Magma Math makes math learning more engaging, visible, and interactive by enabling students to show their work and by giving educators real-time insights into student thinking. Instead of focusing only on final answers, Magma highlights the process, helps students build good habits, and allows teachers to understand how students arrived at their solutions. This leads to deeper learning and more meaningful classroom interaction.

    https://www.magmamath.com/

Macaulay2 is a software system devoted to supporting research in algebraic geometry and commutative algebra, whose creation has been funded by the National Science Foundation since 1992.
Macaulay2 includes core algorithms for computing Gröbner bases and graded or multi-gradedfree resolutions of modules over quotient rings of graded or multi-graded polynomial rings with a monomial ordering. The core algorithms are accessible through a versatile high level interpreted user language with a powerful debugger supporting the creation of new classes of mathematical objects and the installation of methods for computing specifically with them. Macaulay2 can compute Betti numbers, Ext, cohomology of coherent sheaves on projective varieties, primary decomposition of ideals, integral closure of rings, and more.
            https://macaulay2.com/

Singular is an open-source computer algebra system for polynomial computations.
      https://www.singular.uni-kl.de/

SageMath 
Sagemath is free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more. Access their combined power through a common, Python-based language or directly via interfaces or wrappers.
        https://www.sagemath.org/

Polymake is open source software for research in polyhedral geometry. It deals with polytopes, polyhedra and fans as well as simplicial complexes, matroids, graphs, tropical hypersurfaces, and other objects. Supported platforms include various flavors of Linux, FreeBSD and Mac OS.
      https://polymake.org/doku.php/

4ti2 team. 4ti2 -- A software package for algebraic, geometric and combinatorial problems on linear spaces. Available at https://4ti2.github.io.

         https://4ti2.github.io/

LattE (Lattice point Enumeration) is a computer software dedicated to the problems of counting lattice points and integration inside convex polytopes. LattE contains the first ever implementation of Barvinok's algorithm. The LattE macchiato version (by M. Köppe) incorporated fundamental improvements and speed ups.
      https://www.math.ucdavis.edu/

LaHE or CLAHE in a math, data science, or image processing context, it is almost certainly a typo for CLAHE (Contrast Limited Adaptive Histogram Equalization).

In mathematics and data science, DIPHA stands for Distributed Persistent Homology Algorithm. It is an open-source, high-performance C++ software package used in Topological Data Analysis (TDA).

In mathematics, PHAT can refer to two entirely different concepts depending on your field of study: an advanced open-source software library used in computational geometry or a fundamental notation used in introductory statistics.

AUTO-07P is a widely used, open-source mathematical software package designed for numerical continuation and bifurcation problems in dynamical systems.

XPPAUT is a free, open-source mathematical software tool used for simulating, analyzing, and animating dynamical systems. Developed by mathematician G. Bard Ermentrout at the University of Pittsburgh, it serves as a lightweight power-tool for solving complex differential equations and plotting behaviors over time.

In advanced applied mathematics, Perseus stands for Persistent Homology Software. It is a command-line C++ application created by Vidit Nanda at the University of Oxford used in Topological Data Analysis (TDA).
In computational math and statistical data science, Stan (named after mathematician Stanislaw Ulam) refers to a powerful platform for Bayesian inference. At its core lies the Stan Math Library, an open-source C++ template library explicitly engineered for automatic differentiation (AD).

PyMC (frequently misspelled as Py Mc) is a popular, open-source Python library used for Bayesian statistical modeling and probabilistic machine learning.

It allows data scientists, mathematicians, and engineers to build complex statistical models using intuitive Python code, and then find solutions using advanced mathematical sampling algorithms.

OR-Tools (Operations Research Tools) is an open-source, fast, and highly customizable software suite developed by Google for solving complex optimization problems in mathematics and computer science.

Z3 (also known as the Z3 Theorem Prover) is a state-of-the-art, open-source mathematical solver developed by Microsoft Research. It is a specialized tool used to solve SMT (Satisfiability Modulo Theories) problems.

PARI/GP is a highly specialized, open-source computer algebra system designed specifically for fast computations in number theory.

fpLLL is a highly optimized, open-source C++ library used to solve advanced problems in Euclidean lattice geometry.