sympy intro
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# slice 2
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## what we learns
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there are a lot of ways you can iteratively find roots if math cant do it easily
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also its the way your calculator find roots of functions
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## legitimate problems
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it seems like something like pylance cant hold up against super complex gigantic modules like scipy, numpy or sympy.
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also then they dont type hint their functions? or they do? but whatever the fuck
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# i still hate this so much\n",
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"\n",
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"i kinda never liked the syms thing from matlab, probably because i dont understand!!!!\n",
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"\n",
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"why do some fns declare like a variable, but some others you have to `[o] = function(i) end` ???? \n",
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"AND THEN WTF IS @(x)?????????\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## here is an explanation.\n",
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"\n",
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"imagine this. you import sympy:\n"
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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": null,
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"metadata": {
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"vscode": {
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"languageId": "shellscript"
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}
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},
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"outputs": [],
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"source": [
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"pip install sympy"
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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": 2,
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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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"import numpy"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"sympy provides a Symbol class:\n"
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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": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"x_lda = sympy.Symbol(\"x\")\n",
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"y_lda = sympy.Symbol(\"y\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"now here is funny: what you just made are symbols. it has proper `__magic__` functions that do things different than a number. check this out:\n"
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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": 7,
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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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"$\\displaystyle x^{3} - x - 2$"
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],
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"text/plain": [
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"x**3 - x - 2"
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]
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},
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"execution_count": 7,
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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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"f_lda = x_lda**3 - x_lda - 2\n",
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"f_lda"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"fancy ass renders from jupyter aside, this thing is now a sympy something construct. it is NOT a function. it is a variable. it is... certainly something.\n",
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"\n",
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"### symbolic computation\n",
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"\n",
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"[sympy tutorial][st] explains: [mathematical expressions with unevaluated variables are left in symbolic form.][expl]\n",
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"\n",
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"i explain: you do math on paper: you dont write the decimal number out, you just write the final answer as $\\frac{\\sqrt 3 + 1}{2}$\n",
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"\n",
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"so the sympy does the same: it writes that instead of idfk `1.3660254038`\n",
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"\n",
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"[st]: https://docs.sympy.org/latest/tutorials/intro-tutorial/intro.html\n",
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"[expl]: https://docs.sympy.org/latest/tutorials/intro-tutorial/intro.html#:~:text=mathematical%20expressions%20with%20unevaluated%20variables%20are%20left%20in%20symbolic%20form.\n"
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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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"$\\displaystyle \\frac{1 + \\sqrt{3}}{2}$"
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],
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"text/plain": [
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"(1 + sqrt(3))/2"
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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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"root_idk = sympy.factor((sympy.sqrt(3) + 1) / 2)\n",
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"\n",
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"numpy.testing.assert_approx_equal(root_idk.evalf(), (3**0.5 + 1) / 2) # passes!\n",
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"root_idk"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"you see in mat lab they pass this kinda sympy symbolic ahh structure Literally everywhere. i fear that. that is why i dont like this.\n",
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"\n",
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"from [matlab]:\n",
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"\n",
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"[matlab]: https://www.mathworks.com/help/symbolic/create-symbolic-numbers-variables-and-expressions.html#:~:text=Solve%20the%20quadratic,f%20%3D%3D%200%2Cx\n",
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"\n",
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"> Solve the quadratic equation f=0 for x by using solve.\n",
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">\n",
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"> ```matlab\n",
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"> x_0 = solve(f == 0,x)\n",
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"> ```\n",
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"\n",
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"well you can do that with sympy too:\n"
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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": 21,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(-1/2 - sqrt(3)*I/2)*(sqrt(78)/9 + 1)**(1/3) + 1/(3*(-1/2 - sqrt(3)*I/2)*(sqrt(78)/9 + 1)**(1/3)) -0.760689853402284 - 0.857873626595179*I\n",
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"1/(3*(-1/2 + sqrt(3)*I/2)*(sqrt(78)/9 + 1)**(1/3)) + (-1/2 + sqrt(3)*I/2)*(sqrt(78)/9 + 1)**(1/3) -0.760689853402284 + 0.857873626595179*I\n",
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"1/(3*(sqrt(78)/9 + 1)**(1/3)) + (sqrt(78)/9 + 1)**(1/3) 1.52137970680457\n"
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]
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}
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],
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"source": [
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"for i in sympy.solve(f_lda):\n",
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" print(i, i.evalf())"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"god damn\n",
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"\n",
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"### no need (sometimes)\n",
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"\n",
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"well thats cool and all if the thing doesnt start to rely on numerical solves: check [this][ssp] out\n",
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"\n",
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"[ssp]: https://docs.sympy.org/latest/modules/solvers/solvers.html#sympy.solvers.solvers.solve:~:text=Currently%20supported%3A\n",
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"\n",
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"and then when that happen youd rather:\n"
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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": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"try:\n",
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" import scipy.optimize\n",
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"except:\n",
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" # %pip install scipy\n",
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" get_ipython().run_line_magic('pip', 'install scipy') # prev line resolves to this so i use # why is pylance ass\n",
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" import scipy.optimize"
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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": 3,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"np.float64(1.5213797068045676)"
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]
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},
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"execution_count": 3,
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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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"f_lda_py = lambda x: x**3 - x - 2\n",
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"scipy_res = scipy.optimize.root(f_lda_py, 1)\n",
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"scipy_res.x[0] # so much notation to extract the one real root lmfao"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"look: just make a python function? and use an nsolve if you plan to use nsolve anyway? why bother yourself with symbols when you never cares about symbols in your answer?\n",
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"\n",
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"what if i never had a chance to get a concrete answer like this: $\\frac{1}{3\\left(\\frac{\\sqrt{78}}{9} + 1\\right)^{\\frac{1}{3}}} + \\left(\\frac{\\sqrt{78}}{9} + 1\\right)^{\\frac{1}{3}}$? and i dont want to see such shitass anyway. \n",
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"a number like this: `1.5213797068045676` works way better\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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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": "3.12.5"
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}
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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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