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Updated recipes from chapter 15.
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‎notebooks/chapter15_symbolic/02_solvers.ipynb

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"> This is one of the 100 recipes of the [IPython Cookbook](http://ipython-books.github.io/), the definitive guide to high-performance scientific computing and data science in Python.\n"
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"# 15.2. Solving equations and inequalities"
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"input": [
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"from sympy import *\n",
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"init_printing(pretty_print=False)"
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"from sympy import *\n",
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"init_printing()"
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"var('x y z a')"
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"Use the function solve to resolve equations (the right hand side is always 0)."
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"input": [
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"solve(x**2 - a, x)"
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"You can also solve inequations. You may need to specify the domain of your variables. Here, we tell SymPy that x is a real variable."
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"input": [
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"x = Symbol('x')\n",
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"x = Symbol('x')\n",
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"solve_univariate_inequality(x**2 > 4, x)"
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],
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"source": [
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"## Systems of equations"
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]
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"This function also accepts systems of equations (here a linear system)."
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"input": [
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"solve([x + 2*y + 1, x - 3*y - 2], x, y)"
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"Non-linear systems are also supported."
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"solve([x**2 + y**2 - 1, x**2 - y**2 - S(1)/2], x, y)"
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],
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"source": [
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"Singular linear systems can also be solved (here, there are infinitely many equations because the two equations are colinear)."
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"input": [
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"solve([x + 2*y + 1, -x - 2*y - 1], x, y)"
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"Now, let's solve a linear system using matrices with symbolic variables."
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"var('a b c d u v')"
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],
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"We create the augmented matrix, which is the horizontal concatenation of the system's matrix with the linear coefficients, and the right-hand side vector."
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"M = Matrix([[a, b, u], [c, d, v]]); M"
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"solve_linear_system(M, x, y)"
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"This system needs to be non-singular to have a unique solution, which is equivalent to say that the determinant of the system's matrix needs to be non-zero (otherwise the denominators in the fractions above are equal to zero)."
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"det(M[:2,:2])"
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"> You'll find all the explanations, figures, references, and much more in the book (to be released later this summer).\n\n> [IPython Cookbook](http://ipython-books.github.io/), by [Cyrille Rossant](http://cyrille.rossant.net), Packt Publishing, 2014 (400 pages). [Get a 50% discount by pre-ordering now](http://www.packtpub.com/ipython-interactive-computing-and-visualization-cookbook/book) with the code `mK00gPxQM` (time-limited offer)!\n"
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"> You'll find all the explanations, figures, references, and much more in the book (to be released later this summer).\n",
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"\n",
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"> [IPython Cookbook](http://ipython-books.github.io/), by [Cyrille Rossant](http://cyrille.rossant.net), Packt Publishing, 2014 (400 pages). [Get a 50% discount by pre-ordering now](http://www.packtpub.com/ipython-interactive-computing-and-visualization-cookbook/book) with the code `mK00gPxQM` (time-limited offer)!\n"
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