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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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<Chapter Label="OpenMathFunctionality">

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<Heading>&OpenMath; functionality in &GAP;</Heading>    

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<Section Label="ViewOpenMath">

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<Heading>Viewing &OpenMath; representation of an object</Heading>

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<#Include Label="OMPrint">

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Producing &OpenMath; representation of polynomials, one may get a warning:

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<Log>

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<![CDATA[

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gap> x:=Indeterminate(Rationals,"x");; y:=Indeterminate(Rationals,"y");;

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gap> OMPrint(x^2+y);

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#I  Warning : polynomial will be printed using its default ring 

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#I  because the default OpenMath polynomial ring is not specified 

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#I  or it is not contained in the default OpenMath polynomial ring.

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#I  You may ignore this or call SetOpenMathDefaultPolynomialRing to fix it.

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<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">

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	<OMA>

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		<OMS cd="polyd1" name="DMP"/>

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		<OMA id="polyring9qiY2oOaiITWUORb" >

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			<OMS cd="polyd1" name="poly_ring_d"/>

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			<OMS cd="setname1" name="Q"/>

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			<OMI>2</OMI>

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		</OMA>

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		<OMA>

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			<OMS cd="polyd1" name="SDMP"/>

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			<OMA>

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				<OMS cd="polyd1" name="term"/>

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				<OMI>1</OMI>

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				<OMI>0</OMI>

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				<OMI>1</OMI>

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			</OMA>

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			<OMA>

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				<OMS cd="polyd1" name="term"/>

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				<OMI>1</OMI>

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				<OMI>2</OMI>

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				<OMI>0</OMI>

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			</OMA>

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		</OMA>

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	</OMA>

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</OMOBJ>

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]]>

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</Log>

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Indeed, now when another polynomial will be printed, it will belong to a

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ring with a different identifier (despite &GAP; will be able to perform

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arithmetical operations on these polynomials like when they belong to the

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same ground ring):

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<Log>

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<![CDATA[

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gap> OMPrint(x+1);

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#I  Warning : polynomial will be printed using its default ring 

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#I  because the default OpenMath polynomial ring is not specified 

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#I  or it is not contained in the default OpenMath polynomial ring.

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#I  You may ignore this or call SetOpenMathDefaultPolynomialRing to fix it.

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<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">

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	<OMA>

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		<OMS cd="polyd1" name="DMP"/>

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		<OMA id="polyring0LqlkhnCyLldcoBl" >

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			<OMS cd="polyd1" name="poly_ring_d_named"/>

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			<OMS cd="setname1" name="Q"/>

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			<OMV name="x"/>

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		</OMA>

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		<OMA>

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			<OMS cd="polyd1" name="SDMP"/>

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			<OMA>

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				<OMS cd="polyd1" name="term"/>

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				<OMI>1</OMI>

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				<OMI>1</OMI>

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			</OMA>

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			<OMA>

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				<OMS cd="polyd1" name="term"/>

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				<OMI>1</OMI>

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				<OMI>0</OMI>

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			</OMA>

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		</OMA>

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	</OMA>

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</OMOBJ>

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]]>

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</Log>

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Thus, the warning means that it is not guaranteed that the polynomial ring

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will have the same identifier <C>&lt;OMA id="polyring..." ></C> when

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another or same polynomial from this ring will be printed next time.

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If this may constitute a problem, for example, if a list of polynomial

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is being exchanged with another system and it is crucial that all of

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them will belong to the same ring, then such ring must be created

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explicitly and then <C>SetOpenMathDefaultPolynomialRing</C> must be

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called:

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<Log>

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<![CDATA[

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gap> x:=Indeterminate(Rationals,"x");; y:=Indeterminate(Rationals,"y");;

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gap> R:=PolynomialRing(Rationals,[x,y]);;

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gap> SetOpenMathDefaultPolynomialRing(R);

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gap> OMPrint(x^2+y);

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<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">

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	<OMA>

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		<OMS cd="polyd1" name="DMP"/>

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		<OMA id="polyring9eNcBGFHXkjl2kWh" >

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			<OMS cd="polyd1" name="poly_ring_d"/>

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			<OMS cd="setname1" name="Q"/>

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			<OMI>2</OMI>

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		</OMA>

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		<OMA>

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			<OMS cd="polyd1" name="SDMP"/>

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			<OMA>

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				<OMS cd="polyd1" name="term"/>

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				<OMI>1</OMI>

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				<OMI>0</OMI>

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				<OMI>0</OMI>

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			</OMA>

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			<OMA>

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				<OMS cd="polyd1" name="term"/>

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				<OMI>1</OMI>

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				<OMI>0</OMI>

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				<OMI>0</OMI>

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			</OMA>

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		</OMA>

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	</OMA>

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</OMOBJ>

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]]>

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</Log>

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Now we can see that both polynomials belong to the ring with the same 

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identifier, and the &OpenMath; representation of the 2nd polynomial 

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properly reflects that it belongs to a polynomial ring with two variables.

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<Log>

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<![CDATA[

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gap> OMPrint(x+1);  

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<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">

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	<OMA>

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		<OMS cd="polyd1" name="DMP"/>

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		<OMR href="#polyring9eNcBGFHXkjl2kWh" />

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		<OMA>

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			<OMS cd="polyd1" name="SDMP"/>

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			<OMA>

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				<OMS cd="polyd1" name="term"/>

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				<OMI>1</OMI>

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				<OMI>0</OMI>

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				<OMI>0</OMI>

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			</OMA>

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			<OMA>

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				<OMS cd="polyd1" name="term"/>

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				<OMI>1</OMI>

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				<OMI>0</OMI>

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				<OMI>0</OMI>

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			</OMA>

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		</OMA>

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	</OMA>

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</OMOBJ> 

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]]>

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</Log>

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<#Include Label="OMString">

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</Section>

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<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->

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<Section Label="Reading OpenMath from streams">

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<Heading>Reading &OpenMath; code from streams and strings</Heading>

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<#Include Label="OMGetObject">

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<#Include Label="EvalOMString">

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</Section>

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<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->

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<Section Label="Writing OpenMath to streams">

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<Heading>Writing &OpenMath; code to streams</Heading>

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While it is possible to read &OpenMath; code directly from a stream,

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writing &OpenMath; to streams uses a different setup. It requires 

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special objects called &OpenMath; <E>writers</E>, which encapsulate 

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streams and may be viewed as transducers accepting &GAP; objects and 

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writing them to a stream in the XML or binary &OpenMath;

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<P/>

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Such setup makes it possible to re-use the same stream for both binary 

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and XML &OpenMath; communication, using different &OpenMath; writers 

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in different calls. It also allows to re-use most of the high-level

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code for &GAP; to &OpenMath; conversion, having separate methods for

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generating binary and XML &OpenMath; only for low-level output 

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(&OpenMath; tags and basic objects). This makes easier adding support 

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to new mathematical objects and private content dictionaries as described 

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in Chapter <Ref Chap="ExtendingOpenMath"/> since it does not require 

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changing the low-level functionality.

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<P/>

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<#Include Label="IsOpenMathWriter">

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<#Include Label="OpenMathXMLWriter">

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<#Include Label="OpenMathBinaryWriter">

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<#Include Label="OMPutObject">

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<#Include Label="OMPlainString">

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</Section>

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<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->

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<Section Label="Utilities">

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<Heading>Utilities</Heading>

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<#Include Label="OMTestXML">

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<#Include Label="OMTestBinary">

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</Section>

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</Chapter>

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