[Om3] Binding Integral symbols (was [Fwd: MathML CDs])
Michael Kohlhase
m.kohlhase at jacobs-university.de
Thu Jul 5 06:14:17 CEST 2007
Dear James,
could you explain what you have done to the CDs, I have had a short look
at integration, which I consider the most pressing problem in the
alignment. The situation I see is the following: MathML has a binder
symbol for integration and OpenMath an appliccative one. (I see that you
have added an indefinite integral to the CD below to account for the two
usages of <int> in MathML).
I think that the binding symbol for integrals is important to support, I
mean a usage of the following form:
<OMBIND>
<OMS name="int" cd="newint"/>
<OMBVAR><OMV name="x"/></OMBVAR>
<OMA><OMS cd="specfun1" name="sin"/><OMV name="x"/></OMA>
</OMBIND>
This usage of the integral allows to view it as an operation on an
expression with a (bound) variable and does not force one to use the
\lambda (which in my recollection mathematicians do not like, and I do
not like, as I want to be able to use integration in logics that do not
supply a \lambda). So I think we need a symbol for binding integral.
Please also see the my first e-mail to the list
[http://openmath.org/pipermail/om3/2007-June/000002.html], if we adopt
having more than one role per symbol, then we could use the same symbol
for the binding usage above and the apliccative below, and get by with
one symbol.
<OMA>
<OMS name="int" cd="newint"/>
<OMBIND>
<OMS cd="fn1" name="lambda"/>
<OMBVAR><OMV name="x"/></OMBVAR>
<OMA><OMS cd="specfun1" name="sin"/><OMV name="x"/></OMA>
</OMBIND>
</OMA>
I think that we need to support both usages in the aligned OM/MathML
collection.
I am using the CD newint in my examples here to characterize my
proposal. Anything I am saying also applies to other binding symbols
like max, lim, ... and even the MathML symbols union, ... which can be
used in a binding form to represent terms like \bigcup_{i=1}^n S_i. So
we should really discuss this.
I will go into a discussion of the definite integrals in a separate e-mail.
Michael
Michael Kohlhase wrote:
> Dear James,
>
> we should use the OM3 mailing list, so I am forwarding this here.
>
> Michael
>
>
> ------------------------------------------------------------------------
>
> Subject:
> MathML CDs
> From:
> Professor James Davenport <jhd at cs.bath.ac.uk>
> Date:
> Tue, 3 Jul 2007 17:43:45 +0100 (BST)
> To:
> m.kohlhase at iu-bremen.de, olga.caprotti at helsinki.fi
>
> To:
> m.kohlhase at iu-bremen.de, olga.caprotti at helsinki.fi
> CC:
> James Davenport <jhd at cs.bath.ac.uk>
>
>
> Enclosed p,lease find very much a first cut an integration for MathML.
> Ignore differentiation: I haven't really looked at that yet.
> Olga thought we might have a skype confernce call: at your times, I should
> be in 10-12 and 3.30-6 tomorrow.
