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  1. {
  2. "cells": [
  3. {
  4. "cell_type": "code",
  5. "execution_count": 1,
  6. "metadata": {},
  7. "outputs": [
  8. {
  9. "data": {
  10. "image/png": "iVBORw0KGgoAAAANSUhEUgAAABQAAAATBAMAAABiojCGAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarMolUmd1mIrvNRO9/G2jnAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAfUlEQVQIHWNgAAPGUGMBCIuBnYG9Acrkv8D1BcrkFIAzGRhYYQoYGDxg2hi4NkKVMjAsZvCCsrm2uBRCmXz//39gYBBSFglNgIgUMBlBbeJcwPSLeQJYlIWB+wBEGkjyK8CZ9xcwQmySvmDPwAoRznesY7gGYYorsVUmgJkAN5kWSh0we2MAAAAASUVORK5CYII=\n",
  11. "text/latex": [
  12. "$$x^{2}$$"
  13. ],
  14. "text/plain": [
  15. " 2\n",
  16. "x "
  17. ]
  18. },
  19. "execution_count": 1,
  20. "metadata": {},
  21. "output_type": "execute_result"
  22. }
  23. ],
  24. "source": [
  25. "import sympy\n",
  26. "sympy.init_printing()\n",
  27. "\n",
  28. "x = sympy.Symbol('x')\n",
  29. "x**2"
  30. ]
  31. },
  32. {
  33. "cell_type": "code",
  34. "execution_count": 3,
  35. "metadata": {},
  36. "outputs": [],
  37. "source": [
  38. "from IPython.display import display"
  39. ]
  40. },
  41. {
  42. "cell_type": "code",
  43. "execution_count": 4,
  44. "metadata": {},
  45. "outputs": [
  46. {
  47. "data": {
  48. "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAOBAMAAADgeEClAAAAIVBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADdcGRXAAAACnRSTlMAMt0Qq5nNdrvvxbMB0AAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABtJREFUCB1jYGBUZmAwCVvMwMDAThbB0rnIHQBAqQoWQ8kakgAAAABJRU5ErkJggg==\n",
  49. "text/latex": [
  50. "$$1$$"
  51. ],
  52. "text/plain": [
  53. "1"
  54. ]
  55. },
  56. "metadata": {},
  57. "output_type": "display_data"
  58. },
  59. {
  60. "data": {
  61. "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAwAAAAqBAMAAAB1rqf/AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMt0Qq5nNdrvviVRmIkTkPrJOAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAYElEQVQYGWNgYGBUZgACk7DPIIqBnYoUS+cnd7ChZBH/wYAsrVg0mZcYrtrAwBDA7s6qwMBzgf0vywEGRgaOBLBS/gIw9f4CswGDxQN/Bi4Ghv3CkQyvGRhMy7ljNjAAACXSIeFGJud2AAAAAElFTkSuQmCC\n",
  62. "text/latex": [
  63. "$$\\frac{1}{x}$$"
  64. ],
  65. "text/plain": [
  66. "1\n",
  67. "─\n",
  68. "x"
  69. ]
  70. },
  71. "metadata": {},
  72. "output_type": "display_data"
  73. },
  74. {
  75. "data": {
  76. "image/png": "iVBORw0KGgoAAAANSUhEUgAAABYAAAAqBAMAAABFIrbeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMt0Qq5nNdrvviVRmIkTkPrJOAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAkklEQVQYGWNgAAEhAzAFJJhd8+FsBob6gWd7zFcpgDmOlvR/BCDBGuZVLvAgYmVgVYBp5X/A+xHG5jFAsBkYuOBqkIOdgbcZpNy8xHDVBoYrDLJAdgC7O6sCb6NgMAMDzwX2vywHOP///8DAwMjAkQBSCgH8SGHz/gIz1C0WD/wZuKAq9gtHMryGsk3LuWM2QNgAK00tKKHUoBQAAAAASUVORK5CYII=\n",
  77. "text/latex": [
  78. "$$\\frac{1}{x^{2}}$$"
  79. ],
  80. "text/plain": [
  81. "1 \n",
  82. "──\n",
  83. " 2\n",
  84. "x "
  85. ]
  86. },
  87. "metadata": {},
  88. "output_type": "display_data"
  89. },
  90. {
  91. "data": {
  92. "image/png": "iVBORw0KGgoAAAANSUhEUgAAABYAAAAqBAMAAABFIrbeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMt0Qq5nNdrvviVRmIkTkPrJOAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAlElEQVQYGWNgAAEhAzAFJJhd8+FsBob6gWd7zFcpgDmOlvR/BCDBGt6aEgGYcpYF7BNgbEYBrgQYm4GB6QCczZ4OZzIwWCD5jPEjUMK8xHDVBksB3j9AdgC7O6sCkwHPZAYGngvsf1kOMC4vucDAwMjAkYAwgh/JhPcXmA0gMhYP/Bm4oIr2C0cyvIayTcu5YzZA2ADwkSx8WUA0GAAAAABJRU5ErkJggg==\n",
  93. "text/latex": [
  94. "$$\\frac{1}{x^{3}}$$"
  95. ],
  96. "text/plain": [
