Properties of Mathematical Functions & Sequences
TopicOverview »
Function properties such as its domain, period or singularities give additional information about a function or sequence that can be used directly or inform other computations. Similarly, function properties such as its sign, monotonicity or continuity classify functions and enable the use of a whole web of theorems that are true for those classes. Both kinds of function properties can be computed for any expression formed by using special functions, making it easy and efficient to write algorithms based on these high-level concepts rather than covering each individual function.
Domain and Range
FunctionDomain — the domain of a function
FunctionRange — the range of a function
Injectivity and Surjectivity
FunctionInjective — test whether a function is injective or one-to-one
FunctionSurjective — test whether a function is surjective or onto
FunctionBijective — test whether a function is bijective or one-to-one and onto
Inequality Related Properties
FunctionSign — the sign of a function (positive: 
, negative: 
, …)
FunctionMonotonicity — the monotonicity of a function (increasing: 
, decreasing: 
, …)
FunctionConvexity — the convexity of a function (convex: 
, concave: 
, …)
Periodicity Related Properties
FunctionPeriod — the periodicity of a function or sequence
Singularities and Discontinuities
FunctionDiscontinuities — find the discontinuities of a function
FunctionSingularities — find the singularities of a function
FunctionPoles — find the poles of a meromorphic function
Continuous, Holomorphic & Meromorphic
FunctionContinuous — test whether a function is continuous
FunctionAnalytic — test whether a function is analytic
FunctionMeromorphic — test whether a function is meromorphic
Structural Function Classes
PolynomialExpressionQ — structurally test for polynomial expression
RationalExpressionQ — structurally test for rational function expression
Options
Assumptions ▪ GenerateConditions ▪ StrictInequalities ▪ PerformanceGoal