> James
> ------------------------------------------------------------------------
>
> <CDSignatures xmlns="http://www.openmath.org/OpenMathCDS" type="sts" cd="calculus1" >
> <CDSStatus> official </CDSStatus>
>
> <CDSComment>
> Date: 1999-04-13
> Author: David Carlisle
> </CDSComment>
>
>
> <Signature name="diff" >
> <OMOBJ xmlns="http://www.openmath.org/OpenMath">
> <OMA>
> <OMS name="mapsto" cd="sts" />
> <OMA>
> <OMS name="mapsto" cd="sts" />
> <OMS name="Object" cd="sts" />
> <OMS name="Object" cd="sts" />
> </OMA>
> <OMA>
> <OMS name="mapsto" cd="sts" />
> <OMS name="Object" cd="sts" />
> <OMS name="Object" cd="sts" />
> </OMA>
> </OMA>
> </OMOBJ>
> </Signature>
>
> <Signature name="nthdiff" >
> <OMOBJ xmlns="http://www.openmath.org/OpenMath">
> <OMA>
> <OMS name="mapsto" cd="sts" />
> <OMS name="Z" cd="setname1" />
> <OMA>
> <OMS name="mapsto" cd="sts" />
> <OMS name="Object" cd="sts" />
> <OMS name="Object" cd="sts" />
> </OMA>
> <OMA>
> <OMS name="mapsto" cd="sts" />
> <OMS name="Object" cd="sts" />
> <OMS name="Object" cd="sts" />
> </OMA>
> </OMA>
> </OMOBJ>
> </Signature>
>
>
>
>
>
> <Signature name="partialdiff" >
> <OMOBJ xmlns="http://www.openmath.org/OpenMath">
> <OMA>
> <OMS name="mapsto" cd="sts" />
> <OMV name="VariableList" />
> <OMA>
> <OMS name="mapsto" cd="sts" />
> <OMA>
> <OMS name="nary" cd="sts"/>
> <OMS name="Object" cd="sts"/>
> </OMA>
> <OMS name="Object" cd="sts"/>
> </OMA>
> <OMA>
> <OMS name="mapsto" cd="sts" />
> <OMA>
> <OMS name="nary" cd="sts"/>
> <OMS name="Object" cd="sts"/>
> </OMA>
> <OMS name="Object" cd="sts"/>
> </OMA>
> </OMA>
> </OMOBJ>
> </Signature>
>
>
> <Signature name="lowlimit" >
> <OMOBJ xmlns="http://www.openmath.org/OpenMath">
> <OMA>
> <OMS name="mapsto" cd="sts" />
> <OMV name="intqualifier"/>
> <OMS name="Object" cd="sts" />
> </OMA>
> </OMOBJ>
> </Signature>
>
> <Signature name="uplimit" >
> <OMOBJ xmlns="http://www.openmath.org/OpenMath">
> <OMA>
> <OMS name="mapsto" cd="sts" />
> <OMV name="intqualifier"/>
> <OMS name="Object" cd="sts" />
> </OMA>
> </OMOBJ>
> </Signature>
>
>
> <Signature name="int" >
> <OMOBJ xmlns="http://www.openmath.org/OpenMath">
> <OMA>
> <OMS name="mapsto" cd="sts" />
> <OMS name="Object" cd="sts" />
> <OMS name="Object" cd="sts" />
> <OMA>
> <OMS name="nassoc" cd="sts"/>
> <OMV name="intqualifier"/>
> </OMA>
> </OMA>
> </OMOBJ>
> </Signature>
>
>
> </CDSignatures>
>
> ------------------------------------------------------------------------
>
> <CD xmlns="http://www.openmath.org/OpenMathCD">
>
> <CDComment>
>
> 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.
> </CDComment>
>
> <CDName> calcmml1 </CDName>
> <CDBase>http://www.openmath.org/cd</CDBase>
> <CDURL> http://www.openmath.org/cd/calcmml1.ocd </CDURL>
> <CDReviewDate>2008-03-30</CDReviewDate>
> <CDStatus> experimental </CDStatus>
> <CDDate>2007-07-01</CDDate>
> <CDVersion>1</CDVersion>
> <CDRevision>0</CDRevision>
> <Description>
> This CD is intended to be compatible with the calculus operations
> in Content MathML, unlike calculus1 more in 'letter' than in spirit.
>
> Integration is just for the univariate case and is either definite
> or indefinite, but depending on qualifiers, unlike the 'proper'
> calculus1.
> </Description>
>
> <CDDefinition>
> <Name> diff </Name>
> <Role>application</Role>
> <Description>
> This symbol is used to express ordinary differentiation of a unary
> function. The single argument is the unary function.
