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Symbolic Math Toolbox Functions

Alphabetical List By Category

Symbolic Computations in MATLAB

Symbolic Variables, Expressions, Functions, and Preferences

fold Combine (fold) vector using function
piecewise Conditionally defined expression or function
sym Create symbolic variables, expressions, functions, matrices
symfun Create symbolic functions
syms Create symbolic variables and functions
symvar Find symbolic variables in symbolic expression, matrix, or function
argnames Input variables of symbolic function
children Subexpressions or terms of symbolic expression
formula Mathematical expression defining symbolic function
has Check if expression contains particular subexpression
disp Display symbolic input
display Display symbolic input
pretty Prettyprint symbolic expressions
isfinite Check whether symbolic array elements are finite
isinf Check whether symbolic array elements are infinite
isnan Check whether symbolic array elements are NaNs
funtool Function calculator
sympref Set symbolic preferences

Operators and Elementary Operations

minus Symbolic subtraction
plus Symbolic addition
times Symbolic array multiplication
ldivide Symbolic array left division
rdivide Symbolic array right division
power Symbolic array power
mtimes Symbolic matrix multiplication
mldivide Symbolic matrix left division
mrdivide Symbolic matrix right division
mpower Symbolic matrix power
transpose Symbolic matrix transpose
ctranspose Symbolic matrix complex conjugate transpose
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
has Check if expression contains particular subexpression
in Numeric type of symbolic input
isequal Test equality of symbolic inputs
isequaln Test symbolic objects for equality, treating NaN values as equal
piecewise Conditionally defined expression or function
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
has Check if expression contains particular subexpression
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
ceil Round symbolic matrix toward positive infinity
fix Round toward zero
floor Round symbolic matrix toward negative infinity
frac Symbolic matrix element-wise fractional parts
mod Symbolic modulus after division
quorem Quotient and remainder
round Symbolic matrix element-wise round
conj Symbolic complex conjugate
imag Imaginary part of complex number
real Real part of complex number

Conversion Between Symbolic and Numeric

char Convert symbolic objects to character vectors
cell2sym Convert cell array to symbolic array
double Convert symbolic values to MATLAB double precision
int8, int16, int32, int64 Convert symbolic matrix to signed integers
poly2sym Create symbolic polynomial from vector of coefficients
single Convert symbolic matrix to single precision
sym Create symbolic variables, expressions, functions, matrices
sym2cell Convert symbolic array to cell array
sym2poly Extract vector of all numeric coefficients, including zeros, from symbolic polynomial
symfun Create symbolic functions
uint8, uint16, uint32, uint64 Convert symbolic matrix to unsigned integers
vpa Variable-precision arithmetic

Mathematics

Equation Solving

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
dsolve Differential equations and systems solver
massMatrixForm Extract mass matrix and right side of semilinear system of differential algebraic equations
odeFunction Convert system of symbolic algebraic expressions to MATLAB function handle suitable for ode45, ode15s, and other ODE solvers
odeToVectorField Convert higher-order differential equations to systems of first-order differential equations
daeFunction Convert system of differential algebraic equations to MATLAB function handle suitable for ode15i
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
odeFunction Convert system of symbolic algebraic expressions to MATLAB function handle suitable for ode45, ode15s, and other ODE solvers
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

simplify Algebraic simplification
simplifyFraction Symbolic simplification of fractions
subexpr Rewrite symbolic expression in terms of common subexpressions
pretty Prettyprint symbolic expressions
coeffs Coefficients of polynomial
expand Symbolic expansion of polynomials and elementary functions
horner Horner nested polynomial representation
numden Extract numerator and denominator
partfrac Partial fraction decomposition
children Subexpressions or terms of symbolic expression
collect Collect coefficients
combine Combine terms of identical algebraic structure
compose Functional composition
divisors Divisors of integer or expression
factor Factorization
rewrite Rewrite expression in terms of another function
pretty Prettyprint symbolic expressions
subexpr Rewrite symbolic expression in terms of common subexpressions
subs Symbolic substitution

Calculus

diff Differentiate symbolic expression or function
functionalDerivative Functional derivative
int Definite and indefinite integrals
rsums Interactive evaluation of Riemann sums
vpaintegral Numerical integration using variable precision
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
pade Pade approximant
rsums Interactive evaluation of Riemann sums
series Puiseux series
taylor Taylor series
taylortool Taylor series calculator
cumprod Symbolic cumulative product
cumsum Symbolic cumulative sum
symprod Product of series
symsum Sum of series
limit Compute limit of symbolic expression
fourier Fourier transform
ifourier Inverse Fourier transform
ilaplace Inverse Laplace transform
iztrans Inverse Z-transform
laplace Laplace transform
sympref Set symbolic preferences
ztrans Z-transform

