Piecewise

A conditional value: List of {value, condition} pairs, tried in order, plus a $default$ (0 when omitted) for when none holds. Provided by @enumeratio/analytic.

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

Piecewise(pairs)pairs is a List of two-element Lists {value, condition}; the default is 0.

Piecewise(pairs, default)same, with an explicit fallback value.

Typed signatures

Type	Package	Applies
(list, expression?) -> expression	analytic	always

Domain: Analytic

Details

• Conditions are tried in list order via ce.verify (a three-valued check against the current assumptions). The first one known True wins, PROVIDED every condition before it is known False — a Piecewise with an undecided earlier condition stays symbolic rather than guessing which branch is really first.
• A condition known False is dropped; if every condition is eliminated this way, the result is $default$.
• PiecewiseExpand produces this head from Abs, Sign, UnitStep, Clip, and 2-argument Max/Min.

Examples

1 more kept as data, checked against the oracles

Basic #

with $x$ still symbolic, both branches are undecided and the call stays as-is

live ↗

In$\mathrm{Piecewise}(\bigl\lbrack\bigl\lbrack1, x\lt0\bigr\rbrack, \bigl\lbrack2, x≥0\bigr\rbrack\bigr\rbrack)$Out$\mathrm{Piecewise}(\bigl\lbrack\bigl\lbrack1, x\lt0\bigr\rbrack, \bigl\lbrack2, 0≤x\bigr\rbrack\bigr\rbrack)$

at $x = -5$ the first condition is True

live ↗

In$\mathrm{ReplaceAll}(\mathrm{Piecewise}(\bigl\lbrack\bigl\lbrack1, x\lt0\bigr\rbrack, \bigl\lbrack2, x≥0\bigr\rbrack\bigr\rbrack), \mathrm{Rule}(x, -5))$Out$1$

at $x = 5$ the second condition is True

live ↗

In$\mathrm{ReplaceAll}(\mathrm{Piecewise}(\bigl\lbrack\bigl\lbrack1, x\lt0\bigr\rbrack, \bigl\lbrack2, x≥0\bigr\rbrack\bigr\rbrack), \mathrm{Rule}(x, 5))$Out$2$

symbolic $x$ again stays undecided, default kept as given

live ↗

In$\mathrm{Piecewise}(\bigl\lbrack\bigl\lbrack x^2, x\lt0\bigr\rbrack\bigr\rbrack, 99)$Out$\mathrm{Piecewise}(\bigl\lbrack\bigl\lbrack x^2, x\lt0\bigr\rbrack\bigr\rbrack, 99)$

Scope #

A double integral over the plane remains unevaluated

live ↗

In$\int_{-∞}^{∞}\int_{-∞}^{∞}\!\mathrm{Piecewise}(\bigl\lbrack\bigl\lbrack1, x^2+y^2\lt1\bigr\rbrack\bigr\rbrack)\, \mathrm{d}x \mathrm{d}y$Out$\int_{-∞}^{∞}\!\int_{-∞}^{∞}\!\mathrm{Piecewise}(\bigl\lbrack\bigl\lbrack1, x^2+y^2\lt1\bigr\rbrack\bigr\rbrack)\, \mathrm{d}y\, \mathrm{d}x$

live ↗

In$\mathrm{Piecewise}(\bigl\lbrack\bigl\lbrack\mathrm{e1}, \mathrm{True}\bigr\rbrack, \bigl\lbrack\mathrm{e2}, \mathrm{d2}\bigr\rbrack, \bigl\lbrack\mathrm{e3}, \mathrm{d3}\bigr\rbrack\bigr\rbrack, k)$Out$\mathrm{e1}$

live ↗

In$\mathrm{Piecewise}(\bigl\lbrack\bigl\lbrack\mathrm{e1}, \mathrm{d1}\bigr\rbrack, \bigl\lbrack\mathrm{e2}, \mathrm{d2}\bigr\rbrack, \bigl\lbrack\mathrm{e3}, \mathrm{True}\bigr\rbrack, \bigl\lbrack\mathrm{e4}, \mathrm{d4}\bigr\rbrack, \bigl\lbrack\mathrm{e5}, \mathrm{d5}\bigr\rbrack\bigr\rbrack, k)$Out$\mathrm{Piecewise}(\bigl\lbrack\bigl\lbrack\mathrm{e1}, \mathrm{d1}\bigr\rbrack, \bigl\lbrack\mathrm{e2}, \mathrm{d2}\bigr\rbrack, \bigl\lbrack\mathrm{e3}, \mathrm{True}\bigr\rbrack\bigr\rbrack, k)$

live ↗

In$\mathrm{Piecewise}(\bigl\lbrack\bigl\lbrack\mathrm{e1}, \mathrm{d1}\bigr\rbrack, \bigl\lbrack\mathrm{e2}, \mathrm{d2}\bigr\rbrack, \bigl\lbrack\mathrm{e3}, \mathrm{False}\bigr\rbrack, \bigl\lbrack\mathrm{e4}, \mathrm{d4}\bigr\rbrack, \bigl\lbrack\mathrm{e5}, \mathrm{d5}\bigr\rbrack\bigr\rbrack, k)$Out$\mathrm{Piecewise}(\bigl\lbrack\bigl\lbrack\mathrm{e1}, \mathrm{d1}\bigr\rbrack, \bigl\lbrack\mathrm{e2}, \mathrm{d2}\bigr\rbrack, \bigl\lbrack\mathrm{e4}, \mathrm{d4}\bigr\rbrack, \bigl\lbrack\mathrm{e5}, \mathrm{d5}\bigr\rbrack\bigr\rbrack, k)$

About

Examples	9
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