Documentation

This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Symbolic Math Toolbox Functions

Alphabetical List By Category

Symbolic Computations in MATLAB

Symbolic Variables, Expressions, Functions, and Preferences

foldCombine (fold) vector using function
piecewiseConditionally defined expression or function
symCreate symbolic variables, expressions, functions, matrices
str2symEvaluate string representing symbolic expression
symfunCreate symbolic functions
symsCreate symbolic variables and functions
symvarFind symbolic variables in symbolic expression, matrix, or function
argnamesInput variables of symbolic function
childrenSubexpressions or terms of symbolic expression
formulaMathematical expression defining symbolic function
hasCheck if expression contains particular subexpression
dispDisplay symbolic input
displayDisplay symbolic input
prettyPrettyprint symbolic expressions
isfiniteCheck whether symbolic array elements are finite
isinfCheck whether symbolic array elements are infinite
isnanCheck whether symbolic array elements are NaNs
funtoolFunction calculator
symprefSet symbolic preferences

Operators and Elementary Operations

minusSymbolic subtraction
plusSymbolic addition
timesSymbolic array multiplication
ldivideSymbolic array left division
rdivideSymbolic array right division
powerSymbolic array power
mtimesSymbolic matrix multiplication
mldivideSymbolic matrix left division
mrdivideSymbolic matrix right division
mpowerSymbolic matrix power
transposeSymbolic matrix transpose
ctransposeSymbolic matrix complex conjugate transpose
eqDefine equation
geDefine greater than or equal to relation
gtDefine greater than relation
leDefine less than or equal to relation
ltDefine less than relation
neDefine inequality
hasCheck if expression contains particular subexpression
inNumeric type of symbolic input
isequalTest equality of symbolic inputs
isequalnTest symbolic objects for equality, treating NaN values as equal
piecewiseConditionally defined expression or function
andLogical AND for symbolic expressions
notLogical NOT for symbolic expressions
orLogical OR for symbolic expressions
xorLogical XOR for symbolic expressions
allTest whether all equations and inequalities represented as elements of symbolic array are valid
anyTest whether at least one of equations and inequalities represented as elements of symbolic array is valid
hasCheck if expression contains particular subexpression
inNumeric type of symbolic input
isequalnTest symbolic objects for equality, treating NaN values as equal
isfiniteCheck whether symbolic array elements are finite
isinfCheck whether symbolic array elements are infinite
isnanCheck whether symbolic array elements are NaNs
logicalCheck validity of equation or inequality
nnzNumber of nonzero elements
nonzerosNonzero elements
ceilRound symbolic matrix toward positive infinity
fixRound toward zero
floorRound symbolic matrix toward negative infinity
fracSymbolic matrix element-wise fractional parts
modSymbolic modulus after division
quoremQuotient and remainder
roundSymbolic matrix element-wise round
conjSymbolic complex conjugate
imagImaginary part of complex number
realReal part of complex number

Conversion Between Symbolic and Numeric

charConvert symbolic objects to character vectors
cell2symConvert cell array to symbolic array
doubleConvert symbolic values to MATLAB double precision
int8, int16, int32, int64Convert symbolic matrix to signed integers
poly2symCreate symbolic polynomial from vector of coefficients
singleConvert symbolic matrix to single precision
symCreate symbolic variables, expressions, functions, matrices
sym2cellConvert symbolic array to cell array
sym2polyExtract vector of all numeric coefficients, including zeros, from symbolic polynomial
symfunCreate symbolic functions
uint8, uint16, uint32, uint64Convert symbolic matrix to unsigned integers
vpaVariable-precision arithmetic

Units of Measurement

checkUnitsCheck for compatible dimensions and consistent units
findUnitsFind units in input
isUnitDetermine if input is a symbolic unit
newUnitDefine new unit
removeUnitRemove unit
rewriteRewrite expression in terms of another function
separateUnitsSeparate units from expression
simplifyAlgebraic simplification
str2symunitConvert character vector or string to unit
symunitUnits of measurement
symunit2strConvert unit to character vector
unitConversionFactorConversion factor between units
unitInfoInformation on units of measurement
baseUnitsBase units of unit system
derivedUnitsDerived units of unit system
newUnitSystemDefine unit system
removeUnitSystemRemove unit system
unitSystemsList available unit systems

