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fraction_pol jako fkcja; dziala ok

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jgarnek 2022-05-05 11:19:55 +00:00
parent bb63124a4c
commit 15036ab49f
1 changed files with 23 additions and 49 deletions
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76
crystalline_p2.ipynb
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@ -2,7 +2,7 @@
"cells": [ "cells": [
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 83, "execution_count": 110,
"metadata": { "metadata": {
"collapsed": false "collapsed": false
}, },
@ -47,21 +47,20 @@
" def __sub__(self, other):\n", " def __sub__(self, other):\n",
" return self + (-1)*other\n", " return self + (-1)*other\n",
"\n", "\n",
"class fraction_pol:\n", "def fraction_pol(g):\n",
" def __init__(self, g):\n",
" RxX.<x, X> = PolynomialRing(QQ)\n", " RxX.<x, X> = PolynomialRing(QQ)\n",
" g = RxX(g)\n", " g = RxX(g)\n",
" result = 0\n", " result = 0\n",
" for a in g.monomials():\n", " for a in g.monomials():\n",
" c = g.coefficient(a)\n", " c = g.monomial_coefficient(a)\n",
" c = c%9\n", " c = c%(p^2)\n",
" dX = a.degree(X)\n", " dX = a.degree(X)\n",
" dx = a.degree(x)\n", " dx = a.degree(x)\n",
" if dX%p == 0:\n", " if dX%p == 0:\n",
" result += c*x^(dX//p + dx)\n", " result += c*x^(dX//p + dx)\n",
" else:\n", " else:\n",
" result += c*X^(dX + dx*p)\n", " result += c*X^(dX + dx*p)\n",
" self.function = result\n", " return result\n",
" \n", " \n",
"def teichmuller(f):\n", "def teichmuller(f):\n",
" Rx.<x> = PolynomialRing(QQ)\n", " Rx.<x> = PolynomialRing(QQ)\n",
@ -72,6 +71,7 @@
" for i in range(0, len(coeffs)):\n", " for i in range(0, len(coeffs)):\n",
" ff -= coeffs[i]*witt([Rx(x^i), 0])\n", " ff -= coeffs[i]*witt([Rx(x^i), 0])\n",
" f1 = sum(coeffs[i]*RxX(x^(i)) for i in range(0, len(coeffs))) + p*RxX(ff.coordinates[1](x = X))\n", " f1 = sum(coeffs[i]*RxX(x^(i)) for i in range(0, len(coeffs))) + p*RxX(ff.coordinates[1](x = X))\n",
" f1 = fraction_pol(f1)\n",
" #RXp.<Xp> = PolynomialRing(Integers(p^2))\n", " #RXp.<Xp> = PolynomialRing(Integers(p^2))\n",
" #f1 = RXp(f1)\n", " #f1 = RXp(f1)\n",
" return f1" " return f1"
@ -79,7 +79,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 74, "execution_count": 99,
"metadata": { "metadata": {
"collapsed": false "collapsed": false
}, },
@ -484,18 +484,25 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 39, "execution_count": 109,
"metadata": { "metadata": {
"collapsed": false "collapsed": false
}, },
"outputs": [ "outputs": [
{ {
"data": { "name": "stdout",
"text/plain": [ "output_type": "stream",
"Xp^9 + 6*Xp^7 + 3*Xp^5 + 8*Xp^3" "text": [
"-720*X^9 - 15312*X^7 - 107160*X^5 + x^3 - 249984*X^3 - x\n"
] ]
}, },
"execution_count": 39, {
"data": {
"text/plain": [
"6*X^7 + 3*X^5 + x^3 + 8*x"
]
},
"execution_count": 109,
"metadata": { "metadata": {
}, },
"output_type": "execute_result" "output_type": "execute_result"
@ -644,40 +651,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 70, "execution_count": 102,
"metadata": {
"collapsed": false
},
"outputs": [
{
"ename": "ValueError",
"evalue": "cannot differentiate with respect to Xp",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/rings/polynomial/polynomial_element.pyx\u001b[0m in \u001b[0;36msage.rings.polynomial.polynomial_element.Polynomial._derivative (build/cythonized/sage/rings/polynomial/polynomial_element.c:33685)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 3719\u001b[0m \u001b[0;31m# call _derivative() recursively on coefficients\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3720\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_parent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mcoeff\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_derivative\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mcoeff\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3721\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0mAttributeError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/structure/element.pyx\u001b[0m in \u001b[0;36msage.structure.element.Element.__getattr__ (build/cythonized/sage/structure/element.c:4754)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 493\u001b[0m \"\"\"\n\u001b[0;32m--> 494\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgetattr_from_category\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 495\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/structure/element.pyx\u001b[0m in \u001b[0;36msage.structure.element.Element.getattr_from_category (build/cythonized/sage/structure/element.c:4866)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 506\u001b[0m \u001b[0mcls\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mP\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_abstract_element_class\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 507\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mgetattr_from_other_class\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcls\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 