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URL: https://openmath.org/cd/mathmltypes

⇱ mathmltypes

👁 OpenMath

OpenMath is an extensible standard for representing the semantics of mathematical objects.

https://openmath.org

http://www.openmath.org/cd/mathmltypes.ocd
CD Base:
http://www.openmath.org/cd
CD File:
mathmltypes.ocd
CD as XML Encoded OpenMath:
mathmltypes.omcd
Defines:
complex_cartesian_type, complex_polar_type, constant_type, fn_type, integer_type, list_type, matrix_type, rational_type, real_type, set_type, type, vector_type
Date:
2004-03-30
Version:
3 (Revision 1)
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.
 c) The derived work is distributed under terms that allow the
 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.
 If you have questions about this license please contact the OpenMath
 society at http://www.openmath.org.

 Author: OpenMath Consortium
 SourceURL: https://github.com/OpenMath/CDs

This CD holds symbols denoting various types of numbers, vectors and similar constructs. Principally these are required for compatibility with MathML.

Role:
semantic-attribution
Description:

A symbol to be used within an OpenMath attribute to specify the type of the object.

Example:
The variable z is attributed with a type for complex numbers, to be represented in polar notation. 
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
 <OMATTR>
 <OMATP>
 <OMS cd="mathmltypes" name="type"/>
 <OMS cd="mathmltypes" name="complex_polar_type"/>
 </OMATP>
 <OMV name="z"/>
 </OMATTR>
</OMOBJ>
<math xmlns="http://www.w3.org/1998/Math/MathML">
 <semantics>
 <ci>z</ci>
 <annotation-xml cd="mathmltypes" name="type"><csymbol cd="mathmltypes">complex_polar_type</csymbol></annotation-xml>
 </semantics>
</math>
Attrib([ type complex_polar_type ], z)
$z{mathmltypes.type -> mathmltypes.complex_polar_type}
Signatures:
sts
Role:
constant
Description:

A symbol to be used as the argument of the type symbol to convey the type of an integer.

Example:
The variable z is attributed with a type for integers. 
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
 <OMATTR>
 <OMATP>
 <OMS cd="mathmltypes" name="type"/>
 <OMS cd="mathmltypes" name="integer_type"/>
 </OMATP>
 <OMV name="z"/>
 </OMATTR>
</OMOBJ>
<math xmlns="http://www.w3.org/1998/Math/MathML">
 <semantics>
 <ci>z</ci>
 <annotation-xml cd="mathmltypes" name="type"><csymbol cd="mathmltypes">integer_type</csymbol></annotation-xml>
 </semantics>
</math>
Attrib([ type integer_type ], z)
$z{mathmltypes.type -> mathmltypes.integer_type}
Signatures:
sts
Role:
constant
Description:

A symbol to be used as the argument of the type symbol to convey the type of a real number.

Example:
The variable z is attributed with a type for real numbers. 
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
 <OMATTR>
 <OMATP>
 <OMS cd="mathmltypes" name="type"/>
 <OMS cd="mathmltypes" name="real_type"/>
 </OMATP>
 <OMV name="z"/>
 </OMATTR>
</OMOBJ>
<math xmlns="http://www.w3.org/1998/Math/MathML">
 <semantics>
 <ci>z</ci>
 <annotation-xml cd="mathmltypes" name="type"><csymbol cd="mathmltypes">real_type</csymbol></annotation-xml>
 </semantics>
</math>
Attrib([ type real_type ], z)
$z{mathmltypes.type -> mathmltypes.real_type}
Signatures:
sts
Role:
constant
Description:

A symbol to be used as the argument of the type symbol to convey the type of a rational number.

Example:
The variable z is attributed with a type for rational numbers. 
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
 <OMATTR>
 <OMATP>
 <OMS cd="mathmltypes" name="type"/>
 <OMS cd="mathmltypes" name="rational_type"/>
 </OMATP>
 <OMV name="z"/>
 </OMATTR>
</OMOBJ>
<math xmlns="http://www.w3.org/1998/Math/MathML">
 <semantics>
 <ci>z</ci>
 <annotation-xml cd="mathmltypes" name="type"><csymbol cd="mathmltypes">rational_type</csymbol></annotation-xml>
 </semantics>
</math>
Attrib([ type rational_type ], z)
$z{mathmltypes.type -> mathmltypes.rational_type}
Signatures:
sts
Role:
constant
Description:

A symbol to be used as the argument of the type symbol to convey the type of a complex number specified in terms of its real and imaginary parts.

Example:
The variable z is attributed with a type for complex numbers represented in their Cartesian form. 
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
 <OMATTR>
 <OMATP>
 <OMS cd="mathmltypes" name="type"/>
 <OMS cd="mathmltypes" name="complex_cartesian_type"/>
 </OMATP>
 <OMV name="z"/>
 </OMATTR>
</OMOBJ>
<math xmlns="http://www.w3.org/1998/Math/MathML">
 <semantics>
 <ci>z</ci>
 <annotation-xml cd="mathmltypes" name="type"><csymbol cd="mathmltypes">complex_cartesian_type</csymbol></annotation-xml>
 </semantics>
</math>
Attrib([ type complex_cartesian_type ], z)
$z{mathmltypes.type -> mathmltypes.complex_cartesian_type}
Signatures:
sts
Role:
constant
Description:

A symbol to be used as the argument of the type symbol to convey the type of a complex number specified in terms of its modulus and argument.

