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# OpenMath Content Dictionary: piece1

Canonical URL:
http://www.openmath.org/cd/piece1.ocd
CD Base:
http://www.openmath.org/cd
CD File:
piece1.ocd
CD as XML Encoded OpenMath:
piece1.omcd
Defines:
otherwise, piece, piecewise
Date:
2004-03-30
Version:
2
Review Date:
2006-03-30
Status:
official

```
This document is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

The copyright holder grants you permission to redistribute this
document freely as a verbatim copy. Furthermore, the copyright
holder permits you to develop any derived work from this document
provided that the following conditions are met.
a) The derived work acknowledges the fact that it is derived from
this document, and maintains a prominent reference in the
work to the original source.
b) The fact that the derived work is not the original OpenMath
document is stated prominently in the derived work.  Moreover if
both this document and the derived work are Content Dictionaries
then the derived work must include a different CDName element,
chosen so that it cannot be confused with any works adopted by
the OpenMath Society.  In particular, if there is a Content
Dictionary Group whose name is, for example, `math' containing
Content Dictionaries named `math1', `math2' etc., then you should
not name a derived Content Dictionary `mathN' where N is an integer.
However you are free to name it `private_mathN' or some such.  This
is because the names `mathN' may be used by the OpenMath Society
for future extensions.
compilation of derived works, but keep paragraphs a) and b)
intact.  The simplest way to do this is to distribute the derived
work under the OpenMath license, but this is not a requirement.
society at http://www.openmath.org.
```

This CD is intended to be compatible with the corresponding elements in Content MathML 2.

In this CD we give a set of operators for piece-wise defined expressions.

## piecewise

Role:
application
Description:

This operator heads an expression that is being defined piecewise. Its arguments are n objects built with the piece constructor, optionally followed by one built with otherwise constructor.

Example:
$|x|=\left\{\begin{array}{cc}-x& x<0\\ 0& x=0\\ x& \text{otherwise}\end{array}$
Signatures:
sts

 [Next: piece] [Last: otherwise] [Top]

## piece

Role:
application
Description:

This introduces an individual component of a piecewise definition. It has precisely two arguments: the first is the value, and the second is a Boolean (meant to be a predicate) which is true if and only if this piece is to provide the value of the piecewise construct.

Example:
$|x|=\left\{\begin{array}{cc}-x& x<0\\ 0& x=0\\ x& \text{otherwise}\end{array}$
Signatures:
sts

 [Next: otherwise] [Previous: piecewise] [Top]

## otherwise

Role:
application
Description:

This symbol introduces the 'default' value of a piecewise construct. If none of the previous piece constructs can provide the value, this will. It has a single child, the value.

Example:
$|x|=\left\{\begin{array}{cc}-x& x<0\\ 0& x=0\\ x& \text{otherwise}\end{array}$
Signatures:
sts

 [First: piecewise] [Previous: piece] [Top]

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