Functions in Symbolic Math Toolbox

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  • Symbolic Computations in MATLAB

    Symbolic Variables, Expressions, and Functions

    argnames Input variables of symbolic function
    children Subexpressions or terms of symbolic expression
    disp Display symbolic input
    display Display symbolic input
    formula Mathematical expression defining symbolic function
    funtool Function calculator
    pretty Prettyprint symbolic expressions
    sym Create symbolic objects
    symfun Create symbolic functions
    syms Shortcut for creating symbolic variables and functions
    symvar Find symbolic variables in symbolic expression, matrix, or function

    Operators and Elementary Operations

    Arithmetic Operations

    Arithmetic Operations Perform arithmetic operations on symbols
    ceil Round symbolic matrix toward positive infinity
    conj Symbolic complex conjugate
    cumprod Symbolic cumulative product
    cumsum Symbolic cumulative sum
    fix Round toward zero
    floor Round symbolic matrix toward negative infinity
    frac Symbolic matrix element-wise fractional parts
    imag Imaginary part of complex number
    minus Symbolic subtraction
    mod Symbolic modulus after division
    plus Symbolic addition
    quorem Quotient and remainder
    real Real part of complex number
    round Symbolic matrix element-wise round

    Relational Operations

    eq Define equation
    ge Define greater than or equal to relation
    gt Define greater than relation
    le Define less than or equal to relation
    lt Define less than relation
    ne Define inequality
    isequaln Test symbolic objects for equality, treating NaN values as equal

    Logical Operations

    and Logical AND for symbolic expressions
    not Logical NOT for symbolic expressions
    or Logical OR for symbolic expressions
    xor Logical XOR for symbolic expressions
    all Test whether all equations and inequalities represented as elements of symbolic array are valid
    any Test whether at least one of equations and inequalities represented as elements of symbolic array is valid
    in Numeric type of symbolic input
    isequaln Test symbolic objects for equality, treating NaN values as equal
    isfinite Check whether symbolic array elements are finite
    isinf Check whether symbolic array elements are infinite
    isnan Check whether symbolic array elements are NaNs
    logical Check validity of equation or inequality
    nnz Number of nonzero elements
    nonzeros Nonzero elements

    Conversion Between Symbolic and Numeric

    char Convert symbolic objects to strings
    double Convert symbolic matrix to MATLAB numeric form
    int8, int16, int32, int64 Convert symbolic matrix to signed integers
    poly2sym Polynomial coefficient vector to symbolic polynomial
    single Convert symbolic matrix to single precision
    sym Create symbolic objects
    sym2poly Symbolic-to-numeric polynomial conversion
    symfun Create symbolic functions
    uint8, uint16, uint32, uint64 Convert symbolic matrix to unsigned integers
    vpa Variable-precision arithmetic

    Mathematics

    Equation Solving

    Algebraic Equations and Systems

    equationsToMatrix Convert set of linear equations to matrix form
    finverse Functional inverse
    linsolve Solve linear system of equations given in matrix form
    poles Poles of expression or function
    solve Equations and systems solver
    vpasolve Numeric solver

    Ordinary Differential Equations and Systems

    dsolve Ordinary differential equation and system solver
    odeToVectorField Convert higher-order differential equations to systems of first-order differential equations

    Differential Algebraic Equations

    daeFunction Convert system of differential algebraic equations to MATLAB function handle
    decic Find consistent initial conditions for first-order implicit ODE system with algebraic constraints
    findDecoupledBlocks Search for decoupled blocks in systems of equations
    incidenceMatrix Find incidence matrix of system of equations
    isLowIndexDAE Check if differential index of system of equations is lower than 2
    massMatrixForm Extract mass matrix and right side of semilinear system of differential algebraic equations
    reduceDAEIndex Convert system of first-order differential algebraic equations to equivalent system of differential index 1
    reduceDAEToODE Convert system of first-order semilinear differential algebraic equations to equivalent system of differential index 0
    reduceDifferentialOrder Reduce system of higher-order differential equations to equivalent system of first-order differential equations
    reduceRedundancies Simplify system of first-order differential algebraic equations by eliminating redundant equations and variables

