diff --git a/plots_and_expressions.ipynb b/plots_and_expressions.ipynb
index 1d6bf27cf8676aa1b095cec4528d174850e9fd9d..c82dbef17ba27eec4c001dc05833ecbea8dcf0b8 100644
--- a/plots_and_expressions.ipynb
+++ b/plots_and_expressions.ipynb
@@ -53,7 +53,7 @@
},
{
"cell_type": "code",
- "execution_count": 42,
+ "execution_count": 2,
"id": "ab162897",
"metadata": {},
"outputs": [
@@ -66,10 +66,10 @@
"$\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = R \\\\ \\mathrm{ch}_{1} = C \\ell^{1} \\\\ \\mathrm{ch}_{2} = D \\ell^{2} \\end{array}$"
],
"text/plain": [
- "<pseudowalls.chern_character.Chern_Char object at 0x7f554bd7dc90>"
+ "<pseudowalls.chern_character.Chern_Char object at 0x7f1bd72a2010>"
]
},
- "execution_count": 42,
+ "execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@@ -89,7 +89,7 @@
},
{
"cell_type": "code",
- "execution_count": 43,
+ "execution_count": 3,
"id": "0d33d7e1",
"metadata": {},
"outputs": [
@@ -102,10 +102,10 @@
"$\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = r \\\\ \\mathrm{ch}_{1} = c \\ell^{1} \\\\ \\mathrm{ch}_{2} = d \\ell^{2} \\end{array}$"
],
"text/plain": [
- "<pseudowalls.chern_character.Chern_Char object at 0x7f554bd7fd00>"
+ "<pseudowalls.chern_character.Chern_Char object at 0x7f1bccb53110>"
]
},
- "execution_count": 43,
+ "execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@@ -125,7 +125,7 @@
},
{
"cell_type": "code",
- "execution_count": 44,
+ "execution_count": 4,
"id": "23d48b0b",
"metadata": {},
"outputs": [
@@ -141,7 +141,7 @@
"q"
]
},
- "execution_count": 44,
+ "execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@@ -160,7 +160,7 @@
},
{
"cell_type": "code",
- "execution_count": 49,
+ "execution_count": 5,
"id": "49be9bb7",
"metadata": {},
"outputs": [],
@@ -171,7 +171,7 @@
},
{
"cell_type": "code",
- "execution_count": 51,
+ "execution_count": 6,
"id": "4cacebc7",
"metadata": {},
"outputs": [
@@ -187,7 +187,7 @@
"c == beta*r + q"
]
},
- "execution_count": 51,
+ "execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@@ -196,6 +196,107 @@
"c_in_terms_of_q"
]
},
+ {
+ "cell_type": "markdown",
+ "id": "760b306b",
+ "metadata": {},
+ "source": [
+ "## $\\chern_2^{P}(u) > 0$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1f866f7f",
+ "metadata": {},
+ "source": [
+ "For problem 2, this amounts to $\\chern_2^{\\beta}(u) > 0$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "b9bb6e1e",
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<html>\\(\\displaystyle d > \\frac{1}{2} \\, \\beta^{2} r + \\beta q\\)</html>"
+ ],
+ "text/latex": [
+ "$\\displaystyle d > \\frac{1}{2} \\, \\beta^{2} r + \\beta q$"
+ ],
+ "text/plain": [
+ "d > 1/2*beta^2*r + beta*q"
+ ]
+ },
+ "execution_count": 7,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "positive_radius_condition_with_q = (\n",
+ " (\n",
+ " (0 > - u.twist(beta).ch[2])\n",
+ " + d # rearrange for d\n",
+ " )\n",
+ " .subs(solve(q == u.twist(beta).ch[1], c)[0]) # express c in term of q\n",
+ " .expand()\n",
+ ")\n",
+ "positive_radius_condition_with_q"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "392671ee",
+ "metadata": {},
+ "source": [
+ "Separate out the terms of the corresponding lower bound on $d$:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "78a1301a",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<html>\\(\\displaystyle \\left(\\frac{1}{2} \\, \\beta^{2} r, \\beta q, 0\\right)\\)</html>"
+ ],
+ "text/latex": [
+ "$\\displaystyle \\left(\\frac{1}{2} \\, \\beta^{2} r, \\beta q, 0\\right)$"
+ ],
+ "text/plain": [
+ "(1/2*beta^2*r, beta*q, 0)"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "positive_radius_lowerbound_terms = Object()\n",
+ "\n",
+ "positive_radius_lowerbound_terms.const = positive_radius_condition_with_q.rhs().subs(r==0)\n",
+ "\n",
+ "positive_radius_lowerbound_terms.linear = (\n",
+ " positive_radius_condition_with_q.rhs()\n",
+ " - positive_radius_lowerbound_terms.const\n",
