{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 4. Γραφικές απεικονίσεις" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n",
"Η γραφική απεικόνιση ενός μαθηματικού αντικειμένου είναι ένα από τα ισχυρότερα εργαλεία ενός ΣΣΥ. Τα περισσότερα ΣΣΥ έχουν ένα δικό τους σύστημα γραφικών για να σχεδιάζουν καμπύλες ή/και \n",
"επιφάνειες. Αυτές οι ρουτίνες γραφικών είναι γραμμένες ειδικά για το κάθε ΣΣΥ. Όμως στην κοινότητα των ΣΣΥ έχουν αναπτυχθεί ορισμένα εξειδικευμένα συστήματα γραφικών που δεν συνδέονται με κάποιο συγκεκριμένο ΣΣΥ.
\n",
"\n",
"Γενικότερα, είναι δυνατόν να συνδέσουμε οποιοδήποτε εξειδικευμένο σύστημα γραφικών με ένα οποιοδήποτε ΣΣΥ ορίζοντας συναρτήσεις που υπολογίζουν ένα σύνολο σημείων από μια λίστα εξισώσεων και τιμών, και να χρησιμοποιήσουμε αυτό το σύνολο ως είσοδο στο σύστημα γραφικών για την γραφική αναπαράσταση των αποτελεσμάτων μας.\n",
"Στα αρχικά στάδια των ΣΣΥ αυτή μάλιστα ήταν η μέθοδος για να πάρει κανείς μια γραφική αναπαράσταση των δεδομένων του ή της λύσης ενός μαθηματικού προβλήματος. Στο πέρασμα του χρόνου όμως, κι επειδή τα ΣΣΥ χρησιμοποιούνται πλέον και ως εκπαιδευτικά εργαλεία, όλα τα ΣΣΥ έχουν ένα δικό τους, έμφυτο, σύστημα γραφικών.
\n",
"Το Sage χρησιμοποιεί ως κύρια συστήματα γραφικών τα: \n",
"\n",
"
\n",
"\n",
"
\n", "Στο Sage δεν υπάρχει διαφορά στην σύνταξη των εντολών που παράγουν ένα γραφικό ανάμεσα σε εκφράσεις και συναρτήσεις. Για παράδειγμα, η γραφική παράσταση μιας συμβολικής έκφρασης είναι\n", "
" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var('x')\n", "ekf = exp(-x^2)\n", "plotexp = plot(ekf, -4, 4,thickness=2)\n", "plotexp.show(figsize=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Ας πολλαπλασιάσουμε την έκφραση με μια συνάρτηση, και το αποτέλεσμα ας το δηλώσουμε σε μια συνάρτηση $f(x)$, και τέλος ας δούμε την γραφική παράσταση της $f(x)$ ως συνάρτηση\n", "
" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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IIZxAaWlpq8uUW5X8m+v5nyk6w6HsQzRswvwxyPzctY9bOqel91mcc81Hrba0\nY22MNfU1FFcVY1SN+Hr6EugTSEzXGAb1GERsaCxBvkGAaZbt/qz97L24l8/SPyOr9Go91axPSB+W\nTVzGvCHzmv1rvPn4Zn7zialXERYYxqEHDhHSpfEf3IraCga8OoAqQxVdu3Ql/dF0fDx9mmyzJb/7\n/He88/07ACQvSLZY67+zU1WVlXtWsnLPSovnR0eOZkzEGLr5dSPINwiPWg/+8JM/sCF5A1G9ohjc\nfTA9AnroFLVjTX13KoezTct65yzJsSg1tkZVVUZuGEnG5Qw8FA8yfpdBN79uLb6nuq6am/5+k3aD\nOLZ7LIlDE0krTONfJ/+l/e4F+waz9ta1TW5FWl1XTXJGMp+c+YS0wjQKKwvp2qUroX6h9OvajyE9\nhzCg2wB6BfTC18uXKzVXKK0ppbiqmKKqIgz1BouSjq+nL96e3nh7euOpeGJUjY3+qzfWt96DRp8R\nYKMjRzO4x+AmX7NZz19YR1VVDuccZkfGDoqqivD39ue22NsYHTnaonbY3HvnbJrDp2dMN3IfHv0w\nr936WqPzPjj2Aff827SO/G9G/oYNsze0K9aVe1Zqsy83z9vM/Otb+EjcySzbuYzlu5Zrj28fdDvP\nTHym0R848ydaa3pJrub+j+/X/vgfXXhUW+3VGmmFaVy3zjRXZGLfiey8b6dV7ztecJwp/5jCpcpL\nTb4+JnIMm362yWIJCmE/sraPDSmKwujI0YyObHoP3dbeu/Yna/k682sqDZWsO7SOpPikRm2Z15MH\nSBzW8k25lrjquu5bT2+1SPwvTn+RJeOXdOpZufYwuPvVHmNaYVqbkv8npz/RjucMnmP1+4b2Gsq3\n93/LL/79C47kHtGe79qlK0/e9CSPj3+8XZ9iRftI8ncifbv2ZdnEZTyx4wlUVBZ+upCDDxzEy8P0\nz3Qk9wi7zptuHsf1iOOWvre0+1quuK57TnkOv/r4V9rjl6a/xJIbl+gYkfOK6xGnHZ8uPN2m9375\n45fa8W2xbVu5M65HHIcfOMzRvKMczT1K76DeTIieQLCve33ycgYyycvJLB63mGG9TPvCHs07yot7\nXwRMZaEntj+hnfe7sb9rtZTUkn5d+2nHrrKf6wOfPEBRVREAd8bdyePjWxm94cYsev5FaVa/r8pQ\nxZ4LptFt0SHRFhMGraUoCiN7j+TXI3/NrbG3SuLXifT8nYy3pzcbbt/ATW/dhIrKU18/RXVdNSXV\nJdoqnv17WOJRAAAa9klEQVS69mNB/IIOXaenf0/8vf2pNFS6RM9/+4/b2Za+DYCIoAj+NvtvUupp\nwYDQAXgqntSr9W3q+e+5sIeaetMY2en9p8v3uBOzac9/4cKFeHh48Oqrr9qyWZtZvnw51113HYGB\ngYSGhjJ9+nQOHjyod1iNjI8az1M3PQXbQX1d5S8z/8KrP38VtgDlsGbWGvy8/Tp0DUVRtLr/uZJz\nHV7dEWDLli3MmjWLnj174uHhwQ8//NDhNq1Rb6znD9v/oD1+cfqLdPfv7pBr29vu3buZM2cOkZGR\neHh4sHXrVpu06+Ppo63xc7rotNX//g1Xkr12GfEVK1YwZswYgoODCQsL48477+TMGduuHWVL69ev\nJz4+npCQEEJCQrjxxhv54otW5gs4iRUrVuDh4cHjj7f/063Nkv9HH33EwYMHiYx03vVPBg8ezLp1\n6zh+/Dh79+6lX79+zJgxg6KiIr1Da+T3o39PdFU0TMI0e/fnQCH02danTTfZWmKu+9fW15Jbntvh\n9ioqKpgwYQKrVq1yaI9w84nN2nr7I3uP5O6hrUzyu0Zr6/nrqaKighEjRrBu3Tqbf0/Ndf9KQyXZ\nZdYtF2BO/goKU/tPtXht9+7dPPLIIxw4cIAdO3ZgMBiYMWMGVVVVTTWlu6ioKFatWkVKSgopKSlM\nmTKFuXPncuqUc+9tfejQIf72t78RHx/fsYZUG8jKylKjoqLUkydPqv369VPXrFlji2btrqysTFUU\nRf3666/1DqVZB7IOqA9/9rC65Msl6jufvaN6eHioFy9etEnbD3/2sMoyVJah7jm/xyZtqqqqnjt3\nTlUURU1NTbVZm80xGo3qiPUjtK9jx487rH5vaWmpCqilpaV2jNB2FEVRP/74Y5u194ev/qB9375I\n/6LV8wuuFGjnj9wwstXzL126pCqKou7evdsW4TpEaGio+tZbb+kdRrPKy8vVQYMGqcnJyeqkSZPU\nxx57rN1tdbjnr6oqSUlJPPHEE1x33XWtv8FJGAwGNmzYQNeuXTv+F9SOxkSO4bVbX+OlGS8R6ROJ\noih07dq19TdawRVG/Ow6v4vv874H4IaIGzrt3rp6GNprqHZ8rOBYq+e3dee4kpISFEUhNLT17UX1\nZjQa2bRpE5WVlYwfP17vcJr10EMPMXv2bKZM6fjPeYdv+K5cuRIfHx8efvjhDgfjCJ999hl33303\nlZWVREREsH379k7xw1lTU8Mf//hH7rnnHgIDA23SpiuM9V+9f7V2/Pi4x+UGZBsMDxuuHZv3gm5J\nw2XEW0v+qqqyePFiJkyYwJAhQ9ofpJ0dP36c8ePHU11dTVBQEFu2bCEuLq71N+pg06ZNfP/99xw+\nfNgm7bWp579x40aCgoIICgoiODiYb7/9lldffZW3337bJsHY0rWx7t1rWoFwypQppKamsm/fPmbN\nmsVdd91FYWGhztE2Hy+YFtq66667UBSF119/3WbXbNjzb+twz5bidZSLpRe1CUd9gvswb0gLi/WJ\nRq7rcZ223aL5nklzVFXV6v1dvLpwU3TLO8ctWrSIkydPsmnTJtsEaydxcXGkpqZy4MABfvvb35KU\nlERamvVDXx0lKyuLxYsX89577+Ht7W2bRttSI7py5Yr6448/av+tWLFC9fT0VL28vLT/FEVRPT09\n1ZiYmHbXomzh2lirq6ubPC82NlZduXKlg6NrrLl4DQaDescdd6gjRoxQi4uLbXrNy1WXtRru5Hcm\n2yReVXVczf/5b5/X4l++c3mb3+/uNX9VVdWhrw9VWYbq9RcvtcpQ1ex5aZfStO/19Hent9jmQw89\npEZHR6vnz5+3aayOMG3aNPXBBx/UO4xGPvroI9XDw0P19va2yLXm54xGY5vbbFPZJyAggP79r24B\nt3DhQubMsRx5MmPGDJKSkrj//vtt8sepva6NtTlGo5GamhoHRNSypuI19/gzMjL45ptv6Nat5cWz\n2qprl6507dKVkuqSNtf8W/v+2rv8oqoq7/7wrvb43uH32vV6ruqGiBs4XnCcOmMdqXmpjO0ztsnz\nWhri2dDDDz/Mxx9/zK5du4iOjrZ5vPbmLPngWtOmTePYMcv7Mvfddx/XXXcdf/zjH9v1+9ahmn+3\nbt0aJSRvb2/Cw8OJjY1t5l36qKys5LnnnmPOnDn07t2bwsJC1q5dS05ODnfddZfe4TVSX1/Pz372\nM77//ns+/fRTDAYD+fn5AISGhtrso19M1xiO5h3lYulF6ox12lIS7XH58mUuXLhAdnY2qqqSlpaG\nqqqEh4cTFhZmk3jNDuccJq3Q9PH8lr63uOxiYBUVFZw9e1Zb9TIjI4PU1FRCQ0OJimp6Lfe2GB0x\nWlvg7VDOIeuS/4Cmk/+iRYv44IMP2Lp1KwEBAdrPa0hICF26dOlwrLb21FNP8ZOf/ISoqCjKy8t5\n//332bVrF1999ZXeoTUSEBDQ6N5JQEAA3bt3b/dAG5sv7+CsN9w8PT1JS0tj3