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1 | 1 | { |
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2 | 2 | "metadata": { |
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3 |
"name": " |
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3 | "name": "", | |
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4 | "signature": "sha256:c357b93e9480d6347c6677862bf43750745cef4b30129c5bc53cb879a19d4074" | |
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4 | 5 | }, |
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5 | 6 | "nbformat": 3, |
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6 | 7 | "nbformat_minor": 0, |
@@ -79,6 +80,7 b'' | |||
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79 | 80 | "metadata": {}, |
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80 | 81 | "outputs": [ |
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81 | 82 | { |
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83 | "metadata": {}, | |
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82 | 84 | "output_type": "pyout", |
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83 | 85 | "prompt_number": 3, |
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84 | 86 | "text": [ |
@@ -126,6 +128,7 b'' | |||
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126 | 128 | "metadata": {}, |
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127 | 129 | "outputs": [ |
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128 | 130 | { |
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131 | "metadata": {}, | |
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129 | 132 | "output_type": "pyout", |
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130 | 133 | "prompt_number": 5, |
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131 | 134 | "text": [ |
@@ -161,12 +164,12 b'' | |||
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161 | 164 | "from libc.math cimport exp, sqrt, pow, log, erf\n", |
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162 | 165 | "\n", |
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163 | 166 | "@cython.cdivision(True)\n", |
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164 | "cdef double std_norm_cdf(double x) nogil:\n", | |
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167 | "cdef double std_norm_cdf_cy(double x) nogil:\n", | |
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165 | 168 | " return 0.5*(1+erf(x/sqrt(2.0)))\n", |
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166 | 169 | "\n", |
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167 | 170 | "@cython.cdivision(True)\n", |
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168 | "def black_scholes(double s, double k, double t, double v,\n", | |
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169 | " double rf, double div, double cp):\n", | |
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171 | "def black_scholes_cy(double s, double k, double t, double v,\n", | |
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172 | " double rf, double div, double cp):\n", | |
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170 | 173 | " \"\"\"Price an option using the Black-Scholes model.\n", |
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171 | 174 | " \n", |
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172 | 175 | " s : initial stock price\n", |
@@ -181,8 +184,8 b'' | |||
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181 | 184 | " with nogil:\n", |
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182 | 185 | " d1 = (log(s/k)+(rf-div+0.5*pow(v,2))*t)/(v*sqrt(t))\n", |
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183 | 186 | " d2 = d1 - v*sqrt(t)\n", |
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184 | " optprice = cp*s*exp(-div*t)*std_norm_cdf(cp*d1) - \\\n", | |
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185 | " cp*k*exp(-rf*t)*std_norm_cdf(cp*d2)\n", | |
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187 | " optprice = cp*s*exp(-div*t)*std_norm_cdf_cy(cp*d1) - \\\n", | |
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188 | " cp*k*exp(-rf*t)*std_norm_cdf_cy(cp*d2)\n", | |
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186 | 189 | " return optprice" |
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187 | 190 | ], |
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188 | 191 | "language": "python", |
@@ -194,12 +197,13 b'' | |||
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194 | 197 | "cell_type": "code", |
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195 | 198 | "collapsed": false, |
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196 | 199 | "input": [ |
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197 | "black_scholes(100.0, 100.0, 1.0, 0.3, 0.03, 0.0, -1)" | |
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200 | "black_scholes_cy(100.0, 100.0, 1.0, 0.3, 0.03, 0.0, -1)" | |
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198 | 201 | ], |
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199 | 202 | "language": "python", |
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200 | 203 | "metadata": {}, |
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201 | 204 | "outputs": [ |
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202 | 205 | { |
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206 | "metadata": {}, | |
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203 | 207 | "output_type": "pyout", |
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204 | 208 | "prompt_number": 7, |
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205 | 209 | "text": [ |
@@ -210,10 +214,75 b'' | |||
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210 | 214 | "prompt_number": 7 |
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211 | 215 | }, |
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212 | 216 | { |
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217 | "cell_type": "markdown", | |
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218 | "metadata": {}, | |
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219 | "source": [ | |
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220 | "For comparison, the same code is implemented here in pure python." | |
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221 | ] | |
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222 | }, | |
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223 | { | |
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224 | "cell_type": "code", | |
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225 | "collapsed": false, | |
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226 | "input": [ | |
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227 | "from math import exp, sqrt, pow, log, erf\n", | |
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228 | "\n", | |
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229 | "def std_norm_cdf_py(x):\n", | |
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230 | " return 0.5*(1+erf(x/sqrt(2.0)))\n", | |
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231 | "\n", | |
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232 | "def black_scholes_py(s, k, t, v, rf, div, cp):\n", | |
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233 | " \"\"\"Price an option using the Black-Scholes model.\n", | |
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234 | " \n", | |
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235 | " s : initial stock price\n", | |
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236 | " k : strike price\n", | |
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237 | " t : expiration time\n", | |
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238 | " v : volatility\n", | |