  97. "1 \n",
  98. "──\n",
  99. " 3\n",
  100. "x "
  101. ]
  102. },
  103. "metadata": {},
  104. "output_type": "display_data"
  105. },
  106. {
  107. "data": {
  108. "image/png": "iVBORw0KGgoAAAANSUhEUgAAABYAAAAqBAMAAABFIrbeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMt0Qq5nNdrvviVRmIkTkPrJOAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAh0lEQVQYGWNgAAEhAzAFJJhd8+FsBob6gWd7zFcpgDmOlvR/BCDJGjYk1fUINt9+BNvcHsEuQLC5LyDYdxjAbPMSw1UbpFbFrwZqCGB3Z1VgYLgPjAKeC+x/WQ4w8PR7MzAwMnAkIIzjRwqb9xeYodFl8cCfgQuqaL9wJMNrKNu0nDtmA4QNACc/K0/wzAM7AAAAAElFTkSuQmCC\n",
  109. "text/latex": [
  110. "$$\\frac{1}{x^{4}}$$"
  111. ],
  112. "text/plain": [
  113. "1 \n",
  114. "──\n",
  115. " 4\n",
  116. "x "
  117. ]
  118. },
  119. "metadata": {},
  120. "output_type": "display_data"
  121. }
  122. ],
  123. "source": [
  124. "for i in range(5):\n",
  125. " f = 1/x**i\n",
  126. " display(f)"
  127. ]
  128. },
  129. {
  130. "cell_type": "code",
  131. "execution_count": 6,
  132. "metadata": {},
  133. "outputs": [
  134. {
  135. "data": {
  136. "image/png": "iVBORw0KGgoAAAANSUhEUgAAABYAAAAqBAMAAABFIrbeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMt0Qq5nNdrvviVRmIkTkPrJOAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAh0lEQVQYGWNgAAEhAzAFJJhd8+FsBob6gWd7zFcpgDmOlvR/BCDJGjYk1fUINt9+BNvcHsEuQLC5LyDYdxjAbPMSw1UbpFbFrwZqCGB3Z1VgYLgPjAKeC+x/WQ4w8PR7MzAwMnAkIIzjRwqb9xeYodFl8cCfgQuqaL9wJMNrKNu0nDtmA4QNACc/K0/wzAM7AAAAAElFTkSuQmCC\n",
  137. "text/latex": [
  138. "$$\\frac{1}{x^{4}}$$"
  139. ],
  140. "text/plain": [
  141. "1 \n",
  142. "──\n",
  143. " 4\n",
  144. "x "
  145. ]
  146. },
  147. "metadata": {},
  148. "output_type": "display_data"
  149. },
  150. {
  151. "data": {
  152. "text/plain": [
  153. "'\\\\frac{1}{x^{4}}'"
  154. ]
  155. },
  156. "execution_count": 6,
  157. "metadata": {},
  158. "output_type": "execute_result"
  159. }
  160. ],
  161. "source": [
  162. "display(f)\n",
  163. "sympy.latex(f)"
  164. ]
  165. },
  166. {
  167. "cell_type": "code",
  168. "execution_count": 14,
  169. "metadata": {},
  170. "outputs": [
  171. {
  172. "data": {
  173. "text/latex": [
  174. "$$f_n(x) = \\frac{1}{x^n}$$"
  175. ],
  176. "text/plain": [
  177. "<IPython.core.display.Math object>"
  178. ]
  179. },
  180. "metadata": {},
  181. "output_type": "display_data"
  182. }
  183. ],
  184. "source": [
  185. "from IPython.display import Math\n",
  186. "display(Math(r'f_n(x) = \\frac{1}{x^n}'))"
  187. ]
  188. },
  189. {
  190. "cell_type": "code",
  191. "execution_count": 15,
  192. "metadata": {},
  193. "outputs": [
  194. {
  195. "data": {
  196. "text/latex": [
  197. "$$f_{0}(x) = 1$$"
  198. ],
  199. "text/plain": [
  200. "<IPython.core.display.Math object>"
  201. ]
  202. },
  203. "metadata": {},
  204. "output_type": "display_data"
  205. },
  206. {
  207. "data": {
  208. "text/latex": [
  209. "$$f_{1}(x) = \\frac{1}{x}$$"
  210. ],
  211. "text/plain": [
  212. "<IPython.core.display.Math object>"
  213. ]
  214. },
  215. "metadata": {},
  216. "output_type": "display_data"
  217. },
  218. {
  219. "data": {
  220. "text/latex": [
  221. "$$f_{2}(x) = \\frac{1}{x^{2}}$$"
  222. ],
  223. "text/plain": [
  224. "<IPython.core.display.Math object>"
  225. ]
  226. },
  227. "metadata": {},
  228. "output_type": "display_data"
  229. },
  230. {
  231. "data": {
  232. "text/latex": [
  233. "$$f_{3}(x) = \\frac{1}{x^{3}}$$"
  234. ],
  235. "text/plain": [
  236. "<IPython.core.display.Math object>"
