From eac837ddeeb2495bc2e04a46e18043fff542d3e8 Mon Sep 17 00:00:00 2001
From: Luke Naylor <l.naylor@sms.ed.ac.uk>
Date: Wed, 26 Jul 2023 16:47:53 +0100
Subject: [PATCH] Copy recurring examples to separate notebook and integrate
into build
---
.gitignore | 2 +
Makefile | 9 +-
examples.ipynb | 324 +++++++++++++++++++++++++++++++++++++++++++++++++
3 files changed, 334 insertions(+), 1 deletion(-)
create mode 100644 examples.ipynb
diff --git a/.gitignore b/.gitignore
index 3cecb67..57a75c6 100644
--- a/.gitignore
+++ b/.gitignore
@@ -2,6 +2,8 @@ main.*
!main.tex
plots_and_expressions.*
!plots_and_expressions.ipynb
+examples.*
+!examples.ipynb
filtered_sage.txt
_minted-main/*
sage-plots-for-main.tex
diff --git a/Makefile b/Makefile
index 928e47c..164ab58 100644
--- a/Makefile
+++ b/Makefile
@@ -8,7 +8,7 @@ SAGETEXSCRIPT = main.sagetex.sage
main.pdf: ${TEXFILES} main.sagetex.sout.tmp
latexmk
-main.sagetex.sout.tmp: ${SAGETEXSCRIPT} plots_and_expressions.py
+main.sagetex.sout.tmp: ${SAGETEXSCRIPT} plots_and_expressions.py examples.py
PYTHONPATH=./sagetexscripts/ sage ${SAGETEXSCRIPT}
${SAGETEXSCRIPT}: ${TEXFILES}
@@ -21,6 +21,13 @@ plots_and_expressions.py: plots_and_expressions.ipynb
sage --preparse plots_and_expressions.sage
mv plots_and_expressions.sage.py plots_and_expressions.py
+examples.py: plots_and_expressions.py examples.ipynb
+ jupyter nbconvert --to script examples.ipynb
+ mv examples.py examples.sage
+ sed -e "/get_ipython/d" -i examples.sage
+ sage --preparse examples.sage
+ mv examples.sage.py examples.py
+
.PHONY: clean nosage noappendix
clean:
rm -rf **/__pycache__
diff --git a/examples.ipynb b/examples.ipynb
new file mode 100644
index 0000000..affe546
--- /dev/null
+++ b/examples.ipynb
@@ -0,0 +1,324 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "abe149f0",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Requires extra package:\n",
+ "#! sage -pip install \"pseudowalls==0.0.3\" --extra-index-url https://gitlab.com/api/v4/projects/43962374/packages/pypi/simple\n",
+ "%display latex\n",
+ "\n",
+ "from pseudowalls import *\n",
+ "\n",
+ "Δ = lambda v: v.Q_tilt()\n",
+ "mu = stability.Mumford().slope\n",
+ "ts = stability.Tilt\n",
+ "\n",
+ "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",
+ "\n",
+ "class Object(object):\n",
+ " pass"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "77fff07c",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "var(\"m\") # Initialize symbol for variety parameter\n",
+ "recurring = Object()\n",
+ "recurring.chern = Chern_Char(3, 2, -2)\n",
+ "recurring.b = beta_minus(recurring.chern)\n",
+ "recurring.twisted = recurring.chern.twist(recurring.b)\n",
+ "# RENDERED TO LATEX: recurring.b\n",
+ "# RENDERED TO LATEX: recurring.b.denominator()\n",
+ "# RENDERED TO LATEX: recurring.twisted.ch[1]\n",
+ "n = recurring.b.denominator()\n",
+ "m = 2\n",
+ "recurring.loose_bound = (\n",
+ " m*n^2*recurring.twisted.ch[1]^2\n",
+ ") / gcd(m, 2*n^2)\n",
+ "# RENDERED TO LATEX: loose_bound\n",
+ "extravagant = Object()\n",
+ "extravagant.chern = Chern_Char(29, 13, -3/2)\n",
+ "extravagant.b = beta_minus(extravagant.chern)\n",
+ "extravagant.twisted = extravagant.chern.twist(extravagant.b)\n",
+ "extravagant.actual_rmax = 49313\n",
+ "# RENDERED TO LATEX: extravagant.b\n",
+ "# RENDERED TO LATEX: extravagant.b.denominator()\n",
+ "# RENDERED TO LATEX: extravagant.twisted.ch[1]\n",
+ "n = extravagant.b.denominator()\n",
+ "m = 2\n",
+ "extravagant.loose_bound = (\n",
+ " m*n^2*extravagant.twisted.ch[1]^2\n",
+ ") / gcd(m, 2*n^2)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "9edbb954",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<html>\\(\\displaystyle 144\\)</html>"
+ ],
+ "text/latex": [
+ "$\\displaystyle 144$"
+ ],
+ "text/plain": [
+ "144"
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "recurring.loose_bound"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "21b52c4d",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<html>\\(\\displaystyle 215296\\)</html>"
+ ],
+ "text/latex": [
+ "$\\displaystyle 215296$"
+ ],
+ "text/plain": [
+ "215296"
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "extravagant.loose_bound"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "712b7324",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from plots_and_expressions import r_upper_bound_all_q, Delta, nu, n, R"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "ab9a828f",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "recurring.n = recurring.b.denominator()\n",
+ "recurring.bgmlv = recurring.chern.Q_tilt()\n",
+ "recurring.corrolary_bound = (\n",
+ " r_upper_bound_all_q.expand()\n",