+ ")\n",
+ "\n",
+ "positive_radius_lowerbound_terms.hyperbolic = 0\n",
+ "\n",
+ "(positive_radius_lowerbound_terms.linear,\n",
+ " positive_radius_lowerbound_terms.const,\n",
+ " positive_radius_lowerbound_terms.hyperbolic)"
+ ]
+ },
{
"cell_type": "markdown",
"id": "900f332b",
@@ -214,7 +315,7 @@
},
{
"cell_type": "code",
- "execution_count": 76,
+ "execution_count": 9,
"id": "5991acb3",
"metadata": {},
"outputs": [
@@ -230,7 +331,7 @@
"0 <= (beta*r + q)^2 - 2*d*r"
]
},
- "execution_count": 76,
+ "execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
@@ -252,7 +353,7 @@
},
{
"cell_type": "code",
- "execution_count": 77,
+ "execution_count": 10,
"id": "1f66d604",
"metadata": {},
"outputs": [
@@ -268,7 +369,7 @@
"d <= 1/2*(beta*r + q)^2/r"
]
},
- "execution_count": 77,
+ "execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
@@ -293,7 +394,7 @@
},
{
"cell_type": "code",
- "execution_count": 80,
+ "execution_count": 11,
"id": "6ae4f2e7",
"metadata": {},
"outputs": [
@@ -309,7 +410,7 @@
"1/2*beta^2*r + beta*q + 1/2*q^2/r"
]
},
- "execution_count": 80,
+ "execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
@@ -329,7 +430,7 @@
},
{
"cell_type": "code",
- "execution_count": 82,
+ "execution_count": 12,
"id": "653a3340",
"metadata": {},
"outputs": [],
@@ -359,83 +460,31 @@
},
{
"cell_type": "code",
- "execution_count": 91,
+ "execution_count": 13,
"id": "326bb656",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle \\beta q\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle \\beta q$"
- ],
- "text/plain": [
- "beta*q"
- ]
- },
- "execution_count": 91,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "bgmlv2_d_upperbound_terms.const"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 92,
- "id": "fcd9fa2a",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle \\frac{1}{2} \\, \\beta^{2} r\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle \\frac{1}{2} \\, \\beta^{2} r$"
- ],
- "text/plain": [
- "1/2*beta^2*r"
- ]
- },
- "execution_count": 92,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "bgmlv2_d_upperbound_terms.linear"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 93,
- "id": "ade0f7b2",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle \\frac{q^{2}}{2 \\, r}\\)</html>"
+ "<html>\\(\\displaystyle \\left(\\frac{1}{2} \\, \\beta^{2} r, \\beta q, \\frac{q^{2}}{2 \\, r}\\right)\\)</html>"
],
"text/latex": [
- "$\\displaystyle \\frac{q^{2}}{2 \\, r}$"
+ "$\\displaystyle \\left(\\frac{1}{2} \\, \\beta^{2} r, \\beta q, \\frac{q^{2}}{2 \\, r}\\right)$"
],
"text/plain": [
- "1/2*q^2/r"
+ "(1/2*beta^2*r, beta*q, 1/2*q^2/r)"
]
},
- "execution_count": 93,
+ "execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "bgmlv2_d_upperbound_terms.hyperbolic"
+ "(bgmlv2_d_upperbound_terms.linear,\n",
+ " bgmlv2_d_upperbound_terms.const,\n",
+ " bgmlv2_d_upperbound_terms.hyperbolic)"
]
},
{
@@ -448,7 +497,7 @@
},
{
"cell_type": "code",
- "execution_count": 96,
+ "execution_count": 14,
"id": "7ff937ff",
"metadata": {},
"outputs": [],
@@ -477,7 +526,7 @@
},
{
"cell_type": "code",
- "execution_count": 101,
+ "execution_count": 15,
"id": "87544e6e",
"metadata": {},
"outputs": [
@@ -493,7 +542,7 @@
"0 <= (beta*r - C + q)^2 - 2*(D - d)*(R - r)"
]
},
- "execution_count": 101,
+ "execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
@@ -516,9 +565,11 @@
},
{
"cell_type": "code",
- "execution_count": 108,
+ "execution_count": 16,
"id": "8986af54",
- "metadata": {},
+ "metadata": {
+ "scrolled": false
+ },
"outputs": [
{
"data": {
@@ -532,7 +583,7 @@
"d <= D - 1/2*(beta*r - C + q)^2/(R - r)"
]
},
- "execution_count": 108,
+ "execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@@ -551,103 +602,9 @@
"bgmlv3_d_ineq"
]
},
- {
- "cell_type": "code",
- "execution_count": 10,
- "id": "b7799156",
- "metadata": {},
- "outputs": [],
- "source": [
- "\n",