  237. ]
  238. },
  239. "metadata": {},
  240. "output_type": "display_data"
  241. },
  242. {
  243. "data": {
  244. "text/latex": [
  245. "$$f_{4}(x) = \\frac{1}{x^{4}}$$"
  246. ],
  247. "text/plain": [
  248. "<IPython.core.display.Math object>"
  249. ]
  250. },
  251. "metadata": {},
  252. "output_type": "display_data"
  253. }
  254. ],
  255. "source": [
  256. "for i in range(5):\n",
  257. " f = 1/x**i\n",
  258. " display(Math(r'f_{%d}(x) = %s' % (i, sympy.latex(f))))"
  259. ]
  260. },
  261. {
  262. "cell_type": "code",
  263. "execution_count": 16,
  264. "metadata": {},
  265. "outputs": [
  266. {
  267. "data": {
  268. "text/latex": [
  269. "$$\\frac{d x^{0}}{dx} = 0$$"
  270. ],
  271. "text/plain": [
  272. "<IPython.core.display.Math object>"
  273. ]
  274. },
  275. "metadata": {},
  276. "output_type": "display_data"
  277. },
  278. {
  279. "data": {
  280. "text/latex": [
  281. "$$\\frac{d x^{1}}{dx} = 1$$"
  282. ],
  283. "text/plain": [
  284. "<IPython.core.display.Math object>"
  285. ]
  286. },
  287. "metadata": {},
  288. "output_type": "display_data"
  289. },
  290. {
  291. "data": {
  292. "text/latex": [
  293. "$$\\frac{d x^{2}}{dx} = 2 x$$"
  294. ],
  295. "text/plain": [
  296. "<IPython.core.display.Math object>"
  297. ]
  298. },
  299. "metadata": {},
  300. "output_type": "display_data"
  301. },
  302. {
  303. "data": {
  304. "text/latex": [
  305. "$$\\frac{d x^{3}}{dx} = 3 x^{2}$$"
  306. ],
  307. "text/plain": [
  308. "<IPython.core.display.Math object>"
  309. ]
  310. },
  311. "metadata": {},
  312. "output_type": "display_data"
  313. },
  314. {
  315. "data": {
  316. "text/latex": [
  317. "$$\\frac{d x^{4}}{dx} = 4 x^{3}$$"
  318. ],
  319. "text/plain": [
  320. "<IPython.core.display.Math object>"
  321. ]
  322. },
  323. "metadata": {},
  324. "output_type": "display_data"
  325. }
  326. ],
  327. "source": [
  328. "for i in range(5):\n",
  329. " F = x**i \n",
  330. " f = sympy.diff(F,x)\n",
  331. " display(Math(r'\\frac{d x^{%d}}{dx} = %s' % (i,sympy.latex(f))))"
  332. ]
  333. },
  334. {
  335. "cell_type": "code",
  336. "execution_count": 17,
  337. "metadata": {},
  338. "outputs": [
  339. {
  340. "data": {
  341. "text/latex": [
  342. "$$\\int x^{0}dx = x$$"
  343. ],
  344. "text/plain": [
  345. "<IPython.core.display.Math object>"
  346. ]
  347. },
  348. "metadata": {},
  349. "output_type": "display_data"
  350. },
  351. {
  352. "data": {
  353. "text/latex": [
  354. "$$\\int x^{1}dx = \\frac{x^{2}}{2}$$"
  355. ],
  356. "text/plain": [
  357. "<IPython.core.display.Math object>"
  358. ]
  359. },
  360. "metadata": {},
  361. "output_type": "display_data"
  362. },
  363. {
  364. "data": {
  365. "text/latex": [
  366. "$$\\int x^{2}dx = \\frac{x^{3}}{3}$$"
  367. ],
  368. "text/plain": [
  369. "<IPython.core.display.Math object>"
  370. ]
  371. },
  372. "metadata": {},
  373. "output_type": "display_data"
  374. },
  375. {
  376. "data": {
  377. "text/latex": [
  378. "$$\\int x^{3}dx = \\frac{x^{4}}{4}$$"
  379. ],
  380. "text/plain": [
  381. "<IPython.core.display.Math object>"
  382. ]
  383. },
  384. "metadata": {},
  385. "output_type": "display_data"
  386. },
  387. {
  388. "data": {
  389. "text/latex": [
  390. "$$\\int x^{4}dx = \\frac{x^{5}}{5}$$"
  391. ],
  392. "text/plain": [
  393. "<IPython.core.display.Math object>"
  394. ]
  395. },
  396. "metadata": {},
  397. "output_type": "display_data"
  398. }
