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#############################################################################
##
#W proto.gd GAP library Andrew Solomon
##
#H @(#)$Id: proto.gd,v 4.5 2002/04/15 10:05:13 sal Exp $
##
#Y Copyright (C) 1997, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany
#Y (C) 1998 School Math and Comp. Sci., University of St. Andrews, Scotland
#Y Copyright (C) 2002 The GAP Group
##
## Declarations of utilities for fast prototyping of new GAP objects.
##
Revision.proto_gd :=
"@(#)$Id: proto.gd,v 4.5 2002/04/15 10:05:13 sal Exp $";
##########################################################################
##
#F ArithmeticElementCreator(<spec>)
##
## offers a simple interface to create new arithmetic elements by providing
## functions that perform addition, multiplication and so forth, conforming to
## the specification <spec>. `ArithmeticElementCreator'
## creates a new category, representation and family for the new arithmetic
## elements being defined, and returns a function which takes the
## ``defining data'' of an element and returns the corresponding new
## arithmetic element.
##
## <spec> is a record with one or more of the following components:
## \beginitems
## `ElementName'&a string used to identify the new type of object. A global
## identifier `Is<ElementName>' will be defined to indicate a category for
## these now objects. (Therefore it is not clever to have blanks in the
## name). Also a collections category is defined. (You will get an error
## message if the identifier `Is<ElementName>' is already defined.)
##
## `Equality', `LessThan', `One', `Zero', `Multiplication', `Inverse',
## `Addition', `AdditiveInverse'& functions defining the arithmetic
## operations. The functions interface on the level of ``defining data'',
## the actual methods installed will perform the unwrapping and wrapping as
## objects. Components are optional, but of course if no multiplication is
## defined elements cannot be multiplied and so forth.
##
## &There are default methods for `Equality' and `LessThan' which simply
## calculate on the defining data. If one is defined, it must be ensured
## that the other is compatible (so that $a \< b$ implies not($a = b$))
##
## `Print' & a function which prints the object. By default, just
## the defining data is printed.
##
## `MathInfo' & filters determining the
## mathematical properties of the elements created. A typical value is for
## example `IsMultiplicativeElementWithInverse' for group elements.
##
## `RepInfo' & filters determining the representational
## properties of the elements created. The objects created are always
## component objects, so in most cases the only reasonable option is
## `IsAttributeStoringRep' to permit the storing of attributes.
## \enditems
## All components are optional and will be filled in with default values
## (though of course an empty record will not result in useful objects).
##
## Note that the resulting objects are *not equal* to their defining data
## (even though by default they print as only the defining data). The
## operation `UnderlyingElement' can be used to obtain the defining
## data of such an element.
##
DeclareGlobalFunction("ArithmeticElementCreator");
#############################################################################
##
#E
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