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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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2026-10-11