rx5DB48mDlz5nD5\n8mX27NnjlKOUsrKy+PTTT8nKymLEiBFERETQu3dvIiIi2Ldvn82uY06a9Wo9WWWNl6Nui61bt5KQ\nkMDs2bNRFIXExERGjhzJhg3tW3m0Jf/84Z/acUdnOzvzOP/Dhw+TkJDAqFGjUBSFJUuWMHLkSJ55\n5hmbtN9wpdPDOU3fSDTUG/gm8xvANDO84Y3ihtavX09ZWRmTJk0iIiJC++/DDz+0Say2lp+fT1JS\nEnFxcUybNo2UlBS++uorm4ykcYSO5lpZ0tnNLflyCa/sfwWAbxZ8w6R+k/QNyApG1Uj06miyy7Px\n8fSh4PcFTe590Bp3XtLZrKauhqAVQRiMBmJDYznzSOMZud9d/I6b3jLd4E0cmsjGn210dJjCDmRh\nNzcXHXK1Lnux9KKOkVjvYPZBsstNM1JnDJjRrsQvTHy9fBkTOQaA9OL0Jmf6mtdMAuvG94vOQZK/\nm2uY/C+UXtAxEus13Of1p3E/1TES1zC532TteOe5nY1eN3+/FRRujb3VUWEJO5Pk7+aiQq7eNOws\nyX/radPiZp6KJ7MHz9Y5ms5vcszV5P915tcWr526dIpThaa1biZETyAs0LY37oV+JPm7OYuyT5nz\nl30yL2dyusi0BPGNUTfSw9899ty1p/F9xuPnZVol9tP0T6k31muvNbyx/tPr5FOWK5Hk7+Z6+vfE\n19MX6Bw9/4a7SM0cMFPHSFyHn7cfswbOAqCgokDbrKXOWMc/Uv8BgJeHF4lD279tqHA+kvzdnKIo\nWumnMyT/L85eXW/dnLBExzVcGuNvR/4GwIcnPiSnPAcwbdcoJR/XIslfaKWf8tpySqtLdY6mebX1\ntVpNuqd/TxJ6J+gckev46XU/pbufaQOczSc2czD7IM/svDqX4NGxj+oVmrATSf6i04z42XdxH+W1\n5YBpiGdH9jBuyJkneTlKF68uWoKvM9Yx9s2xnC0+C5hmUDccESRcg+zhK4gKthzxMyxsmI7RNM9e\nJZ9Nmza57SSvhp686Uk2Hd+kje4B8Pf2543b33Damfui/aTnLzrNiJ+GN3tnDJihYySuydfLl89/\n8Tk/GfgTvD28GdJzCNvv3c7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A9l3cp83qHRg6kNsH3d5sG3PnzmXcuHHa4+rqalRVJT8/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\nQgg3JMlfCCHckCR/IYRwQ/8f/yI12bonQX8AAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f(x) = ekf*sin(x^3)\n", "plotfun = plot(f, -4, 4,thickness=2,color='green')\n", "plotfun.show(figsize=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Μπορούμε να δούμε την γραφική παράσταση και των δυο προηγούμενων εκφράσεων παρέα, στο ίδιο γραφικό, απλά με μια υπέρθεση των γραφικών αντικειμένων με το σύμβολο της πρόσθεσης +\n", "
" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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R0VY9hXAishREFCn/Vf9zlZ+MUi716tXDxcWFhISC89UvXrxY6NPAzf7zn//w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\nweIvaNc935Snm5Z1GICFn3x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"text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "(plotexp+plotfun).show(figsize=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Στην περίπτωση που η συνάρτηση έχει ανωμαλίες, όπως για παράδειγμα πόλους, το Sage έχει την δυνατότητα τόσο για να εντοπίζει τους πόλους, όσο και να παραγάγει μια αξιοπρεπή γραφική παράσταση της συνάρτησης. Ας δούμε την γραφική παράσταση της υπερβολής $y \\, x =1$.\n", "
" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "yper = plot(1/x, -2, +2, ymin = -4, ymax = 4, thickness=2); yper.show(figsize=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n",
"Στο παραπάνω γραφικό περιορίσαμε την μεταβλητή $y$ να παίρνει ελάχιστες τιμές (ymin) και μέγιστες τιμές (ymax), γιατί η ύπαρξη του x στον παρανομαστή $y=\\frac{1}{x}$ δίνει στην y πάρα πολύ μεγάλες θετικές και αρνητικές τιμές, καθώς το x παίρνει τιμές κοντά στο $0$ από δεξιά και αριστερά, αντίστοιχα.
