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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Andrew Solomon.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## Declarations of utilities for fast prototyping of new GAP objects.
##
##########################################################################
##
#F ArithmeticElementCreator(<spec>)
##
## <#GAPDoc Label="ArithmeticElementCreator">
## <ManSection>
## <Func Name="ArithmeticElementCreator" Arg="spec"/>
##
## <Description>
## offers a simple interface to create new arithmetic elements by providing
## functions that perform addition, multiplication and so forth, conforming
## to the specification <A>spec</A>. <C>ArithmeticElementCreator</C>
## creates a new category, representation and family for the new arithmetic
## elements being defined, and returns a function which takes the
## <Q>defining data</Q> of an element and returns the corresponding new
## arithmetic element.
## <P/>
## <A>spec</A> is a record with one or more of the following components:
## <List>
## <Mark><C>ElementName</C></Mark>
## <Item>
## string used to identify the new type of object. A global
## identifier <C>Is<A>ElementName</A></C> 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
## <C>Is<A>ElementName</A></C> is already defined.)
## </Item>
## <Mark><C>Equality</C>, <C>LessThan</C>, <C>One</C>, <C>Zero</C>,
## <C>Multiplication</C>, <C>Inverse</C>, <C>Addition</C>,
## <C>AdditiveInverse</C></Mark>
## <Item>
## functions defining the arithmetic
## operations. The functions interface on the level of
## <Q>defining data</Q>, 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.
## <P/>
## There are default methods for <C>Equality</C> and <C>LessThan</C>
## which simply calculate on the defining data.
## If one is defined, it must be ensured that the other is compatible
## (so that <M>a < b</M> implies not <M>(a = b)</M>)
## </Item>
## <Mark><C>Print</C></Mark>
## <Item>
## a function which prints the object.
## By default, just the defining data is printed.
## </Item>
## <Mark><C>MathInfo</C></Mark>
## <Item>
## filters determining the mathematical properties of the elements
## created. A typical value is for example
## <C>IsMultiplicativeElementWithInverse</C> for group elements.
## </Item>
## <Mark><C>RepInfo</C></Mark>
## <Item>
## 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
## <C>IsAttributeStoringRep</C> to permit the storing of attributes.
## </Item>
## </List>
## <P/>
## All components are optional and will be filled in with default values
## (though of course an empty record will not result in useful objects).
## <P/>
## Note that the resulting objects are <E>not equal</E> to their defining
## data (even though by default they print as only the defining data). The
## operation <C>UnderlyingElement</C> can be used to obtain the defining
## data of such an element.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction("ArithmeticElementCreator");
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