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 right-angled triangle to ratios of two side lengths
HyperbolicFunction
MonotonicFunction A function that is either entirely non-increasing, or entirely non-decreasing
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 non-negative 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 non-zero 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 non-zero 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