\n",
"Επιπλέον, παρατηρήστε ότι το Sage προεπιλεγμένα μας σχεδιάζει και την ασύμπτωτο, δηλαδή τον y άξονα (x=0). Για να μην μας εμφανίζει την ασύμπτωτο το Sage, δίνουμε μέσα στο όρισμα της εντολής plot την επιλογή detect_poles=True
. Η αντίθετη επιλογή είναι detect_poles=False
. Τις ίδιες επιλογές μπορούμε να εκμεταλλευτούμε για να σχεδιάζουμε την γραφική παράσταση συναρτήσεων που ορίζονται κατά διαστήματα όπως, για παράδειγμα, την συνάρτηση εφαπτομένης $y=\\tan x$, η οποία ορίζεται στην ένωση των ανοικτών διαστημάτων της μορφής $\\left(-\\frac{\\pi}{2} + k\\,\\pi,\\frac{\\pi}{2} + k\\,\\pi \\right)$, με $k\\in \\mathbb{Z}$. \n",
"
\n",
"Μια ελλειπτική καμπύλη είναι μια επίπεδη αλγεβρική καμπύλη που ορίζεται από μια εξίσωση της μορφής
\n",
"$$ f(x,y) = -y^2 + x^3 + a\\,x+b =0 \\,,$$ \n",
"και η οποία δεν έχει ιδιομορφίες. Δηλαδή, δεν υπάρχει σημείο $p=(x,y)$ της καμπύλης με $f(p)=0$ και
\n",
"$$ \\left. \\nabla f \\right|_p =\\left. \\left( \\frac{\\partial f}{\\partial x},\\frac{\\partial f}{\\partial y}\\right)\\right|_p = 0 \\,.$$ \n",
"Γεωμετρικά αυτό σημαίνει ότι μια ελλειπτική καμπύλη δεν έχει κορυφές (cusps), ή κόμβους (nodes), δηλαδή σημεία που τέμνεται με τον εαυτό της.\n",
"
\n",
"Με το Sage μπορούμε να πάρουμε την γραφική παράσταση τριών αντιπροσωπευτικών μελών της παραπάνω οικογένειας ελλειπτικών καμπυλών με την εντολή implicit_plot
.\n",
"
\n",
"Ακόμα καλύτερα, χρησιμοποιώντας τις περιεκτικές λίστες της Python, μπορούμε να σχεδιάσουμε κάποια αντιπροσωπευτικά μέλη της οικογένειας των ελλειπτικές καμπυλών
\n",
"$$ y^2 = x^3 - x + b \\,,$$
\n",
"στο ίδιο γραφικό, επιβάλλοντας στην παράμετρο $b$ να διατρέξει τις τιμές σε μια λίστα της αρεσκείας μας.\n",
"
\n",
"Επιπλέον, μπορούμε να θέσουμε τα δυο γραφικά μας να αποτελούν τις συνιστώσες ενός διανύσματος γραφικών με την εντολή graphics_array
, ή γενικότερα ενός πίνακα, και να τα προβάλλουμε το ένα δίπλα στο άλλο, όπως παρακάτω\n",
"
\n",
"Παρατηρήστε ότι η ελλειπτική καμπύλη $y^2=x^3-x$ αποτελείται από την ένωση μιας κλειστής και μιας ανοικτής καμπύλης (σημειώνονται με μπλε χρώμα στο αριστερό γραφικό και με τυρκουάζ στο δεξί). Επίσης, στο δεξί γραφικό κάθε μια ελλειπτική καμπύλη έχει το δικό της χρώμα, το οποίο διαλέξαμε κατάλληλα με την επιλογή color
, δίνοντας τιμές που αντιστοιχούν σε όλα χρώματα του ουράνιου τόξου, από το ερυθρό μέχρι το ιώδες. \n",
"
\n",
"Στο Sage μπορούμε να απεικονίσουμε μεγάλους πίνακες σε ένα γραφικό. Για παράδειγμα, ας παραγάγουμε έναν τυχαίο τετραγωνικό 50x50 πίνακα με στοιχεία που είναι 0 ή 1. Με την εντολή matrix_plot
το Sage απεικονίζει τα στοιχεία του πίνακα με μαύρο ή λευκό, ανάλογα αν το στοιχείο είναι 1 ή 0, αντίστοιχα. \n",
"
\n", "Τέτοιες απεικονίσεις μεγάλων σε μέγεθος πινάκων έχουν μεγάλες εφαρμογές στην Γενετική. Για παράδειγμα, βοηθούν στην αναπαράσταση γενετικών αλληλεπιδράσεων και σε ποιο βαθμό η παρουσία μιας μετάλλαξης διαμορφώνει τον φαινότυπο μιας δεύτερης μετάλλαξης. Σε μια τέτοια διαδικασία οι γραμμές κι οι στήλες του πίνακα αναφέρονται στις πρωτεΐνες και τα στοιχεία του πίνακα αν άλλαξε, ή όχι, η αλληλουχία των αμινοξέων τους.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.1.4 Καμπύλες σε παραμετρική και πολική μορφή " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n",
"Στο Sage, μπορούμε να απεικονίσουμε δισδιάστατες καμπύλες που δίνονται σε παραμετρική μορφή \n",
"με την εντολή parametric_plot
, όπου οι συνιστώσες της δηλώνονται σε μορφή λίστας, δηλαδή σε αγκύλες\n",
"
\n",
"Επίσης, με την εντολή polar_plot
μπορούμε να απεικονίζουμε στο xy-επίπεδο δισδιάστατες καμπύλες που μας δίνονται σε πολική μορφή, δηλαδή $r=f(\\theta)$. Για παράδειγμα, η σπείρα του Fermat δίνεται από την σχέση $r=\\pm \\sqrt{\\theta}$. Στο Sage μπορούμε να αναπαραστήσουμε γραφικά την καμπύλη αυτή δίνοντας\n",
"
\n", "Επιπλέον μπορούμε να απεικονίσουμε στο ίδιο γραφικό και τους δυο κλάδους της καμπύλης, θέτοντας τους να αποτελούν στοιχεία μιας λίστας, και σημειώνοντας τις δυο καμπύλες με διαφορετικό χρώμα, αντίστοιχα.\n", "
" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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hiuQ0w+6M1jPgZe/FTdDNm8Bvv9G2hQWwebOgJdxSJCkI3hHMuN/6OPrg8tjL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\n/PrrnPRVpGYaESHmSAzeT3pfvy4iMALxUfFo62rFaeiJ+Ni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VOC9JWA1SS0FCQkKA1FKQ\nAMDBW0tKSuDm5ta0grFKiI4kChISEgKk7oOEhIQASRQkJCQESKIgISEhQBIFCQkJAZIoSEhICJBE\nQUJCQoAkChISEgL+H1jSJWRqWopaAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fer2 = polar_plot([sqrt(t),-sqrt(t)], (t, 0, 4*pi),\n", " color=['red','green'], thickness=2,plot_points=450); fer2.show(figsize=3.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.1.5 Απεικόνιση σημείων από δεδομένα " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n",
