Mathematics is a part of theoretical science that deals with number, space, quality or other abstract concepts. Mathematics deals with counting, measurement, calculation along with methodical study of shapes and sizes. In solving mathematical numerical, various hindrances are faced while formulating the results.

Thus, scientist and the programmers have researched and developed various programming languages for solving mathematical numerical more appropriately. They have also attempted to make the process of solving the mathematical numerical intriguing.

Therefore, it is important to acquire proper information on the best programming languages for mathematics. They are as follows: MATLAB programming

The Matrix Laboratory (MATLAB) is a fourth-generation programming language that is used for numerical purpose of computation. It was primitively written in order to provide convenient access to the matrix was developed by LINPACK and EISPACK projects. They are the representatives of the state-of-the-art in software for computation of matrix. Developed by Math Work, this programming integrates visualization, integration along with an easy to use environment. This easy to use environment includes the process of expressing problems and solutions in mathematical notation.

**The authentic uses of MATLAB are the following**:

- Engineering and scientific graphics
- Development of algorithm
- Prototyping, modelling and simulation
- Visualization, data analysis, and explorationIn MATLAB, the variables are represented in the form of array those are used for indexing. A matrix is a part of linear algebra that is represented in a two-dimensional array. In MATLAB workspace the variables are either created or imported from other programs or data files. This program also allows the plotting of 2-d and 3-d graphics functions to envisage results. The functionality of MATLAB can be expanded by the addition of toolboxes that improvise the functionality. It is a high-level array language or matrix, which comprises of flow statements, structures, data; object-oriented programming features along with input and outputs. It is also an immense assemblage of computational algorithms, which ranges from complex arthimatics to trigonometric functions like sine, cos, tan, etc.

**GNU Octave**

The GNU Octave is an improved level software programming language that is framed to solve numeric computation. This programming is used in solving the linear and nonlinear numerical. This is one of the languages that are compatible with MATLAB and thus allows performing various numerical experiments. This is free software since it is under the terms of the GNU General Public License. Furthermore, this mathematical programming language can be utilised in the updated version of Windows, BSD, Mac operating system, Linux and others. This programming might also have prevalence as a batch-oriented language.

The GNU Octave can be used to perform elementary calculations like arithmetic operation, exponential, a trigonometric function and others. This is also used to create matrix and vectors. For example, Octave uses space or comma to spate the entries, and if the command is ended with a semicolon, it operates Octave not to derive the result but rather move to the next row for further calculation. This programming language is used to solve complex differential equations, integration and other high-level mathematics. It is to be noted that, the current version of Octave helps in the execution of graphical user interface (GUI). It hosts Integrated Development Environment (IDE), which comprises of a code editor, along with syntax highl;ighting. It also contains an inbuilt debugger, browser for documentation.

**Sage Math**

The System for Algebra and Geometry experimentation (SAGE) math is the primary software that is used to solve numerical related to algebra, calculus, combinatorics and others. The first version of this mathematical programming was developed under the terms of the GNU General Public License. Their initial goal was to create an open source alternative to programmes like MATLAB, Mathematica, Maple and Magma. The programming uses a syntax that is similar to PYTHON programming those are used to support functional, procedural and object-oriented mathematical constructs. This programming language is easily compatible with Google Chrome, Firefox, opera and others that make it easy for the programmer to run the program feasible. The features of Sage Math include visualisation of graph theory and analysis tool, a huge library with mathematical functions related to theory functions and many others. This programming uses the help of a toolkit to add user interfaces those are related to application and calculations.

**APL**

The central data type of APL programming involves a multi-dimensional array, and it helps to concise the coding process by using a large number of graphic symbols and representation. This programming influences the development of functional programming, variable concept establishment regarding numerical, spreadsheet and others. One of the strongest features of APL is that they can execute any generalised array data without complicating the programming process. The APL programming has operators those help to improve the applied functions giving the programmer the opportunity to build numerical blocks that can collaborate easily. Thus, the flexibility to handle complicated numerical data makes the use of APL programming for solving mathematics a unique programming language. It also facilitates the representation of most operators and functions, which leads to very brief code. Moreover, this has an improved influence on the establishment of functional programming, concept modelling and computer maths packages.

**Wolfram Mathematica**

This software is a symbolic mathematical computation programming that is most often termed as computer algebra system. This programming is used in scientific research, calculating engineering mathematics along with computation in other fields. This programming language is supportive for computation of data related to arithmetic, complex numerical, interval arithmetic along with symbolic computation. Further, the program can generate 2-D and 3-D mesh and supports the censored data, time series, temporal data and others. The real value of this programming lies in its multi-domain standard library that helps to execute various mathematical applications with ease efficiently.

Thus, by using the help of these programming languages, the mathematical operations can be efficiently executed by those keen towards learning mathematics.