Numeric Domains
Domain 
Notation 
Description 
AlgebraicNumber 
\[ \mathbb{A} \] 
Elements are the root of a polynomial 
ComplexNumber 
\(\mathbb{C}\) 
A real or imaginary number 
Integer 
\(\mathbb{Z}\) 
The set of whole numbers and their additive inverse \(\lbrace \ldots 3, 2, 1,0, 1, 2, 3\ldots\rbrace\) 
NegativeInteger 
\( \Z^ \) 
Integers \( \lt 0 \) 
NegativeNumber 
\( \R^ \) 
Real numbers \( \lt 0 \) 
NonNegativeInteger 
\( \Z^{0+} \) 
Integers \( \geq 0 \) 
NonNegativeNumber 
\( \R^{0+} \) 
Real numbers \( \geq 0 \) 
NonPositiveInteger 
\( \Z^{0} \) 
Integers \( \leq 0 \) 
NonPositiveNumber 
\( \R^{0} \) 
Real numbers \( \leq 0 \) 
Number 

Any number, real or complex 
PositiveInteger 
\( \Z^{+} \) 
Integers \( \gt 0 \) 
PositiveNumber 
\( \R^{+} \) 
Real numbers \( \gt 0 \) 
RationalNumber 
\(\mathbb{Q}\) 
A number which can be expressed as the quotient \(p / q\) of two integers \(p, q \in \mathbb{Z}\). 
RealNumber 
\(\mathbb{R}\) 

TranscendentalNumber 
\[ \mathbb{T} \] 
Real numbers that are not algebraic 
Function Domains
Domain 
Description 
ContinuousFunction 
A continuous function is a function that has no abrupt change in value (no discontinuity). The Weirestrass function is continuous, but not differentiable 
TranscendentalFunction 
A function not expressible as a finite combination of the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extracting a root. Example: "Log", "Sin"… 
AlgebraicFunction 
A function that can be defined as the root of a polynomial equation 
PeriodicFunction 
A function that repeats its values at regular intervals 
TrigonometricFunction 
Real functions which relate an angle of a rightangled triangle to ratios of two side lengths 
HyperbolicFunction 

MonotonicFunction 
A function that is either entirely nonincreasing, or entirely nondecreasing 
StrictMonotonicFunction 

DifferentiableFunction 
A function whose derivative exists at each point in its domain 
InfinitelyDifferentiableFunction 

RationalFunction 
A function that can be expressed as the ratio of two polynomials 
PolynomialFunction 
A function expressed only with the operations of addition, subtraction, multiplication, and nonnegative integer exponentiation 
QuadraticFunction 
A function of the form \( x \mapsto \ ax^2+ bx + c\) 
LinearFunction 
A function that is the product of an argument plus a constant: \(x \mapsto ax+ b\) 
ConstantFunction 
A function that always return the same value \(x \mapsto c\) 
MonotonicFunction 

StrictMonotonicFunction 

Predicate 
A function with a codomain of MaybeBoolean 
LogicalFunction 
A predicate whose arguments are in the MaybeBoolean domain, for example the domain of And is LogicalFunction 
Tensor Domains
Domain 
Description 
ComplexTensor 
A tensor whose elements are complex numbers 
RealTensor 
A tensor whose elements are real numbers 
IntegerTensor 
A tensor whose elements are integers 
LogicalTensor 
A tensor whose elements are 0 or 1 
Scalar 
A tensor of rank 0 
Vector
Row
Column 
A tensor of rank 1. The argument of the parametric version specifies the number of elements in the vector. 
Matrix 
A tensor of rank 2. The argument of the parametric version specifies the number of rows and columns in the matrix. 
Quaternion 
A \(2\times2\) matrix of complex elements. Quaternions are commonly used to represent vectors in 3D space (\(\mathbb{R}^3\)) 
SquareMatrix 
A tensor with the same number of rows and columns 
MonomialMatrix 
A square matrix with exactly one nonzero entry in each row and column 
OrthogonalMatrix 
A real square matrix whose transpose is equal to its inverse: \(Q^{\mathrm{T}}=Q^{1}\) 
PermutationMatrix 
A square matrix with with exactly one nonzero entry in each row and column 
DiagonalMatrix 
A matrix in which the elements outside the main diagonal are zero 
IdentityMatrix 
A diagonal matrix whose diagonal elements are 1 
ZeroMatrix 
A matrix whose elements are 0 
SymmetricMatrix 
A real matrix that is equal to its transpose 
HermitianMatrix 
A complex matrix that is equal to its conjugate transpose 

Other Domains
Domain 
Description 
Boolean 
True or False 
Domain 
The domain of all the domains 
MaybeBoolean 
True False or Maybe 
ParametricDomain 
The domain of all the parametric domains, that is the functions that can define a domain 
String 
A string of Unicode characters 
Symbol 
A string used to represent the name of a constant, variable or function in a MathJSON expression 