> </Description>
>
> <CMP>
> diff(lambda y:a(y) + b(y))(x) = diff(lambda y:a(y))(x) + diff(lambda y:b(y))(x)
> </CMP>
>
> <FMP>
> <OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
> <OMA>
> <OMS cd="relation1" name="eq"/>
> <OMA>
> <OMA>
> <OMS cd="calculus1" name="diff"/>
> <OMBIND>
> <OMS cd="fns1" name="lambda"/>
> <OMBVAR>
> <OMV name="y"/>
> </OMBVAR>
> <OMA>
> <OMS cd="arith1" name="plus"/>
> <OMA>
> <OMV name="a"/>
> <OMV name="y"/>
> </OMA>
> <OMA>
> <OMV name="b"/>
> <OMV name="y"/>
> </OMA>
> </OMA>
> </OMBIND>
> </OMA>
> <OMV name="x"/>
> </OMA>
> <OMA>
> <OMS cd="arith1" name="plus"/>
> <OMA>
> <OMA>
> <OMS cd="calculus1" name="diff"/>
> <OMBIND>
> <OMS cd="fns1" name="lambda"/>
> <OMBVAR>
> <OMV name="y"/>
> </OMBVAR>
> <OMA>
> <OMV name="a"/>
> <OMV name="y"/>
> </OMA>
> </OMBIND>
> </OMA>
> <OMV name="x"/>
> </OMA>
> <OMA>
> <OMA>
> <OMS cd="calculus1" name="diff"/>
> <OMBIND>
> <OMS cd="fns1" name="lambda"/>
> <OMBVAR>
> <OMV name="y"/>
> </OMBVAR>
> <OMA>
> <OMV name="b"/>
> <OMV name="y"/>
> </OMA>
> </OMBIND>
> </OMA>
> <OMV name="x"/>
> </OMA>
> </OMA>
> </OMA>
> </OMOBJ>
> </FMP>
>
> <CMP>
> diff(lambda y:a(y) * b(y))(x) = diff(lambda y:a(y))(x) * b(x) +
> a(x) * diff(lambda y:b(y))(x)
> </CMP>
>
> <FMP>
> <OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
> <OMA>
> <OMS cd="relation1" name="eq"/>
> <OMA>
> <OMA>
> <OMS cd="calculus1" name="diff"/>
> <OMBIND>
> <OMS cd="fns1" name="lambda"/>
> <OMBVAR>
> <OMV name="y"/>
> </OMBVAR>
> <OMA>
> <OMS cd="arith1" name="times"/>
> <OMA>
> <OMV name="a"/>
> <OMV name="y"/>
> </OMA>
> <OMA>
> <OMV name="b"/>
> <OMV name="y"/>
> </OMA>
> </OMA>
> </OMBIND>
> </OMA>
> <OMV name="x"/>
> </OMA>
> <OMA>
> <OMS cd="arith1" name="plus"/>
> <OMA>
> <OMS cd="arith1" name="times"/>
> <OMA>
> <OMA>
> <OMS cd="calculus1" name="diff"/>
> <OMBIND>
> <OMS cd="fns1" name="lambda"/>
> <OMBVAR>
> <OMV name="y"/>
> </OMBVAR>
> <OMA>
> <OMV name="a"/>
> <OMV name="y"/>
> </OMA>
> </OMBIND>
> </OMA>
> <OMV name="x"/>
> </OMA>
> <OMA>
> <OMV name="b"/>
> <OMV name="x"/>
> </OMA>
> </OMA>
> <OMA>
> <OMS cd="arith1" name="times"/>
> <OMA>
> <OMV name="a"/>
> <OMV name="x"/>
> </OMA>
> <OMA>
> <OMA>
> <OMS cd="calculus1" name="diff"/>
> <OMBIND>
> <OMS cd="fns1" name="lambda"/>
> <OMBVAR>
> <OMV name="y"/>
> </OMBVAR>
> <OMA>
> <OMV name="b"/>
> <OMV name="y"/>
> </OMA>
> </OMBIND>
> </OMA>
> <OMV name="x"/>
> </OMA>
> </OMA>
> </OMA>
> </OMA>
> </OMOBJ>
> </FMP>
>
> <Example>
> This represents the equation:
> derivative(x + 1.0) = 1.0
> <OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
> <OMA>
> <OMS cd="relation1" name="eq"/>
> <OMA>
> <OMA>
> <OMS cd="calculus1" name="diff"/>
> <OMBIND>
> <OMS cd="fns1" name="lambda"/>
> <OMBVAR>
> <OMV name="x"/>
> </OMBVAR>
> <OMA>
> <OMS cd="arith1" name="plus"/>
> <OMV name="x"/>
> <OMF dec="1.0"/>
> </OMA>
> </OMBIND>
> </OMA>
> <OMV name="y"/>
> </OMA>
> <OMF dec="1.0"/>
> </OMA>
> </OMOBJ>
> </Example>
> </CDDefinition>
>
> <CDDefinition>
> <Name> nthdiff </Name>
> <Role>application</Role>
> <Description>
> This symbol is used to express the nth-iterated ordinary differentiation of
> a unary function. The first argument is n, and the second the unary function.