"Ορισμένες φορές επιθυμούμε να σχεδιάσουμε μόνο ορισμένα σημεία που αντιστοιχούν σε κάποια δεδομένα που βρήκαμε από την επίλυση ενός προβλήματος. Έχοντας αφετηρία την ακολουθία αριθμών του Fibonacci ας δούμε διάφορους τρόπους που μπορούμε να απεικονίσουμε σημεία με το Sage. Η ακολουθία Fibonacci προσεγγίζεται αρκετά καλά (για $n\\geq 5$) από την ακολουθία πραγματικών αριθμών
\n",
"$$ F_n = \\frac{1}{\\sqrt{5}}\\left( \\frac{1+\\sqrt{5}}{2} \\right)^n\\,.$$
\n",
"Στο Sage, συμβολικά άρα και ακριβώς, η ακολουθία Fibonacci είναι καταχωρημένη στην ακολουθία fibonacci_sequence
\n",
"
\n",
"Ας ορίσουμε λοιπόν μια λίστα από ζευγάρια της μορφής $(n,f(n))$, όπου $f(n)$ η παραπάνω προσεγγιστική τιμή $F_n$ της ακολουθίας Fibonacci που αντιστοιχεί στο $n$, την οποία την καταχωρούμε στην λίστα asymptotic, ενώ τους ακριβείς όρους της ακολουθίας Fibonacci τους καταχωρούμε στην λίστα fib
\n",
"
\n", "Στο παρακάτω δεν απεικονίζουμε γραφικά μόνο τις δυο λίστες σημείων, αλλά χρησιμοποιούμε και διάφορες επιλογές που είναι διαθέσιμες στο Sage και βοηθούν στην καλύτερη εποπτεία του γραφικού, όπως για παράδειγμα σημειώνουμε με διαφορετικά σημαδάκια τα σημεία από κάθε λίστα\n", "
" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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EWtz9RLbw8PBqN/BduXKFNWvWsHr1an7++edqnwsKCmL27Nm88sorNGvWTIPk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\nYXNSLEIIm5NiEULY3P8Hq8F+5H9vOcoAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fib_plot=scatter_plot(fib, facecolor='red',marker='o',markersize=40)\n", "asy_plot = line(asymptotic, marker='D',color='black',thickness=2)\n", "show(fib_plot+asy_plot, aspect_ratio=1,figsize=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
\n",
"Οι ισοσταθμικές καμπύλες είναι πολύ χρήσιμες στην μοντελοποίηση και για να απεικονίζουμε επιφάνειες στις δυο διαστάσεις. Για παράδειγμα, ας απεικονίσουμε την συνάρτηση
\n",
"$$ f(x,y) = y^2-x^3-x+1\\,,$$ \n",
"με την εντολή contout_plot
του Sage\n",
"
\n", "Το αποτέλεσμα είναι ένα γραφικό με διάφορες αποχρώσεις του γκρι που δηλώνουν τον τρόπο που η συνάρτηση $f(x,y)$ αλλάζει τιμές από αρνητικές (σκούρο χρώμα) προς θετικές (ανοικτό χρώμα), καθώς τα σημεία $(x,y)$ διατρέχουν το τετράγωγο $[-\\pi,\\pi]\\times [-\\pi,\\pi]$. Μπορούμε να αλλάζουμε χρώματα, να δηλώνουμε περιγράμματα, τις ισοσταθμικές καμπύλες, καθώς και πολλά άλλα ακόμη. Όταν το γραφικό είναι αρκετά περίπλοκο μια χρήσιμη επιλογή που μας διαθέτει το Sage είναι δίπλα στο γραφικό να έχουμε και μια στήλη που αναγράφει τις τιμές της $f(x,y)$, οι οποίες αντιστοιχούν οι διάφορες αποχρώσεις.\n", "
" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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edu5MTegcE/GDOh+RtC+j0RhX7StcAz6AIAQwm6sQxeB2oLExm507Hwege/fn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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cfbar = contour_plot(f, (x,-pi,pi), (y,-pi,pi),colorbar=True,labels=True); \n", "cfbar.show(figsize=3.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n",
"Το παρακάτω γραφικό, χωρίς επιπλέον επεξηγήσεις, δείχνει διάφορες άλλες επιλογές που μας δίνει το Sage για να διαμορφώσουμε ένα δικό μας γραφικό με την εντολή contout_plot
\n",
"
\n",
"Τα διαγράμματα πυκνότητας είνα παρόμοια με τα διαγράμματα των ισοσταθμικών καμπυλών με την διαφορά ότι τους λείπουν τα διακριτά χωρία των διαφορετικών αποχρώσεων. Υλοποιούνται με την εντολή density_plot
. Στο παρακάτω σχεδιάζουμε την ίδια $f(x,y)$ με την τελευταία εντολή\n",
"
\n",
"Για να γίνει αντιληπτή η διαφορά μεταξύ της contour_plot
και της density_plot
με τις παρακάτω εντολές σχεδιάζουμε στο ίδιο γραφικό, μόνο τις ισοσταθμικές καμπύλες με την contour_plot
και υπερθέτουμε το γραφικό που δημιουργήσαμε με την εντολή density_plot
. \n",
"
\n", "Μπορούμε να δούμε τις διάφορες επιλογές που μας δίνουν οι εντολές γραφικών και αν θέλουμε να αλλάξουμε τις προεπιλεγμένες επιλογές του Sage, όπως παρακάτω\n", "
" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{'labels': False, 'linestyles': None, 'region': None, 'axes': False, 'plot_points': 100, 'linewidths': None, 'colorbar': False, 'contours': None, 'aspect_ratio': 1, 'legend_label': None, 'frame': True, 'fill': True}\n" ] } ], "source": [ "print contour_plot.options" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [], "source": [ "contour_plot.options[\"fill\"]=False" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{'labels': False, 'linestyles': None, 'region': None, 'axes': False, 'plot_points': 100, 'linewidths': None, 'colorbar': False, 'contours': None, 'aspect_ratio': 1, 'legend_label': None, 'frame': True, 'fill': False}\n" ] } ], "source": [ "print contour_plot.options" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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vtkVN500s8ENIkkRfX59VAiL8GKbO4Wu1Ws4O+diNqKmO1HQDLJiLWq0WTmYx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\n8AxB1AICPEMQtYAAz/h/1yrXpT/XV8gAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "con_mine = contour_plot(f,(x,-2,2),(y,-2,2)); con_mine.show(figsize=3.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Επαναφέρουμε όλες τις δικές μας επιλογές στις προκαθορισμένες επιλογές του Sage με την εντολή\n", "
" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{'labels': False, 'linestyles': None, 'region': None, 'axes': False, 'plot_points': 100, 'linewidths': None, 'colorbar': False, 'contours': None, 'aspect_ratio': 1, 'legend_label': None, 'frame': True, 'fill': False}\n" ] } ], "source": [ "contour_plot.reset(); print contour_plot.options" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4.2 Διανυσματικά πεδία, πεδία διευθύνσεων και ροές" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Ένα από τα κυριότερα εργαλεία που μας παρέχει το Sage για την ποιοτική μελέτη των διαφορικών εξισώσεων και των δυναμικών συστημάτων, είναι η γραφική απεικόνιση διανυσματικών πεδίων στις δυο και τρεις διαστάσεις. Επιπλέον, μας παρέχει γραφική απεικόνιση των πεδίων διευθύνσεων στο επίπεδο, και την ροή του διανυσματικού πεδίου, δηλαδή τις καμπύλες στις οποίες τα διανυσματικά πεδία είναι εφαπτόμενα σε κάθε σημείο τους. Για παράδειγμα ας θεωρήσουμε το διανυσματικό πεδίο $$ $$\n", "$$ \\vec{\\mathbf{v}} = (-y\\,, x)\\,. $$\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n",
"Η ροή, ή οι ολοκληρωτικές καμπύλες του $\\vec{\\mathbf{v}}$ βρίσκονται ολοκληρώνοντας το σύστημα των συνήθων διαφορικών εξισώσεων (ΣΔΕ)\n",
"$$ \\frac{d x}{d t} = -y\\,,\\qquad \\frac{d y}{d t} = x\\,, \\qquad\\qquad (*)$$
\n",
"όπου $t$ η παράμετρος της καμπύλης. Πολλαπλασιάζοντας την πρώτη ΣΔΕ με $x(t)$, και την δεύτερη με $y(t)$ και προσθέτοντας κατά μέλη παίρνουμε
\n",
"$$ x\\,\\frac{d x}{d t} + y\\,\\frac{d y}{d t} =0\\,\\Rightarrow \\frac{1}{2}\\,\\frac{d }{d t} ( x^2+y^2 )=0\\,\\Rightarrow\\,\n",
"\\frac{d }{d t}( x^2+y^2 ) =0\\,\\Rightarrow x^2+y^2=c^2\\,.$$
\n",
"όπου $c\\in\\mathbb{R}$, η σταθερή ολοκλήρωσης. Δηλαδή, οι ολοκληρωτικές καμπύλες του $\\vec{\\mathbf{v}}$ είναι μια οικογένεια ομόκεντρων κύκλων με κέντρο το σημείο $(0,0)$ και ακτίνα $c$. \n",
"
\n",
"Για να δούμε στο Sage το διανυσματικό πεδίο σε διάφορα σημεία του xy-επιπέδου χρησιμοποιούμε την εντολή plot_vector_field
\n",
"
\n",
"Με την εντολή polar_plot
σχεδιάζουμε διάφορα μέλη της μονοπαραμετρικής οικογένειας των ολοκληρωτικών καμπυλών (κύκλων) \n",
"
\n", "και προβάλλουμε τα δυο γραφικά το ένα δίπλα στο άλλο θέτοντάς τα σε ένα διάνυσμα γραφικών και στο τέλος μαζί το ένα πάνω στο άλλο \n", "
" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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APfdeXl5afa4kE1Yxz+q4ceNgamoqKhO0detWNG3aFDt37hT0cL5+/RoHDhyQCZhEyIRV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TivoqOjwc7OrtB3mZmGw04SEhKgMgscNADmyNFqEyA3N5crDGvx4sVw7BhVujI1rzw9PeHFixfg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FYcOGCc6hDyNWAUAGAPQQ3Lp1i1544QVRcdbW1tSiRQvB2LKyMurQoYNgXG1tLdXX15ONjY1g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\n", "text/plain": [ "Graphics Array of size 1 x 3" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "vec_array = graphics_array([vf,int_curv,int_curv+vf])\n", "vec_array.show(figsize=7,ticks=[[],[]])" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "\n", "Διαιρώντας το σύστημα των ΣΔΕ $(*)$ κατά μέλη παίρνουμε την ΣΔΕ \n", "$$ \\frac{dy}{dx} = -\\frac{x}{y}\\,.$$\n", "Το Sage μας δίνει την δυνατότητα να σχεδιάσουμε το πεδίο διευθύνσεων της παραπάνω ΣΔΕ σε διάφορα σημεία του επιπέδου. Για παράδειγμα \n", "
" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ImJoWXYOFBTBmDCCjKGVUBAQApqYaEAFDhrCyQ2mQJEn2vdAiMjIScXFxQrFL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3gmB2KHj7vTJyB2VXbulKPhu3BB7ntU+10A0Ja+TqfeTgRjr14lIQYuRCaDzDkmJ+e+4/Th4uLC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\nAAAASUVORK5CYII=\n", "text/plain": [ "Graphics Array of size 1 x 3" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df = plot_slope_field(-x/y, (x,-1,1),(y,-1,1),aspect_ratio=1)\n", "vec_array = graphics_array([df,int_curv,int_curv+df])\n", "vec_array.show(figsize=7,ticks=[[],[]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n",