    Formula Manipulation and Simplification

    Simplification

    simplify Algebraic simplification
    simplifyFraction Symbolic simplification of fractions

    Formula Rearrangement and Rewriting

    coeffs Coefficients of polynomial
    collect Collect coefficients
    combine Combine terms of identical algebraic structure
    compose Functional composition
    divisors Divisors of integer or expression
    expand Symbolic expansion of polynomials and elementary functions
    factor Factorization
    horner Horner nested polynomial representation
    numden Numerator and denominator
    rewrite Rewrite expression in new terms
    subexpr Rewrite symbolic expression in terms of common subexpressions

    Substitution

    subexpr Rewrite symbolic expression in terms of common subexpressions
    subs Symbolic substitution

    Calculus

    Differentiation

    diff Differentiate symbolic expression or function

    Integration

    int Definite and indefinite integrals
    rsums Interactive evaluation of Riemann sums

    Vector Analysis

    curl Curl of vector field
    divergence Divergence of vector field
    gradient Gradient vector of scalar function
    hessian Hessian matrix of scalar function
    jacobian Jacobian matrix
    laplacian Laplacian of scalar function
    potential Potential of vector field
    vectorPotential Vector potential of vector field

    Series

    cumprod Symbolic cumulative product
    cumsum Symbolic cumulative sum
    pade Padé approximant
    rsums Interactive evaluation of Riemann sums
    symprod Product of series
    symsum Sum of series
    taylor Taylor series expansion
    taylortool Taylor series calculator

    Limits

    limit Compute limit of symbolic expression

    Transforms

    fourier Fourier transform
    ifourier Inverse Fourier transform
    ilaplace Inverse Laplace transform
    iztrans Inverse Z-transform
    laplace Laplace transform
    ztrans Z-transform

    Linear Algebra

    Matrix Operations and Transformations

    bernstein Bernstein polynomials
    bernsteinMatrix Bernstein matrix
    cat Concatenate symbolic arrays along specified dimension
    diag Create or extract diagonals of symbolic matrices
    expm Matrix exponential
    horzcat Concatenate symbolic arrays horizontally
    inv Compute symbolic matrix inverse
    pinv Moore-Penrose inverse (pseudoinverse) of symbolic matrix
    reshape Reshape symbolic array
    size Symbolic matrix dimensions
    sort Sort elements of symbolic vectors or matrices
    toeplitz Symbolic Toeplitz matrix
    tril Return lower triangular part of symbolic matrix
    triu Return upper triangular part of symbolic matrix
    vertcat Concatenate symbolic arrays vertically

    Linear Equations

    cond Condition number of matrix
    det Compute determinant of symbolic matrix
    equationsToMatrix Convert set of linear equations to matrix form
    inv Compute symbolic matrix inverse
    linsolve Solve linear system of equations given in matrix form
    norm Norm of matrix or vector
    rank Compute rank of symbolic matrix
    rref Compute reduced row echelon form of matrix

    Matrix Decomposition

    chol Cholesky factorization
    jordan Jordan form of matrix
    lu LU factorization
    qr QR factorization
    svd Singular value decomposition of symbolic matrix

    Eigenvalues and Eigenvectors

    charpoly Characteristic polynomial of matrix
    eig Eigenvalues and eigenvectors of symbolic matrix
    jordan Jordan form of matrix

    Vector Spaces and Subspaces

    colon Create symbolic vectors, array subscripting, and for-loop iterators
    colspace Column space of matrix
    null Form basis for null space of matrix
    numel Number of elements of symbolic array
    orth Orthonormal basis for range of symbolic matrix
    rank Compute rank of symbolic matrix
    rref Compute reduced row echelon form of matrix
    size Symbolic matrix dimensions

    Matrix Analysis

    adjoint Adjoint of symbolic square matrix
    charpoly Characteristic polynomial of matrix
    cond Condition number of matrix
    curl Curl of vector field
    det Compute determinant of symbolic matrix
    divergence Divergence of vector field
    gradient Gradient vector of scalar function
    hessian Hessian matrix of scalar function
    jacobian Jacobian matrix
    laplacian Laplacian of scalar function
    minpoly Minimal polynomial of matrix
    norm Norm of matrix or vector
    potential Potential of vector field
    vectorPotential Vector potential of vector field