- "var(\"r_alt\",domain=\"real\") # r_alt = r - R temporary substitution\n",
- "\n",
- "bgmlv3_with_q_reparam = (\n",
- " bgmlv3_with_q\n",
- " .subs(r == r_alt + R)\n",
- " /r_alt # This operation assumes r_alt > 0\n",
- ").expand()\n",
- "\n",
- "bgmlv3_d_ineq = (\n",
- " ((0 <= bgmlv3_with_q_reparam)/2 + d) # Rearrange for d\n",
- " .subs(r_alt == r - R) # Resubstitute r back in\n",
- " .expand()\n",
- ")\n",
- "\n",
- "# Check that this equation represents a bound for d\n",
- "assert bgmlv3_d_ineq.lhs() == d\n",
- "\n",
- "bgmlv3_d_upperbound = bgmlv3_d_ineq.rhs() # Keep hold of lower bound for d\n",
- "\n",
- "# Seperate out the terms of the lower bound for d\n",
- "\n",
- "bgmlv3_d_upperbound_without_hyp = (\n",
- " bgmlv3_d_upperbound\n",
- " .subs(1/(R-r) == 0)\n",
- ")\n",
- "\n",
- "bgmlv3_d_upperbound_const_term = (\n",
- " bgmlv3_d_upperbound_without_hyp\n",
- " .subs(r==0)\n",
- ")\n",
- "\n",
- "bgmlv3_d_upperbound_linear_term = (\n",
- " bgmlv3_d_upperbound_without_hyp\n",
- " - bgmlv3_d_upperbound_const_term\n",
- ").expand()\n",
- "\n",
- "bgmlv3_d_upperbound_exp_term = (\n",
- " bgmlv3_d_upperbound\n",
- " - bgmlv3_d_upperbound_without_hyp\n",
- ").expand()\n",
- "\n",
- "# Verify the simplified forms of the terms that will be mentioned in text\n",
- "\n",
- "var(\"psi phi\", domain=\"real\") # symbol to represent ch_1^\\beta(v) and\n",
- "# ch_2^\\beta(v)\n",
- "\n",
- "assert bgmlv3_d_upperbound_const_term == ( \n",
- " (\n",
- " # keep hold of this alternative expression:\n",
- " bgmlv3_d_upperbound_const_term_alt := (\n",
- " phi\n",
- " + beta*q\n",
- " )\n",
- " )\n",
- " .subs(phi == v.twist(beta).ch[2]) # subs real val of ch_1^\\beta(v)\n",
- " .expand()\n",
- ")\n",
- "\n",
- "assert bgmlv3_d_upperbound_exp_term == (\n",
- " (\n",
- " # Keep hold of this alternative expression:\n",
- " bgmlv3_d_upperbound_exp_term_alt :=\n",
- " (\n",
- " R*phi\n",
- " + (C - q)^2/2\n",
- " + R*beta*q\n",
- " - D*R\n",
- " )/(r-R)\n",
- " )\n",
- " .subs(phi == v.twist(beta).ch[2]) # subs real val of ch_1^\\beta(v)\n",
- " .expand()\n",
- ")\n",
- "\n",
- "assert bgmlv3_d_upperbound_exp_term == (\n",
- " (\n",
- " # Keep hold of this alternative expression:\n",
- " bgmlv3_d_upperbound_exp_term_alt2 :=\n",
- " (\n",
- " (psi - q)^2/2/(r-R)\n",
- " )\n",
- " )\n",
- " .subs(psi == v.twist(beta).ch[1]) # subs real val of ch_1^\\beta(v)\n",
- " .expand()\n",
- ")"
- ]
- },
{
"cell_type": "markdown",
- "id": "9809bd85",
+ "id": "e7eb0057",
"metadata": {},
"source": [
"$\\renewcommand{\\psi}{\\chern_1^{\\beta}(v)}$\n",
@@ -657,245 +614,206 @@
},
{
"cell_type": "code",
- "execution_count": 11,
- "id": "38bbbcd2",
+ "execution_count": 17,
+ "id": "0acd0b7e",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle \\frac{1}{2} \\, \\beta^{2} r\\)</html>"
+ "<html>\\(\\displaystyle \\left(\\psi, \\phi\\right)\\)</html>"
],
"text/latex": [
- "$\\displaystyle \\frac{1}{2} \\, \\beta^{2} r$"
+ "$\\displaystyle \\left(\\psi, \\phi\\right)$"
],
"text/plain": [
- "1/2*beta^2*r"
+ "(psi, phi)"
]
},
- "execution_count": 11,
+ "execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "bgmlv3_d_upperbound_linear_term"
+ "ch1bv, ch2bv = var(\"psi phi\", domain=\"real\") # symbol to represent ch_1^\\beta(v) and\n",
+ "# ch_2^\\beta(v)\n",
+ "ch1bv, ch2bv"
]
},
{
- "cell_type": "code",
- "execution_count": 12,
- "id": "6701d8a7",
+ "cell_type": "markdown",
+ "id": "0d880757",
"metadata": {},
+ "source": [
+ "Define expression for the different terms of this bound of $d$ in terms of $\\phi$ and $\\psi$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "id": "f122a6d5",
+ "metadata": {
+ "scrolled": true
+ },
"outputs": [
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle \\beta q + \\phi\\)</html>"
+ "<html>\\(\\displaystyle \\frac{1}{2} \\, \\beta^{2} r + \\beta q + \\phi - \\frac{{\\left(\\psi - q\\right)}^{2}}{2 \\, {\\left(R - r\\right)}}\\)</html>"
],
"text/latex": [