> </Description>
>
> <FMP>
> <OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
> <OMA>
> <OMS name="eq" cd="relation1"/>
> <OMA>
> <OMS name="nthdiff" cd="calculus1"/>
> <OMS name="zero" cd="alg1"/>
> <OMV name="f"/>
> </OMA>
> <OMV name="f"/>
> </OMA>
> </OMOBJ>
> </FMP>
>
> <FMP>
> <OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
> <OMA>
> <OMS name="eq" cd="relation1"/>
> <OMA>
> <OMS name="nthdiff" cd="calculus1"/>
> <OMA>
> <OMS name="plus" cd="arith1"/>
> <OMV name="n"/>
> <OMS name="one" cd="alg1"/>
> </OMA>
> <OMV name="f"/>
> </OMA>
> <OMA>
> <OMS name="diff" cd="calculus1"/>
> <OMA>
> <OMS name="nthdiff" cd="calculus1"/>
> <OMV name="n"/>
> <OMV name="f"/>
> </OMA>
> </OMA>
> </OMA>
> </OMOBJ>
> </FMP>
>
> </CDDefinition>
>
> <CDDefinition>
> <Name> partialdiff </Name>
> <Role>application</Role>
> <Description>
> This symbol is used to express partial differentiation of a function
> of more than one variable. It has two arguments, the first is a list of
> integers which index the variables of the function, the second is the function.
> </Description>
> <Example>
> An example to represent the equation:
> \partial^2{xyz}/ \partial{x}\partial{z} = y
> <OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
> <OMA>
> <OMS cd="relation1" name="eq"/>
> <OMA>
> <OMA>
> <OMS cd="calculus1" name="partialdiff"/>
> <OMA>
> <OMS cd="list1" name="list"/>
> <OMI> 1 </OMI>
> <OMI> 3 </OMI>
> </OMA>
> <OMBIND>
> <OMS cd="fns1" name="lambda"/>
> <OMBVAR>
> <OMV name="x"/>
> <OMV name="y"/>
> <OMV name="z"/>
> </OMBVAR>
> <OMA>
> <OMS cd="arith1" name="times"/>
> <OMV name="x"/>
> <OMV name="y"/>
> <OMV name="z"/>
> </OMA>
> </OMBIND>
> </OMA>
> <OMV name="y"/>
> </OMA>
> <OMV name="y"/>
> </OMA>
> </OMOBJ>
> </Example>
> </CDDefinition>
>
> <CDDefinition>
> <Name> lowlimit </Name>
> <Role>qualifier</Role>
> <Description>
> This symbol is used to represent the lower limit of indefinite integration
> of unary functions.
> </Description>
> </CDDefinition>
>
> <CDDefinition>
> <Name> uplimit </Name>
> <Role>qualifier</Role>
> <Description>
> This symbol is used to represent the upper limit of indefinite integration
> of unary functions.
> </Description>
> </CDDefinition>
>
> <CDDefinition>
> <Name> int </Name>
> <Role>application</Role>
> <Description>
> This symbol is used to represent indefinite integration of unary functions.
> The arguments are the unary function, followed by any qualifiers.
> </Description>
>
> <CMP>
> In single-argument mode, it is equivalent to the calculus1 version
> </CMP>
>
> <FMP type="extensional">
> <OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
> <OMS name="eq" cd="relation1"/>
> <OMA>
> <OMS name="int" cd="calcmml1"/>
> <OMV name="f"/>
> </OMA>
> <OMA>
> <OMS name="int" cd="calculus1"/>
> <OMV name="f"/>
> <OMA>
> </OMA>
> </OMOBJ>
> </FMP>
>
> <CMP> with upper and lower limits, it is equivalent to defint from calculus1.