"Δεν είναι πάντα εφικτό να βρούμε τις ολοκληρωτικές καμπύλες ενός δοσμένου διανυσματικού πεδίου, ή ισοδύναμα ενός συστήματος ΣΔΕ ή μιας διαφορικής εξίσωσης, σε κλειστή μορφή. Σε αυτές τις περιπτώσεις το Sage μας δίνει την δυνατότητα να έχουμε μια γραφική απεικόνιση των ολοκληρωτικών καμπυλών μέσω της εντολής streamline_plot
. Για παράδειγμα ας θεωρήσουμε το διανυσματικό πεδίο
\n",
"$$\\vec{\\mathbf{v}} = (-1-x^2+y, 1+x-y^2) \\,.$$
\n",
"Για να βρούμε τις ολοκληρωτικές καμπύλες του $\\vec{\\mathbf{v}}$, θα πρέπει να ολοκληρώσουμε το παρακάτω σύστημα ΣΔΕ\n",
"$$ \\dot{x} = -1-x^2+y\\,,\\quad \\dot{y}= 1+x-y^2\\,,\\qquad \\dot{\\phantom{X}} = \\frac{d}{d\\,t}\\quad\\,, $$\n",
"ή ισοδύναμα να λύσουμε την ΣΔΕ\n",
"$$ \\frac{dy}{dx} = \\frac{1+x-y^2}{-1-x^2+y}\\,.$$
\n",
"Με μια πρώτη ματιά δεν είναι καθόλου προφανές πως θα μπορούσαμε να ολοκληρώσουμε την παραπάνω ΣΔΕ. Το Sage όμως μας επιτρέπει να έχουμε μια γρήγορη ποιοτική εικόνα του πεδίου διευθύνσεων, καθώς και της ροής του $\\vec{\\mathbf{v}}$, όπως δείχνουν τα ακόλουθα σχήματα\n",
"
\n",
"Το Sage μας δίνει μια πληθώρα άλλων γραφικών απεικονίσεων που οι σημειώσεις αυτές όλες μαζί δεν φτάνουν για να τις περιγράψουν. Ενδεικτικά αναφέρουμε μερικές από αυτές:\n",
"\n",
"
\n",
"Σας προτρέπω να ρίξετε μια ματιά στην αντίστοιχη ιστοσελίδα των διδιάστατων γραφικών του Sage \n",
"(εδώ)\n",
"όπου θα βρείτε πάρα πολλά παραδείγματα κι εφαρμογές. Αν δεν μπορείτε να υλοποιήσετε αυτό που θέλετε με τις εντολές του Sage, ή για κάποιον λόγο δεν σας αφήνει ικανοποιημένους το Sage με το γραφικό που θέλετε να απεικονίσετε, μπορείτε πάντα να χρησιμοποιήσετε το Sage σε συνδυασμό με την ολοκαίνουρια έκδοση (Ιανουάριος 2017) της πανίσχυρης βιβλιοθήκης γραφικών complex_plot
.region_plot
.\n",
"matplotlib
, εδώ.\n",
"\n",
"
\n", "Το Sage διαθέτει τρισδιάστατες εκδόσεις όλων των βασικών εντολών γραφικών απεικονίσεων στις δυο διαστάσεις για την γραφική απεικόνιση καμπυλών, επιφανειών, γεωμετρικών σχημάτων κ.α. στις τρεις διαστάσεις. Σας παραπέμπω στην αντίστοιχη σελίδα βοήθειας του Sage (εδώ). \n", "Ενδεικτικά μόνο ας δούμε μια τέτοια επιφάνεια \n", "
\n" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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CwBhJZ78QgmpE1Cybeh4zTUQJTqVMhBDGgBAKQ25ZmqYRuUHDoC8cmGAhf+bZ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GBafj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\nOEWJd8Zo0jyDkuoAo2Crl0QRYb0o+vTr7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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var('x y z')\n", "T = RDF(golden_ratio)\n", "F = 2 - (cos(x+T*y) + cos(x-T*y) + cos(y+T*z) + cos(y-T*z) + cos(z-T*x) + cos(z+T*x))\n", "r = 4.77\n", "plt3d = implicit_plot3d(F, (x,-r,r), (y,-r,r), (z,-r,r), plot_points=40, \n", " color='darkkhaki'); plt3d.show(viewer='tachyon',figsize=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n",
"Αξίζει να αναφερθεί ότι το Sage υλοποιεί όλους τους βασικούς μετασχηματισμούς στις τρεις διαστάσεις, οι οποίοι χρησιμοποιούνται πιο συχνά στην ανάλυση επιφανειών, όπως οι κυλινδρικές κι οι σφαιρικές συντεταγμένες. Εδώ θα επικεντρωθούμε σε μια άλλη ενδιαφέρουσα εφαρμογή του Sage και ειδικότερα, στον τρόπο που μπορούμε να χρησιμοποιήσουμε τον χρωματισμό για να έχουμε εποπτεία σε περισσότερες διαστάσεις. Οι διάφοροι χρωματισμοί δίνονται με την εντολή color_maps
. Γι' αρχή ας πάρουμε την λωρίδα του Möbius, κι ας την σχεδιάσουμε χωρίς χρωματισμό\n",
"
\n",
"Αν τρέξετε την παραπάνω εντολή το αποτέλεσμα δεν είναι και πολύ διαφωτιστικό. Ας εφαρμόσουμε τώρα χρωματισμό στην λωρίδα με την μέθοδο color_maps
από την οικογένεια χρωμάτων PiYG, κι ας αλλάξουμε λίγο την οπτική γωνία που βλέπουμε την λωρίδα, με την μέθοδο rotateX, rotatY, rotateZ
.\n",
"
\n", "Το αποτέλεσμα είναι πολύ πιο διαφωτιστικό, κι αξίζει να σώσουμε το γραφικό σε ένα αρχείο για μελλοντική χρήση.\n", "
" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": true }, "outputs": [], "source": [ "mob.save('mob.png', figsize=6, frame=False, viewer='tachyon')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n",
"Κλείνουμε το κεφάλαιο αυτό με μια γραφική απεικόνιση λίγο διαφορετική από αυτές που έχουμε δει μέχρι τώρα. Θα απεικονίσουμε σε ένα \"τετραδιάστατο\" γραφικό, την τετραγωνική ρίζα ενός μιγαδικού αριθμού.
