Скачать или смотреть Mastering SymPy: A Guide to Defining Functions and Symbols in Python

Learn how to replace functions in SymPy using expressions and understand how to define complex functions like `g = x + y*h`.
---
This video is based on the question https://stackoverflow.com/q/69399155/ asked by the user 'Wapiti' ( https://stackoverflow.com/u/2030696/ ) and on the answer https://stackoverflow.com/a/69399467/ provided by the user 'Oscar Benjamin' ( https://stackoverflow.com/u/9450991/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions.

Visit these links for original content and any more details, such as alternate solutions, latest updates/developments on topic, comments, revision history etc. For example, the original title of the Question was: Defining functions of symbols and other functions in sympy

Also, Content (except music) licensed under CC BY-SA https://meta.stackexchange.com/help/l...
The original Question post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/... ) license, and the original Answer post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/... ) license.

If anything seems off to you, please feel free to write me at vlogize [AT] gmail [DOT] com.
---
Mastering SymPy: A Guide to Defining Functions and Symbols in Python

SymPy is a Python library for symbolic mathematics that allows users to work with algebraic expressions and equations symbolically. One common task when using SymPy is defining functions and substituting them within expressions. In this guide, we will explore how to manage this through a practical example to better your understanding of functions and symbols in SymPy.

The Problem

You've defined a function f in SymPy, but you want to replace it with another function g that is built using symbols and other functions. Here’s a scenario to illustrate the issue:

You have an expression like:

[[See Video to Reveal this Text or Code Snippet]]

And now, you want to substitute f with a new function g, defined as:

[[See Video to Reveal this Text or Code Snippet]]

where both x and y are symbols, and h is another function. However, you encounter an error when attempting to define g like this:

[[See Video to Reveal this Text or Code Snippet]]

Understanding the Solution

To resolve this, let's first clarify how functions are treated in SymPy and how we can properly define them. Here’s a step-by-step breakdown of the solution:

1. Define Your Symbols and Functions

Begin by importing the required module and defining your symbols:

[[See Video to Reveal this Text or Code Snippet]]

2. Create a Function

Instead of attempting to multiply a Symbol with an UndefinedFunction, you should instantiate the function using the Function class or Lambda. Here’s how you can do it correctly:

Define f:

[[See Video to Reveal this Text or Code Snippet]]

Create an Expression:

[[See Video to Reveal this Text or Code Snippet]]

Look at the Expression:

[[See Video to Reveal this Text or Code Snippet]]

3. Define Another Function Using Lambda

When defining g, use the Lambda class, which allows you to define a function that can take a symbol:

[[See Video to Reveal this Text or Code Snippet]]

4. Substitute Functions in Your Expression

Once g is defined correctly, you can substitute f in expr with g easily:

[[See Video to Reveal this Text or Code Snippet]]

5. Check the Results

Here’s how you’d evaluate the substitution:

[[See Video to Reveal this Text or Code Snippet]]

Final Thoughts

In conclusion, when working with functions in SymPy, always ensure you're defining and substituting them correctly. Instead of trying to multiply undefined functions directly with symbols, utilize classes like Function and Lambda. This helps you avoid type errors, streamlining algebraic manipulations effectively.

With these concepts, you should now feel more confident in defining and substituting functions in SymPy, paving the way for more complex symbolic computations. Happy coding, and enjoy your journey with SymPy!