HeavisidePi

The Heaviside-family rectangular pulse: 1 for |x| < 1/2, unevaluated at x = ±1/2, 0 for |x| > 1/2.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageHeavisidePi!↗

HeavisidePi(x)1 inside (-1/2, 1/2), 0 outside [-1/2, 1/2], and unevaluated (stays symbolic) exactly at x = ±1/2.

Typed signatures

Type	Package	Applies
(real) -> number	analytic	always

Domain: Elementary functions

Details

• The same rectangular pulse as UnitBox, but the boundary is left open rather than closed -- UnitBox(±1/2) = 1, HeavisidePi(±1/2) unevaluated. The two heads exist for the two conventions.

Examples

Basic #

live ↗

In$\mathrm{HeavisidePi}(0)$Out$1$

Unevaluated at the boundary -- unlike UnitBox

live ↗

In$\mathrm{HeavisidePi}(\frac{1}{2})$Out$\mathrm{HeavisidePi}(\frac{1}{2})$

live ↗

In$\mathrm{HeavisidePi}(-\frac{1}{2})$Out$\mathrm{HeavisidePi}(-\frac{1}{2})$

Scope #

live ↗

In$\mathrm{HeavisidePi}(1)$Out$0$

Zero outside the support $|x|<\frac12$

live ↗

In$\mathrm{HeavisidePi}(-1)$Out$0$

Equals 1 inside the support

live ↗

In$\mathrm{HeavisidePi}(\frac{1}{4})$Out$1$

The matrix function takes the value at each eigenvalue, here both 0

live ↗

In$\mathrm{MatrixFunction}(\mathrm{HeavisidePi}, \bigl\lbrack\bigl\lbrack-1, 0\bigr\rbrack, \bigl\lbrack0, 1\bigr\rbrack\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack0, 0\bigr\rbrack, \bigl\lbrack0, 0\bigr\rbrack\bigr\rbrack$

About

Examples	7
Checked against	Wolfram Language 6 agree1 differ
Crosswalk	Wolfram Language