Piecewise

Usage

• Piecewise[{{, }, {, }, ... }] represents a piecewise function with values in the regions defined by the conditions .
• Piecewise[{{, }, ... }, val] uses default value val if none of the apply. The default for val is 0.

Notes

• The are typically inequalities such as a x < b.

• The are evaluated in turn, until one of them is found to yield True.

• If all preceding yield False, then the corresponding to the first that yields True is returned as the value of the piecewise function.

• If any of the preceding do not literally yield False, the Piecewise function is returned in symbolic form.

• Only those explicitly included in the returned form are evaluated.

• Elements of the form {, False} are dropped, as are all elements after the first {, True}.

• Piecewise[{{, }, {, }, ... }] can be input in the form . can be entered as pw or \[Piecewise]. The grid of values and conditions can be constructed by first entering ,, then using (Control-Return) and ,.

• In StandardForm and TraditionalForm, Piecewise[{{, }, {, }, ... }] is normally output as .

Further Examples