508\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/cpython/getattr.pyx\u001b[0m in \u001b[0;36msage.cpython.getattr.getattr_from_other_class (build/cythonized/sage/cpython/getattr.c:2633)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 360\u001b[0m \u001b[0mdummy_error_message\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mname\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 361\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mAttributeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdummy_error_message\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 362\u001b[0m \u001b[0mattribute\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m<\u001b[0m\u001b[0mobject\u001b[0m\u001b[0;34m>\u001b[0m\u001b[0mattr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mAttributeError\u001b[0m: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute '__custom_name'",
"\nDuring handling of the above exception, another exception occurred:\n",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m/tmp/ipykernel_1111/125743461.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdifferentiate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/rings/polynomial/polynomial_element.pyx\u001b[0m in \u001b[0;36msage.rings.polynomial.polynomial_element.Polynomial.derivative (build/cythonized/sage/rings/polynomial/polynomial_element.c:33473)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 3596\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m^\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m^\u001b[0m\u001b[0;36m3\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m^\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m^\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3597\u001b[0m \"\"\"\n\u001b[0;32m-> 3598\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mmulti_derivative\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3599\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3600\u001b[0m \u001b[0;31m# add .diff(), .differentiate() as aliases for .derivative()\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/misc/derivative.pyx\u001b[0m in \u001b[0;36msage.misc.derivative.multi_derivative (build/cythonized/sage/misc/derivative.c:3218)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 220\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 221\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0marg\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mderivative_parse\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 222\u001b[0;31m \u001b[0mF\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mF\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_derivative\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 223\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mF\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 224\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/rings/polynomial/polynomial_element.pyx\u001b[0m in \u001b[0;36msage.rings.polynomial.polynomial_element.Polynomial._derivative (build/cythonized/sage/rings/polynomial/polynomial_element.c:33782)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 3720\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_parent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mcoeff\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_derivative\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mcoeff\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3721\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0mAttributeError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3722\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf'cannot differentiate with respect to {var}'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3723\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3724\u001b[0m \u001b[0;31m# compute formal derivative with respect to generator\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mValueError\u001b[0m: cannot differentiate with respect to Xp"
]
}
],
"source": [
"t.differentiate(Xp)"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": { "metadata": {
"collapsed": false "collapsed": false
}, },
@ -689,7 +663,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 76, "execution_count": 103,
"metadata": { "metadata": {
"collapsed": false "collapsed": false
}, },
@ -724,7 +698,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 78, "execution_count": 106,
"metadata": { "metadata": {
"collapsed": false "collapsed": false
}, },
@ -732,17 +706,17 @@
{ {
"data": { "data": {
"text/plain": [ "text/plain": [
"2" "<class 'sage.rings.rational.Rational'>"
] ]
}, },
"execution_count": 78, "execution_count": 106,
"metadata": { "metadata": {
}, },
"output_type": "execute_result" "output_type": "execute_result"
} }
], ],
"source": [ "source": [
"g.coefficient(x*X^3)" "type(g.monomial_coefficient(X))"
] ]
}, },
{ {