\n",
"\n",
"Ας θεωρήσουμε το ζευγάρι των μιγαδικών αριθμών $(z,w)\\in \\mathbb{C}\\times \\mathbb{C}$, και μια εξίσωση που συνδέει τα $z,w$ μεταξύ τους, για παράδειγμα την\n",
"$$ z=w^2\\,.$$
\n",
"Η εξίσωση αυτή ορίζει την τετραγωνική ρίζα του $z = x + {\\rm{i}} y$. Δηλαδή, ορίζουμε την τετραγωνική ρίζα του $z$, να είναι το σύνολο των μιγαδικών αριθμών $w=u + {\\rm{i}} v $, έτσι ώστε $w^2=z$. Στόχος μας είναι να απεικονίσουμε γραφικά τους πραγματικούς αριθμούς $(u,v)$ σε συνάρτηση των $(x,y)$. Αλλά πως να απεικονίσουμε γραφικά ένα αντικείμενο, ας το ονομάσουμε $R$, στον $\\mathbb{R}^4$ ; Η ιδέα είναι λοιπόν τρεις από τις τέσσερις πραγματικές μεταβλητές να διατρέχουν τον συνηθισμένο $\\mathbb{R}^3$, ενώ η τέταρτη μεταβλητή να απεικονίζεται στην επιφάνεια $R$, με χρώμα!\n",
"
\n", "Κατ'αρχήν ας βρούμε τις εξισώσεις που συνδέουν τα $(x,y)$ και $(u,v)$, μεταξύ τους.\n", "Χωρίζουμε την εξίσωση $z=w^2$ σε φανταστικό και πραγματικό μέρος \n", "
" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": true }, "outputs": [], "source": [ "u, v = var('u,v')\n", "w = u + I*v\n", "z = w^2\n", "x = real_part(z)\n", "y = imag_part(z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Επειδή το Sage δεν ξέρει αν οι $u,v$ είναι πραγματικοί αριθμοί, το βοηθάμε εμείς\n", "
" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "u^2 - v^2\n", "2*u*v\n" ] } ], "source": [ "D = {real_part(u):u, imag_part(u):0, real_part(v):v, imag_part(v):0}\n", "xx = x.subs(D)\n", "yy = y.subs(D)\n", "print xx\n", "print yy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Επιλέγουμε το ύψος της επιφάνειας $R$ να περιγράφεται από το πραγματικό μέρος του μιγαδικού $w$, οπότε η $R$ περιγράφεται σε παραμετρική μορφή, από τα $(x, y, u)$. Το φανταστικό μέρος του $w$, δηλαδή το $v$, θα το απεικονίσουμε πάνω στην $R$, χρωματίζοντάς την κατάλληλα. Επιπλόν, μετασχηματίζουμε τα $(u,v)$ σε πολικές συντεταγμένες $(r,\\theta)$ για να πάρουμε ένα πιο εποπτικό γραφικό.\n", "
" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "r^2*cos(2*theta)\n", "r^2*sin(2*theta)\n" ] } ], "source": [ "r , theta = var('r,theta')\n", "polikes = {u:r*cos(theta), v:r*sin(theta)}\n", "Rx = xx.subs(polikes).trig_reduce()\n", "Ry = yy.subs(polikes).trig_reduce()\n", "print Rx; print Ry" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n",
"Τέλος απεικονίζουμε γραφικά την επιφάνεια $R$ με την εντολή του Sage parametric_plot3d
, \n",
"
\n",
"Η διαφορά του χρωματισμού στην μεταβλητή $v$, μπορεί να υλοποιηθεί θέτοντας την συνάρτηση\n",
"$v=r\\,\\sin \\theta$, ως όρισμα στην επιλογή color. Αν επιλέξετε ως viewer στην εντολή show τον jsmol, δηλαδή τρέξετε Rcol.show(zoom=1, figsize=5, viewer='jsmol')
έχετε την δυνατότητα να περιστρέψετε την επιφάνεια $R$ και να την περιεργαστείτε. Θα διαπιστώσετε, όπως φαίνεται στο παρακάτω σχήμα, ότι η επιφάνεια $R$ αποτελείται από δυο φύλλα, και περνάμε από το ένα φύλλο στο άλλο κατά μήκος μιας τομής (ευθείας). Μια τέτοια επιφάνεια ονομάζεται επιφάνεια Riemann.\n",
"