> unfortunately, it seems that we need to state this both ways round!
> </CMP>
>
> <FMP type="extensional">
> <OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
> <OMS name="eq" cd="relation1"/>
> <OMA>
> <OMS name="int" cd="calcmml1"/>
> <OMV name="f"/>
> <OMA>
> <OMS cd="calcmml1" name="lowlimit"/>
> <OMV name="l"/>
> </OMA>
> <OMA>
> <OMS cd="calcmml1" name="uplimit"/>
> <OMV name="u"/>
> </OMA>
> </OMA>
> <OMA>
> <OMS name="defint" cd="calculus1"/>
> <OMA>
> <OMS cd="interval1" name="interval"/>
> <OMV name="l"/>
> <OMV name="u"/>
> </OMA>
> <OMV name="f"/>
> <OMA>
> </OMOBJ>
> </FMP>
>
> <FMP type="extensional">
> <OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
> <OMS name="eq" cd="relation1"/>
> <OMA>
> <OMS name="int" cd="calcmml1"/>
> <OMV name="f"/>
> <OMA>
> <OMS cd="calcmml1" name="uplimit"/>
> <OMV name="u"/>
> </OMA>
> <OMA>
> <OMS cd="calcmml1" name="lowlimit"/>
> <OMV name="l"/>
> </OMA>
> </OMA>
> <OMA>
> <OMS name="defint" cd="calculus1"/>
> <OMA>
> <OMS cd="interval1" name="interval"/>
> <OMV name="l"/>
> <OMV name="u"/>
> </OMA>
> <OMV name="f"/>
> <OMA>
> </OMOBJ>
> </FMP>
> </CDDefinition>
>
>
>
>
> <CDDefinition>
> <Name> defint </Name>
> <Role>application</Role>
> <Description>
> This symbol is used to represent definite integration of unary
> functions. It takes two arguments; the first being the range (e.g. a
> set) of integration, and the second the function.
> </Description>
>
> <CMP> for all a,b | integral from a to b = -integral from b to a </CMP>
>
> <FMP>
> <OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
> <OMBIND>
> <OMS cd="quant1" name="forall"/>
> <OMBVAR>
> <OMV name="a"/>
> <OMV name="b"/>
> </OMBVAR>
> <OMA>
> <OMS cd="relation1" name="eq"/>
> <OMA>
> <OMS cd="calculus1" name="defint"/>
> <OMA>
> <OMS cd="interval1" name="interval"/>
> <OMV name="a"/>
> <OMV name="b"/>
> </OMA>
> <OMBIND>
> <OMS cd="fns1" name="lambda"/>
> <OMBVAR>
> <OMV name="x"/>
> </OMBVAR>
> <OMA>
> <OMV name="f"/>
> <OMV name="x"/>
> </OMA>
> </OMBIND>
> </OMA>
> <OMA>
> <OMS cd="arith1" name="unary_minus"/>
> <OMA>
> <OMS cd="calculus1" name="defint"/>
> <OMA>
> <OMS cd="interval1" name="interval"/>
> <OMV name="b"/>
> <OMV name="a"/>
> </OMA>
> <OMBIND>
> <OMS cd="fns1" name="lambda"/>
> <OMBVAR>
> <OMV name="x"/>
> </OMBVAR>
> <OMA>
> <OMV name="f"/>
> <OMV name="x"/>
> </OMA>
> </OMBIND>
> </OMA>
> </OMA>
> </OMA>
> </OMBIND>
> </OMOBJ>
> </FMP>
>
> <CMP>
> for all a < b < c | integral over [a,c] = integral over [a,b] +
> integral over [b,c]
> </CMP>
>
> <FMP>
> <OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
> <OMBIND>
> <OMS cd="quant1" name="forall"/>
> <OMBVAR>
> <OMV name="a"/>
> <OMV name="b"/>
> <OMV name="c"/>
> </OMBVAR>
> <OMA>
> <OMS cd="logic1" name="implies"/>
> <OMA>
> <OMS cd="logic1" name="and"/>
> <OMA>
> <OMS cd="relation1" name="lt"/>
> <OMV name="a"/>
