The primary "symbols" library in Python is SymPy, which is used for symbolic mathematics. There is also the built-in symtable module for accessing compiler symbol tables, and the symbolic library used for working with debug symbol files.

SymPy: Symbolic Mathematics

SymPy is an open-source Python library that functions as a full-featured computer algebra system (CAS). Unlike numerical libraries (like NumPy) which deal with approximate floating-point numbers, SymPy performs computations with mathematical expressions in their exact, symbolic form.

Key features of the SymPy library include:

Defining Symbols: Variables are explicitly declared as symbols using sympy.Symbol() or sympy.symbols() to represent mathematical variables like 'x' or 'y'.

Algebraic Manipulations: It can simplify or expand complex algebraic expressions, perform factoring, and work with rational numbers.

Calculus: Users can perform operations such as computing limits, derivatives, and indefinite or definite integrals.

Equation Solving: The library can solve algebraic, transcendental, and differential equations, returning exact solutions.

Linear Algebra: SymPy provides functionality for creating and manipulating matrices with symbolic entries.

Other "Symbol" Related Libraries

symtable: This is a module within the Python standard library that provides an interface to examine the compiler's symbol tables, which are generated internally by the Python interpreter to manage variable scopes.

symbolic: This is a separate library available on the Python Package Index (PyPI) specifically for dealing with debug symbol files (e.g., from software compilation), a highly specialized use case unrelated to mathematics.

symbol (deprecated standard library module): There was an older standard library module named symbol which contained constants used with Python parse trees. This module is deprecated and will be removed in future Python versions.