## Symbolic computing of mathematical expressions

A computer algebra system (CAS) solves, plots, and manipulates mathematical expressions in an analytical form. CASs support a wide range of mathematics such as linear algebra, calculus, and algebraic and ordinary differential equations.

### Work with Equations Analytically

Computer algebra systems can represent parameters and variables in equations as symbols like \(f(x)=1-ax^2\). Using a CAS you can solve, manipulate, and plot \(f(x)\) without having to generate numeric data. You can perform sensitivity studies to learn how an equation changes due to its parameters by easily substituting numerical values for symbolic parameters and variables. Using the Live Editor in MATLAB^{®}, symbolic calculations look like the equations you write on paper.

### Solve, Manipulate, and Evaluate Mathematical Expressions

MATLAB supports both numeric and symbolic approaches to mathematical modeling, which lets you solve problems using the best approach. CASs have sophisticated algorithms for solving and simplifying algebraic equations, systems of equations, and systems of differential algebraic equations (DAEs). For example, you can improve performance and accuracy in optimization by computing exact analytical gradients and Hessians.

### Improve Accuracy with Exact Math

In contrast to numerical computations, which can suffer from floating-point errors, symbolic computations are carried out exactly. For example, the result of \(\sqrt{56}\) symbolically is \(2\sqrt{14}\), and using variable precision arithmetic you can approximate this result to 100 or more digits of accuracy.

For more information on computer algebra systems, see Symbolic Math Toolbox™.

### Examples and How To

- Computational Mathematics in Symbolic Math Toolbox - Example
- Analytical Plotting with Symbolic Math Toolbox - Example
- Numerical Computations with High Precision - Example
- Using Units in Physics - Example
- Validate a Simulink Model Using Symbolic Math Toolbox - Example
- Improving Accuracy and Performance in Optimization - Example
- Create Analytical Models for Simscape - Example

### Software Reference

- Symbolic Computations in MATLAB - Documentation
- Symbolic Graphics - Documentation
- Increase Precision of Numeric Calculations - Documentation
- Solve Algebraic Equation - Documentation
- Solve Differential Algebraic Equations (DAEs) - Documentation
- Units of Measurement - Documentation
- Use Symbolic Results in MATLAB, Simulink, Simscape, and C - Documentation

*See also:
Symbolic Math Toolbox,
mathematical modeling,
analytical solution,
Live Editor,
dimensional analysis,
Integral
*