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### 3 Extending the OpenMath package

#### 3.1 Exploring the range of supported symbols

The OpenMath package supports such basic OpenMath objects as integers ( <OMI> ), character strings ( <OMSTR> ) and variables ( <OMVAR> ). Besides that, it supports a number of OpenMath content dictionaries (some of them only partially, dependently on their relevance to GAP). To see which symbols from which content dictionaries are supported for the conversion from OpenMath to GAP, explore the global record OMsymRecord. Its components have names of appropriate CDs, and subcomponents of each component have names of symbols from the corresponding CD. If the value of the component is not equal to fail, then it contains the function or the object which is used for conversion. The following example of the entry for the nums1 CD demonstrates a combination of all possible cases:


gap> Display( OMsymRecord.nums1 );
rec(
NaN := nan,
based_integer := fail,
e := 2.718281828459045,
gamma := fail,
i := E(4),
infinity := infinity,
pi := 3.141592653589793,
rational := function ( x )
return OMgapId( [ OMgap2ARGS( x ), x[1] / x[2] ] )[2];
end )



OMsymRecord contains all symbols for which conversion from OpenMath to GAP is supported except some special symbols related with errors and special procedures from the SCSCP package which are treated separately.

To check quickly if GAP can parse a given OpenMath object, copy the OpenMath code and paste it directly into standard input after the following command:


gap> s:= InputTextUser();; g := OMGetObject(s); CloseStream(s);



The main tool for the conversion from GAP to OpenMath is OMPut( <writer>, <object> ). A number of methods for OMPut are installed in the file openmath/gap/omput.gi.

To check quickly whether the object may be converted to OpenMath, call OMprint for that object, for example:


gap> OMPrint( [ [1..10], ZmodnZObj(2,6), (1,2) ] );
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
<OMA>
<OMS cd="list1" name="list"/>
<OMA>
<OMS cd="interval1" name="integer_interval"/>
<OMI>1</OMI>
<OMI>10</OMI>
</OMA>
<OMA>
<OMS cd="integer2" name="class"/>
<OMI>2</OMI>
<OMI>6</OMI>
</OMA>
<OMA>
<OMS cd="permut1" name="permutation"/>
<OMI>2</OMI>
<OMI>1</OMI>
</OMA>
</OMA>
</OMOBJ>



The package is in the continuous development and will support even more symbols in the future. In the meantime, if you will have any requests for the support for particular symbols, please contact Alexander Konovalov.

#### 3.2 Adding support for private content dictionaries and symbols

There is also a way for the user to extend the package adding support for private and experimental CDs or separate symbols. We allocated the directory openmath/private for this purposes, and currently it contain the file private.g for conversions from OpenMath to GAP and the file private.gi for conversions from GAP to OpenMath for some symbols from private CDs contained in the openmath/cds directory.

In particular, we extended the package with the following private OpenMath symbols:

• group1.group_by_generators which allows us to input and output groups given by their generators as this is a natural way to create groups in GAP;

• semigroup1.semigroup_by_generators and monoid1.monoid_by_generators following the same considerations for semigroups and monoids;

• pcgroup1.pcgroup_by_pcgscode for PcGroups given by their pcgs code and order;

• record1.record for records as they are important data structures which we want to pass in a straightforward manner between different GAP instances;

• transform1.transformation to support transformations, transformation semigroups and their automorphism groups.

The file private.g is loaded from openmath/gap/new.g, and the private.gi is loaded from openmath/gap/read.g. If the user would like to add own code, this may be done either by adding it to these files or by placing additional files in openmath/private directory and load them similarly to private.g and private.gi. We will welcome user's contributions in the form of the code to support existing content dictionaries from the OpenMath web site or private content dictionaries, if they may be interesting for a wider community.

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