    Matrix Functions

    expm Matrix exponential
    funm General matrix function
    logm Matrix logarithm
    sqrtm Matrix square root

    Assumptions

    assume Set assumption on symbolic object
    assumeAlso Add assumption on symbolic object
    assumptions Show assumptions set on symbolic variable
    clear all Remove items from MATLAB workspace and reset MuPAD engine
    isAlways Check whether equation or inequality holds for all values of its variables
    isfinite Check whether symbolic array elements are finite
    isinf Check whether symbolic array elements are infinite
    isnan Check whether symbolic array elements are NaNs
    logical Check validity of equation or inequality
    reset Close MuPAD engine

    Polynomials

    charpoly Characteristic polynomial of matrix
    chebyshevT Chebyshev polynomials of the first kind
    chebyshevU Chebyshev polynomials of the second kind
    coeffs Coefficients of polynomial
    gegenbauerC Gegenbauer polynomials
    hermiteH Hermite polynomials
    jacobiP Jacobi polynomials
    laguerreL Generalized Laguerre Function and Laguerre Polynomials
    legendreP Legendre polynomials
    minpoly Minimal polynomial of matrix
    poly2sym Polynomial coefficient vector to symbolic polynomial
    sym2poly Symbolic-to-numeric polynomial conversion

    Mathematical Functions

    Constants

    catalan Catalan constant
    eulergamma Euler-Mascheroni constant

    Logarithms

    log Natural logarithm of entries of symbolic matrix
    log10 Logarithm base 10 of entries of symbolic matrix
    log2 Logarithm base 2 of entries of symbolic matrix

    Trigonometric Functions

    sin Symbolic sine function
    cos Symbolic cosine function
    tan Symbolic tangent function
    cot Symbolic cotangent function
    sec Symbolic secant function
    csc Symbolic cosecant function
    asin Symbolic inverse sine function
    acos Symbolic inverse cosine function
    atan Symbolic inverse tangent function
    acot Symbolic inverse cotangent function
    asec Symbolic inverse secant function
    acsc Symbolic inverse cosecant function

    Hyperbolic Functions

    sinh Symbolic hyperbolic sine function
    cosh Symbolic hyperbolic cosine function
    tanh Symbolic hyperbolic tangent function
    coth Symbolic hyperbolic cotangent function
    sech Symbolic hyperbolic secant function
    csch Symbolic hyperbolic cosecant function
    asinh Symbolic inverse hyperbolic sine function
    acosh Symbolic inverse hyperbolic cosine function
    atanh Symbolic inverse hyperbolic tangent function
    acoth Symbolic inverse hyperbolic cotangent function
    asech Symbolic inverse hyperbolic secant function
    acsch Symbolic inverse hyperbolic cosecant function

    Complex Numbers

    abs Absolute value of real or complex value
    angle Symbolic polar angle
    atan2 Symbolic four-quadrant inverse tangent
    imag Imaginary part of complex number
    real Real part of complex number
    sign Sign of real or complex value
    signIm Sign of the imaginary part of complex number

