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Use sturm sequences to find t between 0 and 1 #10

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3c4c435
Add msolve solutions solver
Jan 15, 2024
49cf1b8
Add tests for timing
Jan 15, 2024
58d2783
Resolve issue with msolve format
Jan 16, 2024
b7ef949
temp
Jan 26, 2024
a3ef485
Use precision checks on reduced system
Jan 31, 2024
a2ffaba
Some code cleanup
Feb 7, 2024
fa207f0
Fix incorrect bound
Feb 7, 2024
cb735f2
Compute non minimal points with reduced system
Feb 7, 2024
7cc4487
Use inequality filter for non-min points
Feb 13, 2024
f8c1b8e
Use inequality filter for non-min points
Feb 13, 2024
ee48cda
Merge branch 'msolve' of https://github.com/ACSVMath/sage_acsv into m…
Feb 15, 2024
c8ea279
Use Sturm's Theorem for finding t
Feb 20, 2024
636088d
Fix doctests
Feb 20, 2024
f218547
Small changes
Mar 1, 2024
8833e57
Fix variable ordering issue with msolve
Mar 1, 2024
491b921
Fix variable ordering issue with msolve
Mar 1, 2024
260f1ef
Merge branch 'msolve' into sturm
Mar 1, 2024
c4dbd27
reset testing file
Mar 1, 2024
ecebbb8
use sage's built in string eval
Mar 12, 2024
24e1148
Merge branch 'msolve' of https://github.com/ACSVMath/sage_acsv into m…
Mar 12, 2024
1bc5eb5
Merge branch 'msolve' into sturm
Mar 12, 2024
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205 changes: 176 additions & 29 deletions examples/Sage-ACSV-Tests.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -49,7 +49,7 @@
"source": [
"# Binomial coefficients\n",
"F1 = 1/(1-x-y)\n",
"diagonal_asy(F1, as_symbolic=True)"
"diagonal_asy(F1, as_symbolic=True, use_msolve=False)"
]
},
{
Expand All @@ -60,14 +60,36 @@
{
"data": {
"text/plain": [
"4*4^n/(pi^1.0*n^1.0)"
"4^n/(sqrt(pi)*sqrt(n))"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Binomial coefficients\n",
"F1 = 1/(1-x-y)\n",
"diagonal_asy(F1, as_symbolic=True, use_msolve=True)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4*4^n/(pi*n)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Lattice paths enumeration sequence (on main diagonal)\n",
"F2 = (1+x)*(1+y)/(1-w*x*y*(x+y+1/x+1/y))\n",
Expand All @@ -76,16 +98,16 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.225275868941647?*33.97056274847714?^n/(pi^1.5*n^1.5)"
"1.225275868941647?*33.97056274847714?^n/(pi^(3/2)*n^(3/2))"
]
},
"execution_count": 5,
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
Expand All @@ -98,19 +120,41 @@
},
{
"cell_type": "code",
"execution_count": 6,
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.225275868941647?*33.97056274847714?^n/(pi^(3/2)*n^(3/2))"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Apéry sequence (on main diagonal)\n",
"F3 = 1/(1 - w*(1 + x)*(1 + y)*(1 + z)*(x*y*z + y*z + y + z + 1))\n",
"diagonal_asy(F3, as_symbolic=True, use_msolve=True)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<html>\\(\\displaystyle \\frac{{\\left(12 \\, \\sqrt{2} + 17\\right)}^{n} \\sqrt{\\frac{17}{2} \\, \\sqrt{2} + 12}}{4 \\, \\pi^{1.5} n^{1.5}}\\)</html>"
"<html>\\(\\displaystyle \\frac{{\\left(12 \\, \\sqrt{2} + 17\\right)}^{n} \\sqrt{\\frac{17}{2} \\, \\sqrt{2} + 12}}{4 \\, \\pi^{\\frac{3}{2}} n^{\\frac{3}{2}}}\\)</html>"
],
"text/latex": [
"$\\displaystyle \\frac{{\\left(12 \\, \\sqrt{2} + 17\\right)}^{n} \\sqrt{\\frac{17}{2} \\, \\sqrt{2} + 12}}{4 \\, \\pi^{1.5} n^{1.5}}$"
"$\\displaystyle \\frac{{\\left(12 \\, \\sqrt{2} + 17\\right)}^{n} \\sqrt{\\frac{17}{2} \\, \\sqrt{2} + 12}}{4 \\, \\pi^{\\frac{3}{2}} n^{\\frac{3}{2}}}$"
],
"text/plain": [
"1/4*(12*sqrt(2) + 17)^n*sqrt(17/2*sqrt(2) + 12)/(pi^1.5*n^1.5)"
"1/4*(12*sqrt(2) + 17)^n*sqrt(17/2*sqrt(2) + 12)/(pi^(3/2)*n^(3/2))"
]
},
"metadata": {},
Expand All @@ -125,29 +169,53 @@
},
{
"cell_type": "code",
"execution_count": 7,
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.09677555757474702?*5.884442204019508?^n/(sqrt(pi)*sqrt(n))"
"(0.09677555757474702?*5.88444220401951?^n/(sqrt(pi)*sqrt(n)),\n",
" [[0.548232473567013?, 0.3099773361396642?]])"
