "display_name": "SageMath 9.8",
+ "display_name": "SageMath 9.7",
"language": "sage",
"name": "sagemath"
},
@@ -488,7 +488,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.11.3"
+ "version": "3.10.8"
}
},
"nbformat": 4,