    Special Functions

    Dirac and Heaviside Functions
    dirac Dirac delta function
    heaviside Heaviside step function
    kroneckerDelta Kronecker delta function
    rectangularPulse Rectangular pulse function
    triangularPulse Triangular pulse function
    Gamma Functions
    beta Beta function
    factorial Factorial function
    gamma Gamma function
    gammaln Logarithmic gamma function
    igamma Incomplete gamma function
    nchoosek Binomial coefficient
    pochhammer Pochhammer symbol
    Zeta Function and Polylogarithms
    catalan Catalan constant
    dilog Dilogarithm function
    polylog Polylogarithm
    psi Digamma function
    zeta Riemann zeta function
    Airy and Bessel Functions
    airy Airy function
    besseli Modified Bessel function of the first kind
    besselj Bessel function of the first kind
    besselk Modified Bessel function of the second kind
    bessely Bessel function of the second kind
    Exponential and Trigonometric Integrals
    coshint Hyperbolic cosine integral function
    cosint Cosine integral function
    dawson Dawson integral
    ei One-argument exponential integral function
    eulergamma Euler-Mascheroni constant
    expint Exponential integral function
    fresnelc Fresnel cosine integral function
    fresnels Fresnel sine integral function
    logint Logarithmic integral function
    sinhint Hyperbolic sine integral function
    sinint Sine integral function
    ssinint Shifted sine integral function
    Error Functions
    erf Error function
    erfc Complementary error function
    erfcinv Inverse complementary error function
    erfi Imaginary error function
    erfinv Inverse error function
    Hypergeometric and Whittaker Functions
    hypergeom Hypergeometric function
    kummerU Confluent hypergeometric Kummer U function
    whittakerM Whittaker M function
    whittakerW Whittaker W function
    Elliptic Integrals
    ellipke Complete elliptic integrals of the first and second kinds
    ellipticCE Complementary complete elliptic integral of the second kind
    ellipticCK Complementary complete elliptic integral of the first kind
    ellipticCPi Complementary complete elliptic integral of the third kind
    ellipticE Complete and incomplete elliptic integrals of the second kind
    ellipticF Incomplete elliptic integral of the first kind
    ellipticK Complete elliptic integral of the first kind
    ellipticPi Complete and incomplete elliptic integrals of the third kind
    Lambert W and Wright Functions
    lambertw Lambert W function
    wrightOmega Wright omega function

    Numbers and Precision

    Precision Control

    digits Variable-precision accuracy
    double Convert symbolic matrix to MATLAB numeric form
    vpa Variable-precision arithmetic

    Operations on Numbers

    ceil Round symbolic matrix toward positive infinity
    conj Symbolic complex conjugate
    fix Round toward zero
    floor Round symbolic matrix toward negative infinity
    frac Symbolic matrix element-wise fractional parts
    imag Imaginary part of complex number
    max Largest elements
    min Smallest elements
    real Real part of complex number
    round Symbolic matrix element-wise round

    Number Theory

    bernoulli Bernoulli numbers and polynomials
    divisors Divisors of integer or expression
    euler Euler numbers and polynomials
    gcd Greatest common divisor
    harmonic Harmonic function (harmonic number)
    lcm Least common multiple
    mod Symbolic modulus after division
    quorem Quotient and remainder
    rem Remainder after division

    Graphics

    Function Plots

    ezcontour Contour plotter
    ezcontourf Filled contour plotter
    ezmesh 3-D mesh plotter
    ezmeshc Combined mesh and contour plotter
    ezplot Plot symbolic expression, equation, or function
    ezplot3 3-D parametric curve plotter
    ezpolar Polar coordinate plotter
    ezsurf Plot 3-D surface
    ezsurfc Combined surface and contour plotter

    Code Generation

    ccode C code representation of symbolic expression
    fortran Fortran representation of symbolic expression
    latex LaTeX representation of symbolic expression
    matlabFunction Convert symbolic expression to function handle or file
    matlabFunctionBlock Convert symbolic expression to MATLAB Function block
    simscapeEquation Convert symbolic expressions to Simscape language equations
    texlabel TeX representation of symbolic expression

    MATLAB and MuPAD Integration

    MuPAD Function Calls

    evalin Evaluate MuPAD expressions without specifying their arguments
    feval Evaluate MuPAD expressions specifying their arguments
    read Read MuPAD program file into symbolic engine

    MuPAD Files and Interfaces

    allMuPADNotebooks All open notebooks
    close Close MuPAD notebook
    doc Get help for MuPAD functions
    evaluateMuPADNotebook Evaluate MuPAD notebook
    mupad Start MuPAD notebook
    mupadNotebookTitle Window title of MuPAD notebook
    mupadwelcome Start MuPAD interfaces
    openmn Open MuPAD notebook
    openmu Open MuPAD program file
    openxvc Open MuPAD uncompressed graphics file (XVC)
    openxvz Open MuPAD compressed graphics file (XVZ)

    Variables and Expressions Exchange

    getVar Get variable from MuPAD notebook
    setVar Assign variable in MuPAD notebook

    MuPAD Engine Commands

    clear all Remove items from MATLAB workspace and reset MuPAD engine
    reset Close MuPAD engine
    symengine Return symbolic engine
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