Computing from LaTeX: automated numerical computing from LaTeX expressions

We present CfL (Computing from LaTeX), a software tool that allows the user to automatically perform numerical computation without any programming activity. The user has just to express his computational problem in the usual mathematical language found in written books, and to typeset it using \latex for a well-formatted printout. CfL is designed so that it parses a LaTeX document to recognize well-defined computational problems. An executable Python script is then automatically generated so that mathematical objects are encoded as Python data objects, and the script's logic reflects an appropriate numerical solution pattern for the recognized computational problem. The results of the numerical computations can also be automatically inserted in a resulting LaTeX document so to be displayed by means of tables and graphics. Therefore, CfL is a numerical problem-solving environment that converts the specification of a mathematical problem into an appropriate resolution pattern that can be directly executed. The use of high-level mathematical abstractions, the familiar LaTeX typesetting and the automated code generation are key design choices that provide ease-of-use and explorative computation, with a negligible overhead