Mathematics

Equation Solving

equationsToMatrixConvert set of linear equations to matrix form
finverseFunctional inverse
linsolveSolve linear system of equations given in matrix form
polesPoles of expression or function
solveEquations and systems solver
vpasolveSolve equations numerically
dsolveDifferential equations and systems solver
massMatrixFormExtract mass matrix and right side of semilinear system of differential algebraic equations
odeFunctionConvert symbolic expressions to function handle for ODE solvers
odeToVectorFieldReduce order of differential equations to 1
daeFunctionConvert system of differential algebraic equations to MATLAB function handle suitable for ode15i
decicFind consistent initial conditions for first-order implicit ODE system with algebraic constraints
findDecoupledBlocksSearch for decoupled blocks in systems of equations
incidenceMatrixFind incidence matrix of system of equations
isLowIndexDAECheck if differential index of system of equations is lower than 2
massMatrixFormExtract mass matrix and right side of semilinear system of differential algebraic equations
odeFunctionConvert symbolic expressions to function handle for ODE solvers
reduceDAEIndexConvert system of first-order differential algebraic equations to equivalent system of differential index 1
reduceDAEToODEConvert system of first-order semilinear differential algebraic equations to equivalent system of differential index 0
reduceDifferentialOrderReduce system of higher-order differential equations to equivalent system of first-order differential equations
reduceRedundanciesSimplify system of first-order differential algebraic equations by eliminating redundant equations and variables

Formula Manipulation and Simplification

simplifyAlgebraic simplification
simplifyFractionSymbolic simplification of fractions
subexprRewrite symbolic expression in terms of common subexpressions
prettyPrettyprint symbolic expressions
coeffsCoefficients of polynomial
expandSymbolic expansion of polynomials and elementary functions
hornerHorner nested polynomial representation
numdenExtract numerator and denominator
partfracPartial fraction decomposition
childrenSubexpressions or terms of symbolic expression
collectCollect coefficients
combineCombine terms of identical algebraic structure
composeFunctional composition
divisorsDivisors of integer or expression
factorFactorization
isolateIsolate variable or expression in equation
lhsLeft side (LHS) of equation
rewriteRewrite expression in terms of another function
rhsRight side (RHS) of equation
prettyPrettyprint symbolic expressions
subexprRewrite symbolic expression in terms of common subexpressions
subsSymbolic substitution

Calculus

diffDifferentiate symbolic expression or function
functionalDerivativeFunctional derivative
intDefinite and indefinite integrals
rsumsInteractive evaluation of Riemann sums
vpaintegralNumerical integration using variable precision
curlCurl of vector field
divergenceDivergence of vector field
gradientGradient vector of scalar function
hessianHessian matrix of scalar function
jacobianJacobian matrix
laplacianLaplacian of scalar function
potentialPotential of vector field
vectorPotentialVector potential of vector field
padePade approximant
rsumsInteractive evaluation of Riemann sums
seriesPuiseux series
taylorTaylor series
taylortoolTaylor series calculator
cumprodSymbolic cumulative product
cumsumSymbolic cumulative sum
symprodProduct of series
symsumSum of series
limitLimit of symbolic expression
fourierFourier transform
ifourierInverse Fourier transform
ilaplaceInverse Laplace transform
iztransInverse Z-transform
laplaceLaplace transform
symprefSet symbolic preferences
ztransZ-transform

Linear Algebra

catConcatenate symbolic arrays along specified dimension
colonCreate symbolic vectors, array subscripting, and for-loop iterators
horzcatConcatenate symbolic arrays horizontally
numelNumber of elements of symbolic array
sizeSymbolic matrix dimensions
sortSort elements of symbolic vectors or matrices
vertcatConcatenate symbolic arrays vertically
diagCreate or extract diagonals of symbolic matrices
reshapeReshape symbolic array
trilReturn lower triangular part of symbolic matrix
triuReturn upper triangular part of symbolic matrix
adjointAdjoint of symbolic square matrix
condCondition number of matrix
detCompute determinant of symbolic matrix
equationsToMatrixConvert set of linear equations to matrix form
invCompute symbolic matrix inverse
linsolveSolve linear system of equations given in matrix form
normNorm of matrix or vector
pinvMoore-Penrose inverse (pseudoinverse) of symbolic matrix
rankFind rank of symbolic matrix
rrefReduced row echelon form of matrix (Gauss-Jordan elimination)
colspaceColumn space of matrix
nullForm basis for null space of matrix
orthOrthonormal basis for range of symbolic matrix
cholCholesky factorization
luLU factorization
qrQR factorization
svdSingular value decomposition of symbolic matrix
charpolyCharacteristic polynomial of matrix
eigEigenvalues and eigenvectors of symbolic matrix
jordanJordan form of matrix
curlCurl of vector field
divergenceDivergence of vector field
gradientGradient vector of scalar function
hessianHessian matrix of scalar function
jacobianJacobian matrix
laplacianLaplacian of scalar function
potentialPotential of vector field
vectorPotentialVector potential of vector field
hermiteFormHermite form of matrix
jordanJordan form of matrix
smithFormSmith form of matrix
bernsteinMatrixBernstein matrix
toeplitzSymbolic Toeplitz matrix
expmMatrix exponential
funmGeneral matrix function
logmMatrix logarithm
sqrtmMatrix square root