]
},
"execution_count": 7,
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Example with two critical points with positive coords, neither of which is obviously non-minimal\n",
"F4 = -1/(1-(1-x-y)*(20-x-40*y))\n",
"diagonal_asy(F4, as_symbolic=True)"
"diagonal_asy(F4, as_symbolic=True, return_points=True)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.09677555757474702?*5.884442204019508?^n/(sqrt(pi)*sqrt(n)),\n",
" [[0.548232473567013?, 0.3099773361396642?]])"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Example with two critical points with positive coords, neither of which is obviously non-minimal\n",
"F4 = -1/(1-(1-x-y)*(20-x-40*y))\n",
"diagonal_asy(F4, as_symbolic=True, use_msolve=True, return_points=True)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
Expand All @@ -169,7 +237,7 @@
},
{
"cell_type": "code",
"execution_count": 9,
"execution_count": 12,
"metadata": {},
"outputs": [
{
Expand All @@ -191,7 +259,7 @@
},
{
"cell_type": "code",
"execution_count": 10,
"execution_count": 13,
"metadata": {},
"outputs": [
{
Expand All @@ -200,7 +268,7 @@
"1.015051765128218?*5.828427124746190?^n/(sqrt(pi)*sqrt(n))"
]
},
"execution_count": 10,
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
Expand All @@ -213,7 +281,29 @@
},
{
"cell_type": "code",
"execution_count": 11,
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.015051765128218?*5.828427124746190?^n/(sqrt(pi)*sqrt(n))"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Delannoy generating function\n",
"F7 = 1/(1 - x - y - x*y)\n",
"diagonal_asy(F7, as_symbolic=True, use_msolve=True)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
Expand All @@ -222,7 +312,7 @@
"1/7*(0.6234898018587335? + 0.7818314824680299?*I)^n + 1/7*(0.6234898018587335? - 0.7818314824680299?*I)^n + 1/7*(-0.2225209339563144? + 0.9749279121818236?*I)^n + 1/7*(-0.2225209339563144? - 0.9749279121818236?*I)^n + 1/7*(-0.9009688679024191? + 0.4338837391175581?*I)^n + 1/7*(-0.9009688679024191? - 0.4338837391175581?*I)^n + 1/7"
]
},
"execution_count": 11,
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
Expand All @@ -235,7 +325,29 @@
},
{
"cell_type": "code",
"execution_count": 12,
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1/7*(0.6234898018587335? + 0.7818314824680299?*I)^n + 1/7*(0.6234898018587335? - 0.7818314824680299?*I)^n + 1/7*(-0.2225209339563144? + 0.9749279121818236?*I)^n + 1/7*(-0.2225209339563144? - 0.9749279121818236?*I)^n + 1/7*(-0.9009688679024191? + 0.4338837391175581?*I)^n + 1/7*(-0.9009688679024191? - 0.4338837391175581?*I)^n + 1/7"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# One variable example with many minimal critical points on same torus\n",
"F8 = 1/(1 - x^7)\n",
"diagonal_asy(F8, as_symbolic=True, use_msolve=True)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
Expand All @@ -244,7 +356,7 @@
"([(1.285654384750451?, 1, 1, 0.03396226416457560?)], [[0.7778140158516262?]])"
]
},
"execution_count": 12,
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
Expand All @@ -257,7 +369,7 @@
},
{
"cell_type": "code",
"execution_count": 13,
"execution_count": 18,
"metadata": {},
"outputs": [
{
Expand All @@ -266,7 +378,7 @@
"0.9430514023983397?*4.518911369262258?^n/(sqrt(pi)*sqrt(n))"
]
},
"execution_count": 13,
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
Expand All @@ -278,12 +390,47 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 19,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"0.9430514023983397?*4.518911369262258?^n/(sqrt(pi)*sqrt(n))"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"F10 = (x^2*y^2 - x*y + 1)/(1-x-y-x*y+x*y^2+x^2*y-x^2*y^3-x^3*y^2)\n",
"diagonal_asy(F10, as_symbolic=True, use_msolve=True)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.068693934883829?*3.910193204291776?^n/(sqrt(pi)*sqrt(n))"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Does not finish computing (hangs on computing GB for critical point system)\n",
"#F = (1-x^3*y^6+x^3*y^4+x^2*y^4+x^2*y^3)/(1-x-y+x^2*y^3-x^3*y^3-x^4*y^4-x^3*y^6+x^4*y^6)"
"#Does not finish computing (hangs on computing GB for critical point system)\n",
"from sage_acsv import diagonal_asy\n",
"var('x,y,w,z,n')\n",
"F = (1-x^3*y^6+x^3*y^4+x^2*y^4+x^2*y^3)/(1-x-y+x^2*y^3-x^3*y^3-x^4*y^4-x^3*y^6+x^4*y^6)\n",
"diagonal_asy(F, as_symbolic=True, use_msolve=True)"
]
},
{
Expand All @@ -307,7 +454,7 @@
"lastKernelId": null
},
"kernelspec": {
"display_name": "SageMath 9.7",
"display_name": "SageMath 10.2",
"language": "sage",
"name": "sagemath"
},
Expand All @@ -321,7 +468,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.11.1"
}
},
"nbformat": 4,
Expand Down
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