- "$\\displaystyle \\beta q + \\phi$"
+ "$\\displaystyle \\frac{1}{2} \\, \\beta^{2} r + \\beta q + \\phi - \\frac{{\\left(\\psi - q\\right)}^{2}}{2 \\, {\\left(R - r\\right)}}$"
],
"text/plain": [
- "beta*q + phi"
+ "1/2*beta^2*r + beta*q + phi - 1/2*(psi - q)^2/(R - r)"
]
},
- "execution_count": 12,
+ "execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "bgmlv3_d_upperbound_const_term_alt"
+ "bgmlv3_d_upperbound_terms = Object()\n",
+ "\n",
+ "bgmlv3_d_upperbound_terms.linear = bgmlv2_d_upperbound_terms.linear\n",
+ "bgmlv3_d_upperbound_terms.const = ch2bv + bgmlv2_d_upperbound_terms.const\n",
+ "bgmlv3_d_upperbound_terms.hyperbolic = (ch1bv - q)^2/2/(r-R)\n",
+ "\n",
+ "(bgmlv3_d_upperbound_terms.linear\n",
+ " + bgmlv3_d_upperbound_terms.const\n",
+ " + bgmlv3_d_upperbound_terms.hyperbolic)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9e813c96",
+ "metadata": {},
+ "source": [
+ "Verify that the expression above indeed is equal the upper bound on $d$ given by $\\originalDelta(v-u) \\geq 0$"
]
},
{
"cell_type": "code",
- "execution_count": 13,
- "id": "7a82d747",
+ "execution_count": 19,
+ "id": "10fb65aa",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "assert (\n",
+ " (bgmlv3_d_upperbound_terms.linear\n",
+ " + bgmlv3_d_upperbound_terms.const\n",
+ " + bgmlv3_d_upperbound_terms.hyperbolic\n",
+ " - bgmlv3_d_ineq.rhs())\n",
+ " .subs(ch2bv == v.twist(beta).ch[2])\n",
+ " .subs(ch1bv == v.twist(beta).ch[1])\n",
+ ") == 0, \"Sanity check\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a777246a",
+ "metadata": {},
+ "source": [
+ "# Specialize to problem 2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9413516f",
+ "metadata": {},
+ "source": [
+ "Add extra attributes to the bound objects above with a specialization to the case $\\chern_2^{\\beta}(v)=0$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "id": "dbc8e7a0",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "for bound_terms in [\n",
+ " positive_radius_lowerbound_terms,\n",
+ " bgmlv2_d_upperbound_terms,\n",
+ " bgmlv3_d_upperbound_terms\n",
+ "]:\n",
+ " bound_terms.problem2 = Object()\n",
+ " bound_terms.problem2.const = bound_terms.const.subs(ch2bv == 0)\n",
+ " bound_terms.problem2.linear = bound_terms.linear.subs(ch2bv == 0)\n",
+ " bound_terms.problem2.hyperbolic = bound_terms.hyperbolic.subs(ch2bv == 0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "95c39f2b",
+ "metadata": {},
+ "source": [
+ "View the specialized bounds:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "id": "2e9a7cdc",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle -\\frac{{\\left(\\psi - q\\right)}^{2}}{2 \\, {\\left(R - r\\right)}}\\)</html>"
+ "<html>\\(\\displaystyle \\beta q \\verb| |\\verb|+| \\frac{1}{2} \\, \\beta^{2} r \\verb| |\\verb|+| 0\\)</html>"
],
"text/latex": [
- "$\\displaystyle -\\frac{{\\left(\\psi - q\\right)}^{2}}{2 \\, {\\left(R - r\\right)}}$"
+ "$\\displaystyle \\beta q \\verb| |\\verb|+| \\frac{1}{2} \\, \\beta^{2} r \\verb| |\\verb|+| 0$"
],
"text/plain": [
- "-1/2*(psi - q)^2/(R - r)"
+ "beta*q ' + ' 1/2*beta^2*r ' + ' 0"
]
},
- "execution_count": 13,
"metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "bgmlv3_d_upperbound_exp_term_alt2"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "id": "927e6929",
- "metadata": {},
- "outputs": [
+ "output_type": "display_data"
+ },
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle \\frac{1}{2} \\, \\beta^{2} r\\)</html>"
+ "<html>\\(\\displaystyle \\beta q \\verb| |\\verb|+| \\frac{1}{2} \\, \\beta^{2} r \\verb| |\\verb|+| \\frac{q^{2}}{2 \\, r}\\)</html>"
],
"text/latex": [
- "$\\displaystyle \\frac{1}{2} \\, \\beta^{2} r$"
+ "$\\displaystyle \\beta q \\verb| |\\verb|+| \\frac{1}{2} \\, \\beta^{2} r \\verb| |\\verb|+| \\frac{q^{2}}{2 \\, r}$"
],
"text/plain": [
- "1/2*beta^2*r"
+ "beta*q ' + ' 1/2*beta^2*r ' + ' 1/2*q^2/r"
]
},
- "execution_count": 14,
"metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "bgmlv2_d_upperbound_linear_term"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "id": "ff25eea1",
- "metadata": {},
- "outputs": [
+ "output_type": "display_data"
+ },
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle \\beta q\\)</html>"
+ "<html>\\(\\displaystyle \\beta q \\verb| |\\verb|+| \\frac{1}{2} \\, \\beta^{2} r \\verb| |\\verb|+| -\\frac{{\\left(\\psi - q\\right)}^{2}}{2 \\, {\\left(R - r\\right)}}\\)</html>"
],
"text/latex": [
- "$\\displaystyle \\beta q$"
+ "$\\displaystyle \\beta q \\verb| |\\verb|+| \\frac{1}{2} \\, \\beta^{2} r \\verb| |\\verb|+| -\\frac{{\\left(\\psi - q\\right)}^{2}}{2 \\, {\\left(R - r\\right)}}$"
],
"text/plain": [
- "beta*q"
+ "beta*q ' + ' 1/2*beta^2*r ' + ' -1/2*(psi - q)^2/(R - r)"
]
},
- "execution_count": 15,
"metadata": {},
- "output_type": "execute_result"
+ "output_type": "display_data"
}
],
"source": [
- "bgmlv2_d_upperbound_const_term"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "id": "e8359c0f",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle \\frac{q^{2}}{2 \\, r}\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle \\frac{q^{2}}{2 \\, r}$"
- ],
- "text/plain": [
- "1/2*q^2/r"
- ]
- },
- "execution_count": 16,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "bgmlv2_d_upperbound_exp_term"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 17,
- "id": "6823c5b8",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle \\frac{1}{2} \\, \\beta^{2} r\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle \\frac{1}{2} \\, \\beta^{2} r$"
- ],
- "text/plain": [
- "1/2*beta^2*r"
- ]
- },
- "execution_count": 17,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "bgmlv3_d_upperbound_linear_term"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 18,
- "id": "160871f2",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle \\beta q\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle \\beta q$"
- ],
- "text/plain": [
- "beta*q"
- ]
- },
- "execution_count": 18,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "bgmlv3_d_upperbound_const_term_alt.subs(phi == 0)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 19,
- "id": "1da23b29",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle -\\frac{{\\left(\\psi - q\\right)}^{2}}{2 \\, {\\left(R - r\\right)}}\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle -\\frac{{\\left(\\psi - q\\right)}^{2}}{2 \\, {\\left(R - r\\right)}}$"
- ],
- "text/plain": [
- "-1/2*(psi - q)^2/(R - r)"
- ]
- },
- "execution_count": 19,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "bgmlv3_d_upperbound_exp_term_alt2"
+ "for bound_terms in [\n",
+ " positive_radius_lowerbound_terms,\n",
+ " bgmlv2_d_upperbound_terms,\n",
+ " bgmlv3_d_upperbound_terms\n",
+ "]:\n",
+ " pretty_print(bound_terms.problem2.const,\n",
+ " \" + \",bound_terms.problem2.linear,\n",
+ " \" + \",bound_terms.problem2.hyperbolic)"
]
},
{
@@ -908,21 +826,11 @@
},
{
"cell_type": "code",
- "execution_count": 20,
+ "execution_count": 22,
"id": "d7235dc3",
"metadata": {},
"outputs": [],
"source": [
- "positive_radius_condition = (\n",
- " (\n",
- " (0 > - u.twist(beta).ch[2])\n",
- " + d # rearrange for d\n",
- " )\n",
- " .subs(solve(q == u.twist(beta).ch[1], c)[0]) # express c in term of q\n",
- " .expand()\n",
- ")\n",
- "\n",
- "\n",
"v_example = Chern_Char(3,2,-2)\n",
"q_example = 7/3\n",
"\n",
@@ -997,20 +905,21 @@
},
{
"cell_type": "code",
- "execution_count": 21,
+ "execution_count": 23,
"id": "f5b1d9bf",
"metadata": {},
"outputs": [
{
- "data": {
- "image/png": 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\n",
- "text/plain": [
- "Graphics object consisting of 3 graphics primitives"
- ]
- },
- "execution_count": 21,
- "metadata": {},
- "output_type": "execute_result"
+ "ename": "NameError",
+ "evalue": "name 'bgmlv3_d_upperbound' is not defined",
+ "output_type": "error",