Assumptions

assumeSet assumption on symbolic object
assumeAlsoAdd assumption on symbolic object
assumptionsShow assumptions affecting symbolic variable, expression, or function
clear allRemove items from MATLAB workspace and reset MuPAD engine
inNumeric type of symbolic input
piecewiseConditionally defined expression or function
resetClose MuPAD engine
isAlwaysCheck whether equation or inequality holds for all values of its variables
logicalCheck validity of equation or inequality

Polynomials

coeffsCoefficients of polynomial
poly2symCreate symbolic polynomial from vector of coefficients
rootRepresent roots of polynomial
sym2polyExtract vector of all numeric coefficients, including zeros, from symbolic polynomial
charpolyCharacteristic polynomial of matrix
minpolyMinimal polynomial of matrix
bernsteinBernstein polynomials
chebyshevTChebyshev polynomials of the first kind
chebyshevUChebyshev polynomials of the second kind
gegenbauerCGegenbauer polynomials
hermiteHHermite polynomials
jacobiPJacobi polynomials
laguerreLGeneralized Laguerre Function and Laguerre Polynomials
legendrePLegendre polynomials

Mathematical Functions

catalanCatalan constant
eulergammaEuler-Mascheroni constant
logNatural logarithm of entries of symbolic matrix
log10Logarithm base 10 of entries of symbolic matrix
log2Logarithm base 2 of entries of symbolic matrix
dilogDilogarithm function
polylogPolylogarithm
psiDigamma function
zetaRiemann zeta function
sinSymbolic sine function
cosSymbolic cosine function
tanSymbolic tangent function
cotSymbolic cotangent function
secSymbolic secant function
cscSymbolic cosecant function
asinSymbolic inverse sine function
acosSymbolic inverse cosine function
atanSymbolic inverse tangent function
acotSymbolic inverse cotangent function
asecSymbolic inverse secant function
acscSymbolic inverse cosecant function
sinhSymbolic hyperbolic sine function
coshSymbolic hyperbolic cosine function
tanhSymbolic hyperbolic tangent function
cothSymbolic hyperbolic cotangent function
sechSymbolic hyperbolic secant function
cschSymbolic hyperbolic cosecant function
asinhSymbolic inverse hyperbolic sine function
acoshSymbolic inverse hyperbolic cosine function
atanhSymbolic inverse hyperbolic tangent function
acothSymbolic inverse hyperbolic cotangent function
asechSymbolic inverse hyperbolic secant function
acschSymbolic inverse hyperbolic cosecant function
absAbsolute value of real or complex value
angleSymbolic polar angle
atan2Symbolic four-quadrant inverse tangent
imagImaginary part of complex number
realReal part of complex number
signSign of real or complex value
signImSign of the imaginary part of complex number
betaBeta function
factorialFactorial function
gammaGamma function
gammalnLogarithmic gamma function
igammaIncomplete gamma function
nchoosekBinomial coefficient
pochhammerPochhammer symbol
dawsonDawson integral
erfError function
erfcComplementary error function
erfcinvInverse complementary error function
erfiImaginary error function
erfinvInverse error function
fresnelcFresnel cosine integral function
fresnelsFresnel sine integral function
coshintHyperbolic cosine integral function
cosintCosine integral function
eiOne-argument exponential integral function
expintExponential integral function
eulergammaEuler-Mascheroni constant
logintLogarithmic integral function
sinhintHyperbolic sine integral function
sinintSine integral function
ssinintShifted sine integral function
ellipkeComplete elliptic integrals of the first and second kinds
ellipticCEComplementary complete elliptic integral of the second kind
ellipticCKComplementary complete elliptic integral of the first kind
ellipticCPiComplementary complete elliptic integral of the third kind
ellipticEComplete and incomplete elliptic integrals of the second kind
ellipticFIncomplete elliptic integral of the first kind
ellipticKComplete elliptic integral of the first kind
ellipticNomeElliptic nome function
ellipticPiComplete and incomplete elliptic integrals of the third kind
jacobiAMJacobi amplitude function
jacobiCDJacobi CD elliptic function
jacobiCNJacobi CN elliptic function
jacobiCSJacobi CS elliptic function
jacobiDCJacobi DC elliptic function
jacobiDNJacobi DN elliptic function
jacobiDSJacobi DS elliptic function
jacobiNCJacobi NC elliptic function
jacobiNDJacobi ND elliptic function
jacobiNSJacobi NS elliptic function
jacobiSCJacobi SC elliptic function
jacobiSDJacobi SD elliptic function
jacobiSNJacobi SN elliptic function
jacobiZetaJacobi zeta function
diracDirac delta function
heavisideHeaviside step function
kroneckerDeltaKronecker delta function
rectangularPulseRectangular pulse function
triangularPulseTriangular pulse function
airyAiry function
besseliModified Bessel function of the first kind
besseljBessel function of the first kind
besselkModified Bessel function of the second kind
besselyBessel function of the second kind
hypergeomHypergeometric function
kummerUConfluent hypergeometric Kummer U function
meijerGMeijer G-function
whittakerMWhittaker M function
whittakerWWhittaker W function
lambertwLambert W function
wrightOmegaWright omega function