Example:
The variable z is attributed with a type for complex numbers represented in their polar form. 
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
 <OMATTR>
 <OMATP>
 <OMS cd="mathmltypes" name="type"/>
 <OMS cd="mathmltypes" name="complex_polar_type"/>
 </OMATP>
 <OMV name="z"/>
 </OMATTR>
</OMOBJ>
<math xmlns="http://www.w3.org/1998/Math/MathML">
 <semantics>
 <ci>z</ci>
 <annotation-xml cd="mathmltypes" name="type"><csymbol cd="mathmltypes">complex_polar_type</csymbol></annotation-xml>
 </semantics>
</math>
Attrib([ type complex_polar_type ], z)
$z{mathmltypes.type -> mathmltypes.complex_polar_type}
Signatures:
sts
Role:
constant
Description:

A symbol to be used as the argument of the type symbol to convey a type for the common constants, pi ~= 3.1415, e ~= 2.718, i = square root of -1, gamma ~= .5772, NaN, infinity (all in the nums cd), true and false (in the logic cd). Also for MathML variables declared to have type constant, as in <ci type="constant">x</ci>.

Example:
The variable z is attributed with a type for constants. 
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
 <OMATTR>
 <OMATP>
 <OMS cd="mathmltypes" name="type"/>
 <OMS cd="mathmltypes" name="constant_type"/>
 </OMATP>
 <OMV name="z"/>
 </OMATTR>
</OMOBJ>
<math xmlns="http://www.w3.org/1998/Math/MathML">
 <semantics>
 <ci>z</ci>
 <annotation-xml cd="mathmltypes" name="type"><csymbol cd="mathmltypes">constant_type</csymbol></annotation-xml>
 </semantics>
</math>
Attrib([ type constant_type ], z)
$z{mathmltypes.type -> mathmltypes.constant_type}
Signatures:
sts
Role:
constant
Description:

A symbol to be used as the argument of the type symbol to convey the type of a (column) vector, an n-tuple of entries.

Example:
The variable z is attributed with a type for vectors. 
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
 <OMATTR>
 <OMATP>
 <OMS cd="mathmltypes" name="type"/>
 <OMS cd="mathmltypes" name="vector_type"/>
 </OMATP>
 <OMV name="z"/>
 </OMATTR>
</OMOBJ>
<math xmlns="http://www.w3.org/1998/Math/MathML">
 <semantics>
 <ci>z</ci>
 <annotation-xml cd="mathmltypes" name="type"><csymbol cd="mathmltypes">vector_type</csymbol></annotation-xml>
 </semantics>
</math>
Attrib([ type vector_type ], z)
$z{mathmltypes.type -> mathmltypes.vector_type}
Signatures:
sts
Role:
constant
Description:

A symbol to be used as the argument of the type symbol to convey the type for a list.

Example:
The variable z is attributed with a type for lists. 
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
 <OMATTR>
 <OMATP>
 <OMS cd="mathmltypes" name="type"/>
 <OMS cd="mathmltypes" name="list_type"/>
 </OMATP>
 <OMV name="z"/>
 </OMATTR>
</OMOBJ>
<math xmlns="http://www.w3.org/1998/Math/MathML">
 <semantics>
 <ci>z</ci>
 <annotation-xml cd="mathmltypes" name="type"><csymbol cd="mathmltypes">list_type</csymbol></annotation-xml>
 </semantics>
</math>
Attrib([ type list_type ], z)
$z{mathmltypes.type -> mathmltypes.list_type}
Signatures:
sts
Role:
constant
Description:

A symbol to be used as the argument of the type symbol to convey the type for a set.

Example:
The variable z is attributed with a type for sets. 
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
 <OMATTR>
 <OMATP>
 <OMS cd="mathmltypes" name="type"/>
 <OMS cd="mathmltypes" name="set_type"/>
 </OMATP>
 <OMV name="z"/>
 </OMATTR>
</OMOBJ>
<math xmlns="http://www.w3.org/1998/Math/MathML">
 <semantics>
 <ci>z</ci>
 <annotation-xml cd="mathmltypes" name="type"><csymbol cd="mathmltypes">set_type</csymbol></annotation-xml>
 </semantics>
</math>
Attrib([ type set_type ], z)
$z{mathmltypes.type -> mathmltypes.set_type}
Signatures:
sts
Role:
constant
Description:

A symbol to be used as the argument of the type symbol to convey the type for a matrix (n tuple of rows, where each row is an m tuple for some m, it should be noted that each row must be the same length).

Example:
The variable z is attributed with a type for matrices. 
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
 <OMATTR>
 <OMATP>
 <OMS cd="mathmltypes" name="type"/>
 <OMS cd="mathmltypes" name="matrix_type"/>
 </OMATP>
 <OMV name="z"/>
 </OMATTR>
</OMOBJ>
<math xmlns="http://www.w3.org/1998/Math/MathML">
 <semantics>
 <ci>z</ci>
 <annotation-xml cd="mathmltypes" name="type"><csymbol cd="mathmltypes">matrix_type</csymbol></annotation-xml>
 </semantics>
</math>
Attrib([ type matrix_type ], z)
$z{mathmltypes.type -> mathmltypes.matrix_type}
Signatures:
sts
Role:
constant
Description:

A symbol to be used as the argument of the type symbol to convey the type for a function name.

Example:
The variable f is attributed to say it represents a function. 
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
 <OMATTR>
 <OMATP>
 <OMS cd="mathmltypes" name="type"/>
 <OMS cd="mathmltypes" name="fn_type"/>
 </OMATP>
 <OMV name="f"/>
 </OMATTR>
</OMOBJ>
<math xmlns="http://www.w3.org/1998/Math/MathML">
 <semantics>
 <ci>f</ci>
 <annotation-xml cd="mathmltypes" name="type"><csymbol cd="mathmltypes">fn_type</csymbol></annotation-xml>
 </semantics>
</math>
Attrib([ type fn_type ], f)
$f{mathmltypes.type -> mathmltypes.fn_type}
Signatures:
sts