> <OMV name="b"/>
> </OMA>
> <OMA>
> <OMS cd="relation1" name="lt"/>
> <OMV name="b"/>
> <OMV name="c"/>
> </OMA>
> </OMA>
> <OMA>
> <OMS cd="relation1" name="eq"/>
> <OMA>
> <OMS cd="calculus1" name="defint"/>
> <OMA>
> <OMS cd="interval1" name="interval"/>
> <OMV name="a"/>
> <OMV name="c"/>
> </OMA>
> <OMBIND>
> <OMS cd="fns1" name="lambda"/>
> <OMBVAR>
> <OMV name="x"/>
> </OMBVAR>
> <OMA>
> <OMV name="f"/>
> <OMV name="x"/>
> </OMA>
> </OMBIND>
> </OMA>
> <OMA>
> <OMS cd="arith1" name="plus"/>
> <OMA>
> <OMS cd="calculus1" name="defint"/>
> <OMA>
> <OMS cd="interval1" name="interval"/>
> <OMV name="a"/>
> <OMV name="b"/>
> </OMA>
> <OMBIND>
> <OMS cd="fns1" name="lambda"/>
> <OMBVAR>
> <OMV name="x"/>
> </OMBVAR>
> <OMA>
> <OMV name="f"/>
> <OMV name="x"/>
> </OMA>
> </OMBIND>
> </OMA>
> <OMA>
> <OMS cd="calculus1" name="defint"/>
> <OMA>
> <OMS cd="interval1" name="interval"/>
> <OMV name="b"/>
> <OMV name="c"/>
> </OMA>
> <OMBIND>
> <OMS cd="fns1" name="lambda"/>
> <OMBVAR>
> <OMV name="x"/>
> </OMBVAR>
> <OMA>
> <OMV name="f"/>
> <OMV name="x"/>
> </OMA>
> </OMBIND>
> </OMA>
> </OMA>
> </OMA>
> </OMA>
> </OMBIND>
> </OMOBJ>
> </FMP>
> <Example>
> An example to represent the definite integration of sin(x) between the points
> -1.0 and 1.0.
> <OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
> <OMA>
> <OMS cd="calculus1" name="defint"/>
> <OMA>
> <OMS cd="interval1" name="interval"/>
> <OMF dec="-1.0"/>
> <OMF dec="1.0"/>
> </OMA>
> <OMBIND>
> <OMS cd="fns1" name="lambda"/>
> <OMBVAR>
> <OMV name="x"/>
> </OMBVAR>
> <OMA>
> <OMS cd="transc1" name="sin"/>
> <OMV name="x"/>
> </OMA>
> </OMBIND>
> </OMA>
> </OMOBJ>
> </Example>
>
> <Example>
> An example to represent the definite integration of f(x), for x in the
> set C:
> <OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
> <OMA>
> <OMS name="defint" cd="calculus1"/>
> <OMV name="C"/>
> <OMBIND>
> <OMS name="lambda" cd="fns1"/>
> <OMBVAR>
> <OMV name="x"/>
> </OMBVAR>
> <OMA>
> <OMV name="f"/>
> <OMV name="x"/>
> </OMA>
> </OMBIND>
> </OMA>
> </OMOBJ>
>
> </Example>
> </CDDefinition>
>
> </CD>
>
> ------------------------------------------------------------------------
>
> _______________________________________________
> Om3 mailing list
> Om3 at openmath.org
> http://openmath.org/mailman/listinfo/om3
>
--
----------------------------------------------------------------------
Prof. Dr. Michael Kohlhase, Office: Research 1, Room 62
Professor of Computer Science Campus Ring 12,
School of Engineering & Science D-28759 Bremen, Germany
Jacobs University Bremen* tel/fax: +49 421 200-3140/-493140
m.kohlhase at jacobs-university.de http://kwarc.info/kohlhase
skype: m.kohlhase * International University Bremen until Feb. 2007
----------------------------------------------------------------------
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