+ "traceback": [
+ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+ "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
+ "Cell \u001b[0;32mIn[23], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m bounds_on_d_qmin \u001b[38;5;241m=\u001b[39m \u001b[43mplot_d_bound\u001b[49m\u001b[43m(\u001b[49m\u001b[43mv_example\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mInteger\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mymin\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[43mRealNumber\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43m0.5\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 2\u001b[0m bounds_on_d_qmin\n",
+ "Cell \u001b[0;32mIn[22], line 21\u001b[0m, in \u001b[0;36mplot_d_bound\u001b[0;34m(v_example, q_example, ymax, ymin, xmax, aspect_ratio)\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mplot_d_bound\u001b[39m(\n\u001b[1;32m 5\u001b[0m v_example,\n\u001b[1;32m 6\u001b[0m q_example,\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 11\u001b[0m \n\u001b[1;32m 12\u001b[0m \u001b[38;5;66;03m# Equations to plot imminently representing the bounds on d:\u001b[39;00m\n\u001b[1;32m 13\u001b[0m eq2 \u001b[38;5;241m=\u001b[39m (bgmlv2_d_upperbound\n\u001b[1;32m 14\u001b[0m \u001b[38;5;241m.\u001b[39msubs(R \u001b[38;5;241m==\u001b[39m v_example\u001b[38;5;241m.\u001b[39mch[Integer(\u001b[38;5;241m0\u001b[39m)])\n\u001b[1;32m 15\u001b[0m \u001b[38;5;241m.\u001b[39msubs(C \u001b[38;5;241m==\u001b[39m v_example\u001b[38;5;241m.\u001b[39mch[Integer(\u001b[38;5;241m1\u001b[39m)])\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[38;5;241m.\u001b[39msubs(q \u001b[38;5;241m==\u001b[39m q_example)\n\u001b[1;32m 19\u001b[0m )\n\u001b[0;32m---> 21\u001b[0m eq3 \u001b[38;5;241m=\u001b[39m (\u001b[43mbgmlv3_d_upperbound\u001b[49m\n\u001b[1;32m 22\u001b[0m \u001b[38;5;241m.\u001b[39msubs(R \u001b[38;5;241m==\u001b[39m v_example\u001b[38;5;241m.\u001b[39mch[Integer(\u001b[38;5;241m0\u001b[39m)])\n\u001b[1;32m 23\u001b[0m \u001b[38;5;241m.\u001b[39msubs(C \u001b[38;5;241m==\u001b[39m v_example\u001b[38;5;241m.\u001b[39mch[Integer(\u001b[38;5;241m1\u001b[39m)])\n\u001b[1;32m 24\u001b[0m \u001b[38;5;241m.\u001b[39msubs(D \u001b[38;5;241m==\u001b[39m v_example\u001b[38;5;241m.\u001b[39mch[Integer(\u001b[38;5;241m2\u001b[39m)])\n\u001b[1;32m 25\u001b[0m \u001b[38;5;241m.\u001b[39msubs(beta \u001b[38;5;241m=\u001b[39m beta_minus(v_example))\n\u001b[1;32m 26\u001b[0m \u001b[38;5;241m.\u001b[39msubs(q \u001b[38;5;241m==\u001b[39m q_example)\n\u001b[1;32m 27\u001b[0m )\n\u001b[1;32m 29\u001b[0m eq4 \u001b[38;5;241m=\u001b[39m (positive_radius_condition\u001b[38;5;241m.\u001b[39mrhs()\n\u001b[1;32m 30\u001b[0m \u001b[38;5;241m.\u001b[39msubs(q \u001b[38;5;241m==\u001b[39m q_example)\n\u001b[1;32m 31\u001b[0m \u001b[38;5;241m.\u001b[39msubs(beta \u001b[38;5;241m=\u001b[39m beta_minus(v_example))\n\u001b[1;32m 32\u001b[0m )\n\u001b[1;32m 34\u001b[0m example_bounds_on_d_plot \u001b[38;5;241m=\u001b[39m (\n\u001b[1;32m 35\u001b[0m plot(\n\u001b[1;32m 36\u001b[0m eq3,\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 55\u001b[0m )\n\u001b[1;32m 56\u001b[0m )\n",
+ "\u001b[0;31mNameError\u001b[0m: name 'bgmlv3_d_upperbound' is not defined"
+ ]
}
],
"source": [
@@ -1028,22 +937,10 @@
},
{
"cell_type": "code",
- "execution_count": 22,
+ "execution_count": null,
"id": "47b30d7e",
"metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- "Graphics object consisting of 3 graphics primitives"
- ]
- },
- "execution_count": 22,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"bounds_on_d_qmax = plot_d_bound(v_example, 4, ymin=-3, ymax=3)\n",
"bounds_on_d_qmax"
@@ -1059,22 +956,10 @@
},
{
"cell_type": "code",
- "execution_count": 23,
+ "execution_count": null,
"id": "25e4850b",
"metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- "Graphics object consisting of 3 graphics primitives"
- ]
- },
