Page - 113 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

5.4 MakingOurOwnModule 113 package is that the results cannot automatically be imported into your code and used for further analysis. On the other hand, WolframAlpha has the advantage that it displays many additional mathematical results related to the given problem. For example, if we type 2x + 3x - y in WolframAlpha, it not only simplifies the expression to 5x - y, but it also makes plots of the functionf(x,y) = 5x−y, solves the equation5x−y= 0, and calculates the integral∫ ∫(5x+y)dxdy.The commercial Pro version also offers a step-by-step demonstration of the analytical computationsthatsolvetheproblem.Youareencouragedtotryout thesecommands inWolframAlpha: • diff(x^2, x)ordiff(x**2, x) • integrate(cos(x), x) • simplify((x**2 + x**3)/x**2) • limit(sin(x)/x, x, 0) • solve(5*x - 15, x) WolframAlpha is very flexible with respect to syntax. In fact, WolframAlpha will use your input to guess what you want it to do! Depending on what you write, it may be more or less easy to do that guess, of course. However, in WolframAlpha’s response, you are also told how your input was interpreted, so that you may adjust your input ina second try. Another impressive tool for symbolic computations is Sage,6 which is a very comprehensive package with the aim of “creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab”. Sage is implemented in Python. Projects with extensive symbolic computations will certainly benefit from exploringSage. 5.4 MakingOurOwnModule As we knowby now,Pythonhasa hugecollectionof usefulmodulesand packages written by clever people. This far, we have experienced how these libraries (math, numpy,matplotlib,etc.)couldsimplifyourownprogramming,makingreadyand professionalcodeavailable throughsimpleimportstatements.This isverygood,but itgetsevenbetter,sinceit isstraightforward(whetherweareprogrammingnewbies ornot) toalso createmodulescontainingourowncode. What is a module then, really? The truth is, that we may regard any of the Python scripts we have presented in this book as a module! In fact, any text file withextension.py thatcontainsPythoncodewrittenwitha texteditor, isamodule. If the file name ismy_module.py, then the module name ismy_module. Up until now, we have written.pyfiles for execution as programs. To design and use such filesasmodulefiles, however, therearea few thingswe bettergetconsciousabout. Tobringacross theessentialpoints,wewilldevelopourownlittledemonstration module for vertical motion, named vertical_motion (surprising!). The motion is of the kind we have addressed also previously in this book, i.e., a special case of projectile motion, in which an object starts out with some vertical velocity, and 6 http://sagemath.org/.