Quelle unknown.gd Sprache: unbekannt

#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Martin Schönert.
##
## 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
##
## This file declares the operations for unknowns.
##

#############################################################################
##
## <#GAPDoc Label="[1]{unknown}">
## Sometimes the result of an operation does not allow further
## computations with it.
## In many cases, then an error is signalled,
## and the computation is stopped.
## 
## This is not appropriate for some applications in character theory.
## For example, if one wants to induce a character of a group to a
## supergroup (see <Ref Oper="InducedClassFunction"
## Label="for the character table of a supergroup"/>)
## but the class fusion is only a parametrized map
## (see Chapter <Ref Chap="Maps Concerning Character Tables"/>),
## there may be values of the induced character which are determined by the
## fusion map, whereas other values are not known.
## 
## For this and other situations, &GAP; provides the data type
## <E>unknown</E>.
## An object of this type, further on called an <E>unknown</E>,
## may stand for any cyclotomic
## (see Chapter <Ref Chap="Cyclotomic Numbers"/>),
## in particular its family (see <Ref Sect="Families"/>)
## is <C>CyclotomicsFamily</C>.
## 
## Unknowns are parametrized by positive integers.
## When a &GAP; session is started, no unknowns exist.
## 
## The only ways to create unknowns are to call the function
## <Ref Oper="Unknown"/> or a function that calls it,
## or to do arithmetical operations with unknowns.
## 
## &GAP; objects containing unknowns will contain <E>fixed</E> unknowns
## when they are printed to files, i.e.,
## function calls <C>Unknown(</C><M>n</M><C>)</C> instead of
## <C>Unknown()</C>.
## So be careful to read files printed in different &GAP; sessions,
## since there may be the same unknown at different places.
## 
## The rest of this chapter contains information about the unknown
## constructor, the category,
## and comparison of and arithmetical operations for unknowns.
## More is not known about unknowns in &GAP;.
## <#/GAPDoc>
##

#############################################################################
##
## <#GAPDoc Label="[2]{unknown}">
## <Subsection>
## <Heading>Comparison of Unknowns</Heading>
##
## Unknowns can be <E>compared</E> via <C>=</C> and <C><</C>
## with all cyclotomics and with certain other &GAP; objects
## (see <Ref Sect="Comparisons"/>).
## We have <C>Unknown( <A>n</A> ) >= Unknown( <A>m</A> )</C>
## if and only if <C><A>n</A> >= <A>m</A></C> holds,
## unknowns are larger than all cyclotomics that are not unknowns.
## 
## <Example><![CDATA[
## gap> Unknown() >= Unknown(); Unknown(2) < Unknown(3);
## false
## true
## gap> Unknown() > 3; Unknown() > E(3);
## true
## true
## gap> Unknown() > Z(8); Unknown() > [];
## false
## false
## ]]></Example>
## </Subsection>
## <#/GAPDoc>
##

#############################################################################
##
## <#GAPDoc Label="[3]{unknown}">
## <Subsection>
## <Heading>Arithmetical Operations for Unknowns</Heading>
##
## The usual arithmetic operations <C>+</C>, <C>-</C>, <C>*</C> and <C>/</C>
## are defined for addition, subtraction, multiplication and division
## of unknowns and cyclotomics.
## The result will be a new unknown except in one of the following cases.
## 
## Multiplication with zero yields zero,
## and multiplication with one or addition of zero yields the old unknown.
## <E>Note</E> that division by an unknown causes an error,
## since an unknown might stand for zero.
## 
## As unknowns are cyclotomics, dense lists of unknowns and other
## cyclotomics are row vectors and
## they can be added and multiplied in the usual way.
## Consequently, lists of such row vectors of equal length are (ordinary)
## matrices (see <Ref Filt="IsOrdinaryMatrix"/>).
## </Subsection>
## <#/GAPDoc>
##

#############################################################################
##
#C IsUnknown( <obj> )
##
## <#GAPDoc Label="IsUnknown">
## <ManSection>
## <Filt Name="IsUnknown" Arg='obj' Type='Category'/>
##
## <Description>
## is the category of unknowns in &GAP;.
## <Example><![CDATA[
## gap> Unknown(); List( [ 1 .. 20 ], i -> Unknown() );;
## Unknown(1)
## gap> Unknown(); # note that we have already created 21 unknowns.
## Unknown(22)
## gap> Unknown(2000); Unknown();
## Unknown(2000)
## Unknown(2001)
## gap> LargestUnknown;
## 2001
## gap> IsUnknown( Unknown ); IsUnknown( Unknown() );
## false
## true
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsUnknown", IsCyclotomic );

#############################################################################
##
#V LargestUnknown . . . . . . . . . . . . largest used index for an unknown
##
## <#GAPDoc Label="LargestUnknown">
## <ManSection>
## <Var Name="LargestUnknown"/>
##
## <Description>
## <Ref Var="LargestUnknown"/> is the largest <A>n</A> that is used in any
## <C>Unknown( <A>n</A> )</C> in the current &GAP; session.
## This is used in <Ref Oper="Unknown"/> which increments this value
## when asked to make a new unknown.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
LargestUnknown := 0;

#############################################################################
##
#O Unknown( [<n>] )
##
## <#GAPDoc Label="Unknown">
## <ManSection>
## <Oper Name="Unknown" Arg='[n]'/>
##
## <Description>
## Called without argument, <Ref Oper="Unknown"/> returns a new unknown
## value, i.e., the first one that is larger than all unknowns which exist
## in the current &GAP; session.
## 
## Called with a positive integer <A>n</A>, <Ref Oper="Unknown"/> returns
## the <A>n</A>-th unknown; if this did not exist yet, it is created.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation( "Unknown", [] );
DeclareOperation( "Unknown", [ IsPosInt ] );

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