- "execution_count": 23,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"typical_bounds_on_d = plot_d_bound(v_example, 2, ymax=4, ymin=-2, aspect_ratio=1)\n",
"typical_bounds_on_d"
@@ -1090,7 +975,7 @@
},
{
"cell_type": "code",
- "execution_count": 24,
+ "execution_count": null,
"id": "553bba31",
"metadata": {},
"outputs": [],
@@ -1122,61 +1007,27 @@
},
{
"cell_type": "code",
- "execution_count": 25,
+ "execution_count": null,
"id": "990a2840",
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle n^{2} q^{2}\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle n^{2} q^{2}$"
- ],
- "text/plain": [
- "n^2*q^2"
- ]
- },
- "execution_count": 25,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"r_upper_bound1.subs(kappa==1).rhs()"
]
},
{
"cell_type": "code",
- "execution_count": 26,
+ "execution_count": null,
"id": "5a3c7037",
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle n^{2} {\\left(\\psi - q\\right)}^{2} + R\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle n^{2} {\\left(\\psi - q\\right)}^{2} + R$"
- ],
- "text/plain": [
- "n^2*(psi - q)^2 + R"
- ]
- },
- "execution_count": 26,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"r_upper_bound2.subs(kappa==1).rhs()"
]
},
{
"cell_type": "code",
- "execution_count": 27,
+ "execution_count": null,
"id": "82add957",
"metadata": {},
"outputs": [],
@@ -1199,61 +1050,27 @@
},
{
"cell_type": "code",
- "execution_count": 28,
+ "execution_count": null,
"id": "d33e3459",
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle \\frac{q^{2}}{2 \\, r}\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle \\frac{q^{2}}{2 \\, r}$"
- ],
- "text/plain": [
- "1/2*q^2/r"
- ]
- },
- "execution_count": 28,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"bgmlv2_d_upperbound_exp_term"
]
},
{
"cell_type": "code",
- "execution_count": 29,
+ "execution_count": null,
"id": "3728c192",
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle -\\frac{{\\left(\\psi - q\\right)}^{2}}{2 \\, {\\left(R - r\\right)}}\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle -\\frac{{\\left(\\psi - q\\right)}^{2}}{2 \\, {\\left(R - r\\right)}}$"
- ],
- "text/plain": [
- "-1/2*(psi - q)^2/(R - r)"
- ]
- },
- "execution_count": 29,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"bgmlv3_d_upperbound_exp_term_alt2"
]
},
{
"cell_type": "code",
- "execution_count": 30,
+ "execution_count": null,
"id": "90149eb2",
"metadata": {},
"outputs": [],
@@ -1288,169 +1105,67 @@
},
{
"cell_type": "code",
- "execution_count": 31,
+ "execution_count": null,
"id": "8b0b0bf4",
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/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": [
- "$\\displaystyle \\frac{1}{2} \\, R + \\frac{\\Delta n^{2}}{4 \\, \\nu^{2}} + \\frac{R^{2} \\nu^{2}}{4 \\, \\Delta n^{2}}$"
- ],
- "text/plain": [
- "1/2*R + 1/4*Delta*n^2/nu^2 + 1/4*R^2*nu^2/(Delta*n^2)"
- ]
- },
- "execution_count": 31,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"r_upper_bound_all_q.expand()"
]
},
{
"cell_type": "code",
- "execution_count": 32,
+ "execution_count": null,
"id": "53bd2a9c",
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle n^{2} q^{2}\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle n^{2} q^{2}$"
- ],
- "text/plain": [
- "n^2*q^2"
- ]
- },
- "execution_count": 32,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"r_upper_bound1.subs(kappa==1).rhs()"
]
},
{
"cell_type": "code",
- "execution_count": 33,
+ "execution_count": null,
"id": "cfa6e1af",
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle n^{2} {\\left(\\psi - q\\right)}^{2} + R\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle n^{2} {\\left(\\psi - q\\right)}^{2} + R$"
- ],
- "text/plain": [
- "n^2*(psi - q)^2 + R"
- ]
- },
- "execution_count": 33,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"r_upper_bound2.subs(kappa==1).rhs()"
]
},
{
"cell_type": "code",
- "execution_count": 34,