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239 | " rf : risk-free rate\n", | |
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240 | " div : dividend\n", | |
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241 | " cp : +1/-1 for call/put\n", | |
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242 | " \"\"\"\n", | |
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243 | " d1 = (log(s/k)+(rf-div+0.5*pow(v,2))*t)/(v*sqrt(t))\n", | |
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244 | " d2 = d1 - v*sqrt(t)\n", | |
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245 | " optprice = cp*s*exp(-div*t)*std_norm_cdf_py(cp*d1) - \\\n", | |
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246 | " cp*k*exp(-rf*t)*std_norm_cdf_py(cp*d2)\n", | |
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247 | " return optprice" | |
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248 | ], | |
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249 | "language": "python", | |
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250 | "metadata": {}, | |
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251 | "outputs": [], | |
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252 | "prompt_number": 8 | |
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253 | }, | |
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254 | { | |
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213 | 255 | "cell_type": "code", |
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214 | 256 | "collapsed": false, |
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215 | 257 | "input": [ |
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216 |
" |
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258 | "black_scholes_py(100.0, 100.0, 1.0, 0.3, 0.03, 0.0, -1)" | |
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259 | ], | |
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260 | "language": "python", | |
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261 | "metadata": {}, | |
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262 | "outputs": [ | |
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263 | { | |
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264 | "metadata": {}, | |
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265 | "output_type": "pyout", | |
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266 | "prompt_number": 9, | |
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267 | "text": [ | |
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268 | "10.327861752731728" | |
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269 | ] | |
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270 | } | |
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271 | ], | |
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272 | "prompt_number": 9 | |
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273 | }, | |
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274 | { | |
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275 | "cell_type": "markdown", | |
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276 | "metadata": {}, | |
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277 | "source": [ | |
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278 | "Below we see the runtime of the two functions: the Cython version is nearly a factor of 10 faster." | |
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279 | ] | |
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280 | }, | |
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281 | { | |
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282 | "cell_type": "code", | |
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283 | "collapsed": false, | |
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284 | "input": [ | |
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285 | "%timeit black_scholes_cy(100.0, 100.0, 1.0, 0.3, 0.03, 0.0, -1)" | |
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217 | 286 | ], |
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218 | 287 | "language": "python", |
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219 | 288 | "metadata": {}, |
@@ -222,11 +291,30 b'' | |||
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222 | 291 | "output_type": "stream", |
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223 | 292 | "stream": "stdout", |
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224 | 293 | "text": [ |
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225 |
"1000000 loops, best of 3: |
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294 | "1000000 loops, best of 3: 319 ns per loop\n" | |
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226 | 295 | ] |
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227 | 296 | } |
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228 | 297 | ], |
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229 |
"prompt_number": |
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298 | "prompt_number": 10 | |
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299 | }, | |
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300 | { | |
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301 | "cell_type": "code", | |
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302 | "collapsed": false, | |
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303 | "input": [ | |
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304 | "%timeit black_scholes_py(100.0, 100.0, 1.0, 0.3, 0.03, 0.0, -1)" | |
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305 | ], | |
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306 | "language": "python", | |
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307 | "metadata": {}, | |
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308 | "outputs": [ | |
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309 | { | |
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310 | "output_type": "stream", | |
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311 | "stream": "stdout", | |
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312 | "text": [ | |
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313 | "100000 loops, best of 3: 2.28 \u00b5s per loop\n" | |
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314 | ] | |
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315 | } | |
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316 | ], | |
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317 | "prompt_number": 11 | |
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230 | 318 | }, |
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231 | 319 | { |
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232 | 320 | "cell_type": "heading", |
@@ -262,7 +350,7 b'' | |||
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262 | 350 | ] |
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263 | 351 | } |
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264 | 352 | ], |
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265 |
"prompt_number": |
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353 | "prompt_number": 12 | |
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266 | 354 | }, |
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267 | 355 | { |
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268 | 356 | "cell_type": "markdown", |
@@ -275,4 +363,4 b'' | |||
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275 | 363 | "metadata": {} |
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276 | 364 | } |
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277 | 365 | ] |
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278 | } | |
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366 | } No newline at end of file |
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