  399. ],
  400. "source": [
  401. "for i in range(5):\n",
  402. " f = x**i \n",
  403. " F = sympy.integrate(f,x)\n",
  404. " display(Math(r'\\int x^{%d}dx = %s' % (i,sympy.latex(F))))"
  405. ]
  406. },
  407. {
  408. "cell_type": "code",
  409. "execution_count": 18,
  410. "metadata": {},
  411. "outputs": [
  412. {
  413. "data": {
  414. "text/plain": [
  415. "'\\\\left[\\\\begin{matrix}1 & 2\\\\\\\\3 & 4\\\\end{matrix}\\\\right]'"
  416. ]
  417. },
  418. "metadata": {},
  419. "output_type": "display_data"
  420. },
  421. {
  422. "data": {
  423. "image/png": "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\n",
  424. "text/latex": [
  425. "$$\\left[\\begin{matrix}1 & 2\\\\3 & 4\\end{matrix}\\right]$$"
  426. ],
  427. "text/plain": [
  428. "⎡1 2⎤\n",
  429. "⎢ ⎥\n",
  430. "⎣3 4⎦"
  431. ]
  432. },
  433. "metadata": {},
  434. "output_type": "display_data"
  435. }
  436. ],
  437. "source": [
  438. "A = sympy.Matrix([[1,2],[3,4]])\n",
  439. "display(sympy.latex(A))\n",
  440. "display(A)"
  441. ]
  442. },
  443. {
  444. "cell_type": "code",
  445. "execution_count": 19,
  446. "metadata": {},
  447. "outputs": [
  448. {
  449. "data": {
  450. "text/latex": [
  451. "$$A^{0} = \\left[\\begin{matrix}1 & 0\\\\0 & 1\\end{matrix}\\right]$$"
  452. ],
  453. "text/plain": [
  454. "<IPython.core.display.Math object>"
  455. ]
  456. },
  457. "metadata": {},
  458. "output_type": "display_data"
  459. },
  460. {
  461. "data": {
  462. "text/latex": [
  463. "$$A^{1} = \\left[\\begin{matrix}1 & 2\\\\3 & 4\\end{matrix}\\right]$$"
  464. ],
  465. "text/plain": [
  466. "<IPython.core.display.Math object>"
  467. ]
  468. },
  469. "metadata": {},
  470. "output_type": "display_data"
  471. },
  472. {
  473. "data": {
  474. "text/latex": [
  475. "$$A^{2} = \\left[\\begin{matrix}7 & 10\\\\15 & 22\\end{matrix}\\right]$$"
  476. ],
  477. "text/plain": [
  478. "<IPython.core.display.Math object>"
  479. ]
  480. },
  481. "metadata": {},
  482. "output_type": "display_data"
  483. },
  484. {
  485. "data": {
  486. "text/latex": [
  487. "$$A^{3} = \\left[\\begin{matrix}37 & 54\\\\81 & 118\\end{matrix}\\right]$$"
  488. ],
  489. "text/plain": [
  490. "<IPython.core.display.Math object>"
  491. ]
  492. },
  493. "metadata": {},
  494. "output_type": "display_data"
  495. },
  496. {
  497. "data": {
  498. "text/latex": [
  499. "$$A^{4} = \\left[\\begin{matrix}199 & 290\\\\435 & 634\\end{matrix}\\right]$$"
  500. ],
  501. "text/plain": [
  502. "<IPython.core.display.Math object>"
  503. ]
  504. },
  505. "metadata": {},
  506. "output_type": "display_data"
  507. }
  508. ],
  509. "source": [
  510. "for i in range(5):\n",
  511. " display(Math(r'A^{%d} = %s' % (i,sympy.latex(A**i))))"
  512. ]
  513. },
  514. {
  515. "cell_type": "code",
  516. "execution_count": null,
  517. "metadata": {},
  518. "outputs": [],
  519. "source": []
  520. }
  521. ],
  522. "metadata": {
  523. "kernelspec": {
  524. "display_name": "Python 3",
  525. "language": "python",
  526. "name": "python3"
  527. },
  528. "language_info": {
  529. "codemirror_mode": {
  530. "name": "ipython",
  531. "version": 3
  532. },
  533. "file_extension": ".py",
  534. "mimetype": "text/x-python",
  535. "name": "python",
  536. "nbconvert_exporter": "python",
  537. "pygments_lexer": "ipython3",
  538. "version": "3.6.7"
  539. }
  540. },
  541. "nbformat": 4,
  542. "nbformat_minor": 2
  543. }
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