+ "execution_count": null,
"id": "801a348a",
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle \\frac{1}{2} \\, \\psi + \\frac{R}{2 \\, n^{2} \\psi}\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle \\frac{1}{2} \\, \\psi + \\frac{R}{2 \\, n^{2} \\psi}$"
- ],
- "text/plain": [
- "1/2*psi + 1/2*R/(n^2*psi)"
- ]
- },
- "execution_count": 34,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"q_sol.expand()"
]
},
{
"cell_type": "code",
- "execution_count": 35,
+ "execution_count": null,
"id": "d4bf7486",
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle \\frac{1}{4} \\, n^{2} \\psi^{2} + \\frac{1}{2} \\, R + \\frac{R^{2}}{4 \\, n^{2} \\psi^{2}}\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle \\frac{1}{4} \\, n^{2} \\psi^{2} + \\frac{1}{2} \\, R + \\frac{R^{2}}{4 \\, n^{2} \\psi^{2}}$"
- ],
- "text/plain": [
- "1/4*n^2*psi^2 + 1/2*R + 1/4*R^2/(n^2*psi^2)"
- ]
- },
- "execution_count": 35,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"r_upper_bound_all_q.expand().subs([nu==1,Delta==psi^2])"
]
},
{
"cell_type": "code",
- "execution_count": 36,
+ "execution_count": null,
"id": "896d26dd",
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle \\frac{a_{v} r}{n} + \\frac{b_{q}}{n}\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle \\frac{a_{v} r}{n} + \\frac{b_{q}}{n}$"
- ],
- "text/plain": [
- "a_v*r/n + b_q/n"
- ]
- },
- "execution_count": 36,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"c_in_terms_of_q.subs([q_value_expr,beta_value_expr])"
]
},
{
"cell_type": "code",
- "execution_count": 37,
+ "execution_count": null,
"id": "51f22f7d",
"metadata": {},
"outputs": [],
@@ -1465,27 +1180,10 @@
},
{
"cell_type": "code",
- "execution_count": 38,
+ "execution_count": null,
"id": "8148f5cd",
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle d > \\frac{{\\left(a_{v} r + 2 \\, b_{q}\\right)} a_{v}}{2 \\, n^{2}}\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle d > \\frac{{\\left(a_{v} r + 2 \\, b_{q}\\right)} a_{v}}{2 \\, n^{2}}$"
- ],
- "text/plain": [
- "d > 1/2*(a_v*r + 2*b_q)*a_v/n^2"
- ]
- },
- "execution_count": 38,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"(positive_radius_condition\n",
" .subs([q_value_expr,beta_value_expr])\n",
@@ -1494,81 +1192,30 @@
},
{
"cell_type": "code",
- "execution_count": 39,
+ "execution_count": null,
"id": "af5315c8",
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle \\delta\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle \\delta$"
- ],
- "text/plain": [
- "delta"
- ]
- },
- "execution_count": 39,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"var(\"delta\", domain=\"real\") # placeholder symbol to be replaced by k_{q,i}"
]
},
{
"cell_type": "code",
- "execution_count": 40,
+ "execution_count": null,
"id": "e3e75309",
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle \\frac{n^{2} q^{2}}{\\kappa}\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle \\frac{n^{2} q^{2}}{\\kappa}$"
- ],
- "text/plain": [
- "n^2*q^2/kappa"
- ]
- },
- "execution_count": 40,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"r_upper_bound1.rhs()"
]
},
{
"cell_type": "code",
- "execution_count": 41,
+ "execution_count": null,
"id": "203b216b",
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<html>\\(\\displaystyle \\frac{n^{2} {\\left(\\psi - q\\right)}^{2}}{\\kappa} + R\\)</html>"
- ],
- "text/latex": [
- "$\\displaystyle \\frac{n^{2} {\\left(\\psi - q\\right)}^{2}}{\\kappa} + R$"
- ],
- "text/plain": [
- "n^2*(psi - q)^2/kappa + R"
- ]
- },
- "execution_count": 41,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"r_upper_bound2.rhs()"
]
@@ -1576,7 +1223,7 @@
],
"metadata": {
"kernelspec": {
- "display_name": "SageMath 9.7",
+ "display_name": "SageMath 9.8",
"language": "sage",
"name": "sagemath"
},
@@ -1590,7 +1237,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.10.8"
+ "version": "3.11.3"
}
},
"nbformat": 4,