Yes in pure Mathematics this exist.

Hello! For group theory, there's the free software GAP: https://www.gap-system.org/

There are several specialized software programs and computer algebra systems (CAS) that are commonly used for various mathematical tasks. These software programs provide tools and functionalities to perform computations, symbolic manipulations, visualizations, and explorations in different areas of pure mathematics. Here are some notable examples:

1. Mathematica: Mathematica is a powerful and widely used CAS developed by Wolfram Research. It provides a comprehensive range of mathematical functions and algorithms for symbolic and numerical computations, as well as visualization capabilities. Mathematica covers a broad spectrum of pure mathematics topics, including algebra, calculus, number theory, geometry, graph theory, and more.

2. MATLAB: MATLAB is a popular numerical computing environment that offers extensive mathematical functionality. While it is primarily focused on numerical analysis and scientific computing, it also includes symbolic computation capabilities through the Symbolic Math Toolbox. MATLAB is commonly used in various branches of pure mathematics, such as linear algebra, optimization, differential equations, and numerical analysis.

3. Maple: Maple is a versatile CAS developed by Maplesoft. It provides a rich set of mathematical tools for symbolic computation, numerical analysis, and visualization. Maple supports a wide range of mathematical areas, including algebra, calculus, differential equations, number theory, and combinatorics. It also offers specialized packages for specific mathematical disciplines.

4. SageMath: SageMath is an open-source mathematical software system that integrates various open-source mathematical software packages. It combines the functionality of multiple CAS and programming languages, including Python, to provide extensive mathematical capabilities. SageMath covers a wide range of pure mathematics topics and is actively developed and maintained by a community of mathematicians and developers.

5. Coq: Coq is an interactive proof assistant and formal verification tool. It is used in the field of mathematical logic and formalized mathematics. Coq allows users to construct formal proofs, verify mathematical theorems, and perform automated theorem proving. It is particularly useful for formalizing mathematical theories and conducting rigorous formal reasoning.

6. LaTeX: Although not a software program per se, LaTeX is a widely used typesetting system for mathematical documents. It provides a powerful and flexible way to write and format mathematical equations, symbols, and structures. LaTeX is extensively used in academia for writing research papers, theses, and books in pure mathematics.

Software programs commonly used in pure mathematics are mentioned above. Depending on the specific area of mathematics and the tasks at hand, there may be other specialized software tools available as well. It's important to explore and select the software that best suits your needs and aligns with the specific requirements of your mathematical research or exploration.

Good luck

credit AI tools

For universal algebra you can search the software by writing jre-6-windows-i586 for UA

GAP (Group theory, algebras, and representation theory)

Sage (algebra, combinatorics, graph theory number theory and lots more)