finds the real sign of the function f with variables x1,x2,… over the reals.
finds the real sign with variables restricted to the domain dom.
gives the sign when variables are restricted by the constraints cons.
Details and Options
- Function sign is also known as positive, non-negative, negative, non-positive, strictly positive and strictly negative.
- By default, the following definitions are used:
+1 non-negative, i.e. for all 0 identically zero, i.e. for all -1 non-positive, i.e. for all Indeterminate neither non-negative nor non-positive
- The zero function is both non-negative and non-positive.
- With the setting StrictInequalitiesTrue, the following definitions are used:
+1 positive, i.e. for all -1 negative, i.e. for all Indeterminate neither positive nor negative
- Possible values for dom include: Reals, Integers, PositiveReals, PositiveIntegers, etc. The default is Reals.
- The function f should be a real-valued function for all xi in the domain dom that satisfy the constraints cons.
- cons can contain equations, inequalities or logical combinations of these.
- The following options can be given:
Assumptions $Assumptions assumptions on parameters GenerateConditions True whether to generate conditions on parameters PerformanceGoal $PerformanceGoal whether to prioritize speed or quality StrictInequalities False whether to require a strict sign
- Possible settings for GenerateConditions include:
Automatic nongeneric conditions only True all conditions False no conditions None return unevaluated if conditions are needed
- Possible settings for PerformanceGoal are "Speed" and "Quality".
Examplesopen allclose all
Basic Examples (3)
A function that is not real valued has an Indeterminate sign:
FunctionSign gives a conditional answer here:
By default, FunctionSign may generate conditions on symbolic parameters:
Use PerformanceGoal to avoid potentially expensive computations:
Basic Applications (3)
Probability & Statistics (3)
RegionDistance is always non-negative:
Properties & Relations (2)
Use Integrate to compute an anti-derivative:
Use FunctionContinuous to check that the anti-derivative is continuous:
Use FunctionMonotonicity to verify that the anti-derivative is non-decreasing:
Wolfram Research (2020), FunctionSign, Wolfram Language function, https://reference.wolfram.com/language/ref/FunctionSign.html.
Wolfram Language. 2020. "FunctionSign." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FunctionSign.html.
Wolfram Language. (2020). FunctionSign. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FunctionSign.html