Linear Algebra

cat Concatenate symbolic arrays along specified dimension
colon Create symbolic vectors, array subscripting, and for-loop iterators
horzcat Concatenate symbolic arrays horizontally
numel Number of elements of symbolic array
size Symbolic matrix dimensions
sort Sort elements of symbolic vectors or matrices
vertcat Concatenate symbolic arrays vertically
diag Create or extract diagonals of symbolic matrices
reshape Reshape symbolic array
tril Return lower triangular part of symbolic matrix
triu Return upper triangular part of symbolic matrix
adjoint Adjoint of symbolic square matrix
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
pinv Moore-Penrose inverse (pseudoinverse) of symbolic matrix
rank Find rank of symbolic matrix
rref Reduced row echelon form of matrix (Gauss-Jordan elimination)
colspace Column space of matrix
null Form basis for null space of matrix
orth Orthonormal basis for range of symbolic matrix
chol Cholesky factorization
lu LU factorization
qr QR factorization
svd Singular value decomposition of symbolic matrix
charpoly Characteristic polynomial of matrix
eig Eigenvalues and eigenvectors of symbolic matrix
jordan Jordan form of matrix
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
hermiteForm Hermite form of matrix
jordan Jordan form of matrix
smithForm Smith form of matrix
bernsteinMatrix Bernstein matrix
toeplitz Symbolic Toeplitz matrix
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 affecting symbolic variable, expression, or function
clear all Remove items from MATLAB workspace and reset MuPAD engine
in Numeric type of symbolic input
piecewise Conditionally defined expression or function
reset Close MuPAD engine
isAlways Check whether equation or inequality holds for all values of its variables
logical Check validity of equation or inequality

Polynomials

coeffs Coefficients of polynomial
poly2sym Create symbolic polynomial from vector of coefficients
root Represent roots of polynomial
sym2poly Extract vector of all numeric coefficients, including zeros, from symbolic polynomial
charpoly Characteristic polynomial of matrix
minpoly Minimal polynomial of matrix
bernstein Bernstein polynomials
chebyshevT Chebyshev polynomials of the first kind
chebyshevU Chebyshev polynomials of the second kind
gegenbauerC Gegenbauer polynomials
hermiteH Hermite polynomials
jacobiP Jacobi polynomials
laguerreL Generalized Laguerre Function and Laguerre Polynomials
legendreP Legendre polynomials

Mathematical Functions

catalan Catalan constant
eulergamma Euler-Mascheroni constant
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
dilog Dilogarithm function
polylog Polylogarithm
psi Digamma function
zeta Riemann zeta function
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
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
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
beta Beta function
factorial Factorial function
gamma Gamma function
gammaln Logarithmic gamma function
igamma Incomplete gamma function
nchoosek Binomial coefficient
pochhammer Pochhammer symbol
dawson Dawson integral
erf Error function
erfc Complementary error function
erfcinv Inverse complementary error function
erfi Imaginary error function
erfinv Inverse error function
fresnelc Fresnel cosine integral function
fresnels Fresnel sine integral function
coshint Hyperbolic cosine integral function
cosint Cosine integral function
ei One-argument exponential integral function
expint Exponential integral function
eulergamma Euler-Mascheroni constant
logint Logarithmic integral function
sinhint Hyperbolic sine integral function
sinint Sine integral function
ssinint Shifted sine integral function
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
dirac Dirac delta function
heaviside Heaviside step function
kroneckerDelta Kronecker delta function
rectangularPulse Rectangular pulse function
triangularPulse Triangular pulse function
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
hypergeom Hypergeometric function
kummerU Confluent hypergeometric Kummer U function
whittakerM Whittaker M function
whittakerW Whittaker W function
lambertw Lambert W function
wrightOmega Wright omega function

Numbers and Precision

digits Change variable precision used
double Convert symbolic values to MATLAB double precision
vpa Variable-precision arithmetic
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
nextprime Next prime number
prevprime Previous prime number
quorem Quotient and remainder
rem Remainder after division

Graphics

fcontour Plot contours
fimplicit Plot implicit symbolic equation or function
fimplicit3 Plot 3-D implicit equation or function
fmesh Plot 3-D mesh
fplot Plot symbolic expression or function
fplot3 Plot 3-D parametric curve
fsurf Plot 3-D surface
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

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
symReadSSCParameters Load parameters from Simscape component
symReadSSCVariables Load variables from Simscape component
symWriteSSC Create new Simscape component
ccode C code representation of symbolic expression
fortran Fortran representation of symbolic expression
latex LaTeX form of symbolic expression
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

MuPAD to MATLAB Code Conversion

convertMuPADNotebook Convert MuPAD notebook to MATLAB live script
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