Symbolic Math Toolbox

Reference

This chapter provides detailed descriptions of all Symbolic Math Toolbox functions. It begins with tables of these functions and continues with the reference entries in alphabetical order.

Calculus

diff
Differentiate.

int
Integrate.

jacobian
Jacobian matrix.

limit
Limit of an expression.

symsum
Summation of series.

taylor
Taylor series expansion.

Calculus
`diff`	Differentiate.
`int`	Integrate.
`jacobian`	Jacobian matrix.
`limit`	Limit of an expression.
`symsum`	Summation of series.
`taylor`	Taylor series expansion.


Linear Algebra
`colspace`	Basis for column space.
`det`	Determinant.
`diag`	Create or extract diagonals.
`eig`	Eigenvalues and eigenvectors.
`expm`	Matrix exponential.
`inv`	Matrix inverse.
`jordan`	Jordan canonical form.
`null`	Basis for null space.
`poly`	Characteristic polynomial.
`rank`	Matrix rank.
`rref`	Reduced row echelon form.
`svd`	Singular value decomposition.
`tril`	Lower triangle.
`triu`	Upper triangle.


Simplification
`collect`	Collect common terms.
`expand`	Expand polynomials and elementary functions.
`factor`	Factor.
`horner`	Nested polynomial representation.
`numden`	Numerator and denominator.
`simple`	Search for shortest form.
`simplify`	Simplification.
`subexpr`	Rewrite in terms of subexpressions.


Solution of Equations
`compose`	Functional composition.
`dsolve`	Solution of differential equations.
`finverse`	Functional inverse.
`solve`	Solution of algebraic equations.


Variable Precision Arithmetic
`digits`	Set variable precision accuracy.
`vpa`	Variable precision arithmetic.


Arithmetic Operations
`+`	Addition.
`-`	Subtraction.
`*`	Multiplication.
`.*`	Array multiplication.
`/`	Right division.
`./`	Array right division.
`\`	Left division.
`.\`	Array left division.
`^`	Matrix or scalar raised to a power.
`.^`	Array raised to a power.
`'`	Complex conjugate transpose.
`.'`	Real transpose.


Special Functions
`cosint`	Cosine integral, Ci(x).
`hypergeom`	Generalized hypergeometric function.
`lambertw`	Solution of .
`sinint`	Sine integral, Si(x).
`zeta`	Riemann `zeta` function.


Access To Maple
`maple`	Access Maple kernel.
`mapleinit`	Initialize Maple.
`mfun`	Numeric evaluation of Maple functions.
`mhelp`	Maple help.
`mfunlist`	List of functions for `mfun`.
`procread`	Install a Maple procedure.


Pedagogical and Graphical Applications
`ezcontour`	Contour plotter.
`ezcontourf`	Filled contour plotter.
`ezmesh`	Mesh plotter.
`ezmeshc`	Combined mesh and contour plotter.
`ezplot`	Function plotter.
`ezplot3`	3-D curve plotter.
`ezpolar`	Polar coordinate plotter.
`ezsurf`	Surface plotter.
`ezsurfc`	Combined surface and contour plotter.
`funtool`	Function calculator.
`rsums`	Riemann sums.
`taylortool`	Taylor series calculator.


Conversions
`char`	Convert sym object to string.
`double`	Convert symbolic matrix to double.
`poly2sym`	Function calculator.
`sym2poly`	Symbolic polynomial to coefficient vector.


Basic Operations
`ccode`	C code representation of a symbolic expression.
`conj`	Complex conjugate.
`findsym`	Determine symbolic variables.
`fortran`	Fortran representation of a symbolic expression.
`imag`	Imaginary part of a complex number.
`latex`	LaTeX representation of a symbolic expression.
`pretty`	Pretty print a symbolic expression.
`real`	Real part of an imaginary number.
`sym`	Create symbolic object.
`syms`	Shortcut for creating multiple symbolic objects.


Integral Transforms
`fourier`	Fourier transform.
`ifourier`	Inverse Fourier transform.
`ilaplace`	Inverse Laplace transform.
`iztrans`	Inverse z-transform.
`laplace`	Laplace transform.
`ztrans`	z-transform.

Precompiled Maple Procedures