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Symbolic Math Toolbox

Perform symbolic math computations

Symbolic Math Toolbox™ provides functions for solving, plotting, and manipulating symbolic math equations. You can create, run, and share symbolic math code. In the MATLAB^® Live Editor, you can get next-step suggestions for symbolic workflows. The toolbox provides functions in common mathematical areas such as calculus, linear algebra, algebraic and differential equations, equation simplification, and equation manipulation.

Symbolic Math Toolbox lets you analytically perform differentiation, integration, simplification, transforms, and equation solving. You can perform dimensional computations and convert between units. Your computations can be performed either analytically or using variable-precision arithmetic, with the results displayed in mathematical typeset.

You can share your symbolic work with other MATLAB users as live scripts or convert them to HTML, Word, LaTex, or PDF documents. You can generate MATLAB functions, Simulink^® function blocks, and Simscape™ equations directly from symbolic expressions.

What Is Symbolic Math Toolbox?

Next Step Suggestions for Symbolic Workflows in Live Editor

See how to use the next step suggestions menu in Live Editor for guidance on symbolic math workflows.

A function, its first derivative, and second derivative together with a plot showing local maxima, minima, and inflection points

Calculus

Evaluate exact analytical solutions for definite or indefinite integral, calculate derivatives of symbolic expressions or functions, and approximate functions using series expansions.

Documentation | Examples

Plot showing under-damped, over-damped, and critically-damped cases.

Solving, Simplification, and Substitution

Solve linear and nonlinear algebraic and differential equations analytically, simplify and rewrite symbolic expressions, and evaluate symbolic expressions using substitution.

Documentation | Examples

A 3D plot of eigenfunctions of the Laplace operator.

Linear Algebra

Analyze, transform, and decompose symbolic matrices to study the properties of linear equations, perform linear algebra operations, and solve systems of linear equations in matrix or equation form.

Documentation | Examples

Visualization

Use built-in functions to plot symbolic expressions and functions using extended MATLAB graphics capabilities and visualize the behavior of symbolic expressions using animations.

Documentation | Examples

Live script that increases the speed of computation by reducing precision.

Variable-Precision Arithmetic (VPA)

Explicitly set the number of significant digits to avoid hidden round-off errors. Increase the speed of calculations by reducing the precision with variable-precision arithmetic.

Documentation | Examples

Graphs showing the terminal velocity of a falling paratrooper in SI and imperial units.

Units and Dimensional Analysis

Perform dimensional analysis and verify the dimensional compatibility and consistency of units in symbolic calculations. Create custom unit systems and convert between existing unit systems.

Documentation | Examples

Computational and analytical mathematics using Symbolic Math toolbox in Live Editor.

Documentation and Sharing

Interactively update and display symbolic math computations and get next-step suggestions for symbolic workflows using the MATLAB Live Editor. Share your work as live scripts or publish your code to create formatted documents including HTML, Word, LaTeX, and PDF.

Documentation | Examples

Code Generation

Generate MATLAB functions, Simulink function blocks, custom equation-based Simscape components, and C or Fortran code directly from symbolic expressions.

Documentation | Examples