240 lines
28 KiB
Plaintext
240 lines
28 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 33,
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"metadata": {},
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"outputs": [],
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"source": [
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"import sympy\n",
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"from sympy import Symbol, Function, cos, diff\n",
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"from sympy.codegen.ast import Assignment, Print\n",
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"from sympy.integrals.integrals import integrate, Integral\n",
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"from sympy.plotting import plot\n",
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"from sympy.plotting.pygletplot import PygletPlot as Plot\n",
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"from IPython.display import Markdown"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle f{\\left(x \\right)} = x^{2}$"
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],
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"text/plain": [
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"Eq(f(x), x**2)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\operatorname{f'}{\\left(x \\right)} = 2 x$"
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],
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"text/plain": [
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"Eq(f'(x), 2*x)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\operatorname{f''}{\\left(x \\right)} = 2$"
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],
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"text/plain": [
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"Eq(f''(x), 2)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"x = Symbol('x')\n",
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"\n",
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"def f(x):\n",
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" return x**2\n",
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"\n",
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"display(sympy.Eq(Function('f')(x), f(x)))\n",
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"display(sympy.Eq(Function('f\\'')(Symbol('x')), diff(f(x))))\n",
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"display(sympy.Eq(Function('f\\'\\'')(Symbol('x')), diff(diff(f(x)))))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\int \\left(x^{2} + x + 1\\right)\\, dx$"
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],
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"text/plain": [
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"Integral(x**2 + x + 1, x)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\frac{x^{3}}{3} + \\frac{x^{2}}{2} + x$"
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],
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"text/plain": [
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"x**3/3 + x**2/2 + x"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"x = Symbol('x')\n",
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"i = Integral(x**2 + x + 1, x)\n",
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"sympy.solvers.solve(i, x)\n",
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"display(i)\n",
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"display(i.doit())"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\int \\cos{\\left(x \\right)}\\, dx$"
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],
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"text/plain": [
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"Integral(cos(x), x)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\sin{\\left(x \\right)}$"
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],
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"text/plain": [
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"sin(x)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"i = Integral(cos(x), x)\n",
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"display(i)\n",
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"display(i.doit())"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 19,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\left\\{-1, 1\\right\\}$"
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],
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"text/plain": [
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"{-1, 1}"
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]
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},
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"execution_count": 19,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"x = Symbol('x')\n",
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"y = Symbol('y')\n",
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"sympy.FiniteSet(*sympy.solvers.solve(sympy.Eq(x**2, 1), x))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 40,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/markdown": [
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""
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|
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],
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"text/plain": [
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"<IPython.core.display.Markdown object>"
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]
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},
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"execution_count": 40,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"data": {
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"image/png": "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|
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"text/plain": [
|
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|
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"<Figure size 432x288 with 1 Axes>"
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]
|
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},
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"metadata": {
|
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"needs_background": "light"
|
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|
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},
|
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"output_type": "display_data"
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}
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],
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"source": [
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"from sympy import symbols\n",
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"from sympy.plotting import plot\n",
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"x = symbols('x')\n",
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"p1 = plot(x**2, show=False, label='$f(x)=x^2$', legend=True)\n",
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"p2 = plot(x, label='$g(x)=x$', show=False)\n",
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"p2.extend(plot(-x**2, label='$h(x)=-x$', show=False))\n",
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"p1.extend(p2)\n",
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"p1.save('plot.svg')\n",
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"Markdown('')"
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]
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}
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|
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],
|
||
|
|
"metadata": {
|
||
|
|
"interpreter": {
|
||
|
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"hash": "96fc3968b0459c7bb0304f66d2259bbe1d74f60096901795baa92b56e1ba9010"
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},
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"kernelspec": {
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"display_name": "Python 3.10.2 ('AN2_Analysis_2-DUdzbZjr')",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.2"
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},
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"orig_nbformat": 4
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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