+ " .subs(Delta==recurring.bgmlv)\n",
+ " .subs(nu==1) ## \\ell^2=1 on P^2\n",
+ " .subs(R==recurring.chern.ch[0])\n",
+ " .subs(n==recurring.n)\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "2965357d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "extravagant.n = extravagant.b.denominator()\n",
+ "extravagant.bgmlv = extravagant.chern.Q_tilt()\n",
+ "extravagant.corrolary_bound = (\n",
+ " r_upper_bound_all_q.expand()\n",
+ " .subs(Delta==extravagant.bgmlv)\n",
+ " .subs(nu==1) ## \\ell^2=1 on P^2\n",
+ " .subs(R==extravagant.chern.ch[0])\n",
+ " .subs(n==extravagant.n)\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "5baed51c",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<html>\\(\\displaystyle 53838.5009765625\\)</html>"
+ ],
+ "text/latex": [
+ "$\\displaystyle 53838.5009765625$"
+ ],
+ "text/plain": [
+ "53838.5009765625"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "float(extravagant.corrolary_bound)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "fcc15f60",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<html>\\(\\displaystyle 37.515625\\)</html>"
+ ],
+ "text/latex": [
+ "$\\displaystyle 37.515625$"
+ ],
+ "text/plain": [
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+ ]
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+ "execution_count": 9,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "float(recurring.corrolary_bound)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "id": "ef8f09ff",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "def bound_comparisons(example):\n",
+ " n = example.b.denominator()\n",
+ " a_v = example.b.numerator()\n",
+ "\n",
+ " def theorem_bound(v_twisted, q_val, k):\n",
+ " return int(min(\n",
+ " n^2*q_val^2/k\n",
+ " ,\n",
+ " v_twisted.ch[0]\n",
+ " + n^2*(v_twisted.ch[1] - q_val)^2/k\n",
+ " ))\n",
+ "\n",
+ " def k(n, a_v, b_q):\n",
+ " n = int(n)\n",
+ " a_v = int(a_v)\n",
+ " b_q = int(b_q)\n",
+ " k = -a_v*b_q % n\n",
+ " return k if k > 0 else k + n\n",
+ "\n",
+ " b_qs = list(range(example.twisted.ch[1]*n+1))\n",
+ " qs = list(map(lambda x: x/n,b_qs))\n",
+ " ks = list(map(lambda b_q: k(n, a_v, b_q), b_qs))\n",
+ " theorem2_bounds = [\n",
+ " theorem_bound(example.twisted, q_val, 1)\n",
+ " for q_val in qs\n",
+ " ]\n",
+ " theorem3_bounds = [\n",
+ " theorem_bound(example.twisted, q_val, k)\n",
+ " for q_val, k in zip(qs,ks)\n",
+ " ]\n",
+ " return qs, theorem2_bounds, theorem3_bounds"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "id": "9cd102ac",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<html>\\(\\displaystyle \\begin{array}{l}\n",
+ "\\verb|[[0|\\verb| |\\verb|1/3|\\verb| |\\verb|2/3|\\verb| |\\verb|1|\\verb| |\\verb|4/3|\\verb| |\\verb|5/3|\\verb| |\\verb|2|\\verb| |\\verb|7/3|\\verb| |\\verb|8/3|\\verb| |\\verb|3|\\verb| |\\verb|10/3|\\verb| |\\verb|11/3|\\verb| |\\verb|4]|\\\\\n",
+ "\\verb| |\\verb|[0|\\verb| |\\verb|1|\\verb| |\\verb|4|\\verb| |\\verb|9|\\verb| |\\verb|16|\\verb| |\\verb|25|\\verb| |\\verb|36|\\verb| |\\verb|28|\\verb| |\\verb|19|\\verb| |\\verb|12|\\verb| |\\verb|7|\\verb| |\\verb|4|\\verb| |\\verb|3]|\\\\\n",
+ "\\verb| |\\verb|[0|\\verb| |\\verb|0|\\verb| |\\verb|4|\\verb| |\\verb|3|\\verb| |\\verb|8|\\verb| |\\verb|25|\\verb| |\\verb|12|\\verb| |\\verb|15|\\verb| |\\verb|19|\\verb| |\\verb|6|\\verb| |\\verb|5|\\verb| |\\verb|4|\\verb| |\\verb|3]]|\n",
+ "\\end{array}\\)</html>"
+ ],
+ "text/latex": [
+ "$\\displaystyle \\begin{array}{l}\n",
+ "\\verb|[[0|\\verb| |\\verb|1/3|\\verb| |\\verb|2/3|\\verb| |\\verb|1|\\verb| |\\verb|4/3|\\verb| |\\verb|5/3|\\verb| |\\verb|2|\\verb| |\\verb|7/3|\\verb| |\\verb|8/3|\\verb| |\\verb|3|\\verb| |\\verb|10/3|\\verb| |\\verb|11/3|\\verb| |\\verb|4]|\\\\\n",
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+ "\\verb| |\\verb|[0|\\verb| |\\verb|0|\\verb| |\\verb|4|\\verb| |\\verb|3|\\verb| |\\verb|8|\\verb| |\\verb|25|\\verb| |\\verb|12|\\verb| |\\verb|15|\\verb| |\\verb|19|\\verb| |\\verb|6|\\verb| |\\verb|5|\\verb| |\\verb|4|\\verb| |\\verb|3]]|\n",
+ "\\end{array}$"
+ ],
+ "text/plain": [
+ "array([[0, 1/3, 2/3, 1, 4/3, 5/3, 2, 7/3, 8/3, 3, 10/3, 11/3, 4],\n",
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+ " [0, 0, 4, 3, 8, 25, 12, 15, 19, 6, 5, 4, 3]], dtype=object)"
+ ]
+ },
+ "execution_count": 11,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "np.array(bound_comparisons(recurring))"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "SageMath 9.7",
+ "language": "sage",
+ "name": "sagemath"
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+ "version": 3
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+}
--
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