HeavisideLambda

The Heaviside-family triangle function: 1 - |x| for -1 <= x <= 1, 0 otherwise.

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

HeavisideLambda(x)max(1 - |x|, 0).

Typed signatures

Type	Package	Applies
(real) -> number	analytic	always

Domain: Elementary functions

Details

• Continuous everywhere, so HeavisideLambda(±1) = 0 falls out of the formula, no special case.
• The same function as UnitTriangle -- Wolfram gives it a second name for the Heaviside/Dirac generalized-function family it belongs to (it is HeavisideTheta convolved with itself).
• N(x, d) past a double's digits keeps the bignum operand and returns $1 - |x|$ in its digits.

Examples

1 more kept as data, checked against the oracles

Basic #

live ↗

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

Zero at the endpoint

live ↗

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

live ↗

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

Scope #

live ↗

In$\mathrm{HeavisideLambda}(2)$Out$0$

Exact rational input, exact rational output

live ↗

In$\mathrm{HeavisideLambda}(\frac{1}{4})$Out$\frac{3}{4}$

An exact irrational input: 1 - |v| stays exact

live ↗

In$\mathrm{HeavisideLambda}(\frac{π}{4})$Out$1-\frac{π}{4}$

Known value · 1 - |v| for |v| = π/4 < 1

Matrix function of the triangle function, with entries $0$ and $\frac12$

live ↗

In$\mathrm{MatrixFunction}(\mathrm{HeavisideLambda}, \bigl\lbrack\bigl\lbrack-1, 0\bigr\rbrack, \bigl\lbrack-\frac{1}{2}, \frac{1}{2}\bigr\rbrack\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack0, 0\bigr\rbrack, \bigl\lbrack-\frac{1}{6}, \frac{1}{2}\bigr\rbrack\bigr\rbrack$

live ↗

In$N(\mathrm{HeavisideLambda}(\frac{5}{17}), 50)$Out$0.\overline{7058823529411764}$

About

Examples	9
Checked against	Wolfram Language 9 agree
Crosswalk	Wolfram Language