Numbers and Precision

digitsChange variable precision used
doubleConvert symbolic values to MATLAB double precision
vpaVariable-precision arithmetic
ceilRound symbolic matrix toward positive infinity
conjSymbolic complex conjugate
fixRound toward zero
floorRound symbolic matrix toward negative infinity
fracSymbolic matrix element-wise fractional parts
imagImaginary part of complex number
maxLargest elements
minSmallest elements
realReal part of complex number
roundSymbolic matrix element-wise round

Number Theory

bernoulliBernoulli numbers and polynomials
divisorsDivisors of integer or expression
eulerEuler numbers and polynomials
fibonacciFibonacci numbers
gcdGreatest common divisor
harmonicHarmonic function (harmonic number)
lcmLeast common multiple
modSymbolic modulus after division
nextprimeNext prime number
prevprimePrevious prime number
quoremQuotient and remainder
remRemainder after division

Graphics

fcontourPlot contours
fimplicitPlot implicit symbolic equation or function
fimplicit3Plot 3-D implicit equation or function
fmeshPlot 3-D mesh
fplotPlot symbolic expression or function
fplot3Plot 3-D parametric curve
fsurfPlot 3-D surface
ezcontourContour plotter
ezcontourfFilled contour plotter
ezmesh3-D mesh plotter
ezmeshcCombined mesh and contour plotter
ezplotPlot symbolic expression, equation, or function
ezplot33-D parametric curve plotter
ezpolarPolar coordinate plotter
ezsurfPlot 3-D surface
ezsurfcCombined surface and contour plotter

Code Generation

matlabFunctionConvert symbolic expression to function handle or file
matlabFunctionBlockConvert symbolic expression to MATLAB function block
simscapeEquationConvert symbolic expressions to Simscape language equations
symReadSSCParametersLoad parameters from Simscape component
symReadSSCVariablesLoad variables from Simscape component
symWriteSSCCreate new Simscape component
ccodeC code representation of symbolic expression
fortranFortran representation of symbolic expression
latexLaTeX form of symbolic expression
texlabelTeX representation of symbolic expression

MATLAB and MuPAD Integration

MuPAD Function Calls

evalinEvaluate MuPAD expressions without specifying their arguments
fevalEvaluate MuPAD expressions specifying their arguments
readRead MuPAD program file into symbolic engine

MuPAD Files and Interfaces

allMuPADNotebooksAll open notebooks
closeClose MuPAD notebook
docGet help for MuPAD functions
evaluateMuPADNotebookEvaluate MuPAD notebook
mupadStart MuPAD notebook
mupadNotebookTitleWindow title of MuPAD notebook
mupadwelcomeStart MuPAD interfaces
openmnOpen MuPAD notebook
openmuOpen MuPAD program file
openxvcOpen MuPAD uncompressed graphics file (XVC)
openxvzOpen MuPAD compressed graphics file (XVZ)

Variables and Expressions Exchange

getVarGet variable from MuPAD notebook
setVarAssign variable in MuPAD notebook

MuPAD Engine Commands

clear allRemove items from MATLAB workspace and reset MuPAD engine
resetClose MuPAD engine
symengineReturn symbolic engine

MuPAD to MATLAB Code Conversion

convertMuPADNotebookConvert MuPAD notebook to MATLAB live script
Was this topic helpful?