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##
#W perlist.gd Laurent Bartholdi
##
##
#Y Copyright (C) 2006, Laurent Bartholdi
##
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##
## This file declares periodic lists and FIFO's
##
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##
#H Periodic lists
##
## <#GAPDoc Label="PeriodicLists">
## <ManSection>
## <Fam Name="PeriodicListsFamily"/>
## <Filt Name="IsPeriodicList"/>
## <Description>
## The family, respectively filter, of <Ref Oper="PeriodicList"/>s.
## </Description>
## </ManSection>
##
## <ManSection>
## <Oper Name="PeriodicList" Arg="preperiod[,period]"/>
## <Oper Name="PeriodicList" Arg="list,i" Label="period, looping point"/>
## <Oper Name="PeriodicList" Arg="list,f" Label="list, function"/>
## <Oper Name="CompressedPeriodicList" Arg="preperiod[,period]"/>
## <Oper Name="CompressedPeriodicList" Arg="list,i" Label="period, looping point"/>
## <Oper Name="PrePeriod" Arg="list"/>
## <Oper Name="Period" Arg="list"/>
## <Description>
## These functions manipulate <E>periodic lists</E>, i.e. lists of
## infinite length such that elements follow a periodic order after
## some point.
##
## The first command creates a periodic list, specified by
## its preperiod and period, which must both be lists. If the period
## is absent, this is actually a finite list.
##
## The second command creates a periodic list by decreeing that
## the entries after the end of the list start again at position
## <A>i</A>.
##
## The third command creates a list by applying function <A>f</A>
## to all elements of <A>l</A>.
##
## The fourth and fifth command compress the newly created
## periodic list, see <Ref Oper="CompressPeriodicList"/>.
##
## The sixth and seventh commands return respectively the preperiod
## and period of a periodic list.
##
## Most of the methods applied for lists have an obvious equivalent
## for periodic lists: <Ref Oper="List" BookName="ref"/>,
## <Ref Oper="Filtered" BookName="ref"/>,
## <Ref Oper="First" BookName="ref"/>,
## <Ref Oper="ForAll" BookName="ref"/>,
## <Ref Oper="ForAny" BookName="ref"/>,
## <Ref Oper="Number" BookName="ref"/>.
## <Example><![CDATA[
## gap> l := PeriodicList([1],[2,3,4]);
## [ 1, / 2, 3, 4 ]
## gap> l[5];
## 2
## gap> Add(l,100,3); l;
## [ 1, 2, 100, / 3, 4, 2 ]
## gap> Remove(l,5);
## 4
## gap> l;
## [ 1, 2, 100, 3, / 2, 3, 4 ]
## gap> PrePeriod(l);
## [ 1, 2, 100, 3 ]
## gap> Period(l);
## [ 2, 3, 4 ]
## ]]></Example>
## </Description>
## </ManSection>
##
## <ManSection>
## <Oper Name="CompressPeriodicList" Arg="l"/>
## <Description>
## This function compresses a periodic list, in replacing the
## period by a minimal period, and shortening the preperiod. No
## value is returned, but the list <A>l</A> is modified. It remains
## equal (under <C>=</C>) to the original list.
## <Example><![CDATA[
## gap> l := PeriodicList([1],[2,3,4,2,3,4]);
## [ 1, / 2, 3, 4, 2, 3, 4 ]
## gap> Add(l,4,5); l;
## [ 1, 2, 3, 4, 4, / 2, 3, 4, 2, 3, 4 ]
## gap> CompressPeriodicList(l);
## gap> l;
## [ 1, 2, 3, 4, / 4, 2, 3 ]
## ]]></Example>
## </Description>
## </ManSection>
##
## <ManSection>
## <Oper Name="IsConfinal" Arg="l,m"/>
## <Returns><K>true</K> if <A>l</A> and <A>m</A> are eventually equal.</Returns>
## <Description>
## This function tests whether two lists are <E>confinal</E>, i.e.
## whether, after removal of the same suitable number of elements
## from both lists, they become equal.
## <Example><![CDATA[
## gap> l := PeriodicList([1],[2,3,2,3]);
## [ 1, / 2, 3, 2, 3 ]
## gap> m := PeriodicList([0,1],[3,2]);
## [ 0, 1, / 3, 2 ]
## gap> IsConfinal(l,m);
## true
## ]]></Example>
## </Description>
## </ManSection>
##
## <ManSection>
## <Oper Name="ConfinalityClass" Arg="l"/>
## <Returns>The strictly periodic list with same tail as <A>l</A>.</Returns>
## <Description>
## There exists a unique periodic list, with no preperiod, which is
## confinal (see <Ref Oper="IsConfinal"/>) to <A>l</A>. This strictly
## periodic list is returned by this command.
## <Example><![CDATA[
## gap> l := PeriodicList([1],[2,3,2,3]);
## [ 1, / 2, 3, 2, 3 ]
## gap> ConfinalityClass(l);
## [/ 3, 2 ]
## ]]></Example>
## </Description>
## </ManSection>
##
## <ManSection>
## <Oper Name="LargestCommonPrefix" Arg="c"/>
## <Returns>The longest list that is a prefix of all elements of <A>c</A>.</Returns>
## <Description>
## This command computes the longest (finite or periodic) list which is a
## prefix of all elements of <A>c</A>. The argument <A>c</A> is a
## collection of finite and periodic lists.
## <Example><![CDATA[
## gap> LargestCommonPrefix([PeriodicList([1],[2,3,2,3]),[1,2,3,4]]);
## [ 1, 2, 3 ]
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory("IsPeriodicList",IsList);
BindGlobal("PeriodicListsFamily",
 NewFamily("PeriodicListsFamily",IsPeriodicList));
BindGlobal("TYPE_LIST_PERIODIC",
 NewType(PeriodicListsFamily,IsPeriodicList and IsPositionalObjectRep));
DeclareOperation("PeriodicList",[IsList]);
DeclareOperation("PeriodicList",[IsList,IsList]);
DeclareOperation("PeriodicList", [IsList, IsPosInt]);
DeclareOperation("PeriodicList", [IsList, IsFunction]);
DeclareOperation("Period", [IsPeriodicList]);
DeclareOperation("PrePeriod", [IsPeriodicList]);
DeclareOperation("CompressPeriodicList", [IsPeriodicList]);
DeclareGlobalFunction("CompressedPeriodicList");
DeclareOperation("IsConfinal",[IsPeriodicList,IsPeriodicList]);
DeclareOperation("ConfinalityClass",[IsPeriodicList]);
DeclareOperation("LargestCommonPrefix",[IsList]);
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##
#H FIFOs
##
## <#GAPDoc Label="FIFOs">
## <ManSection>
## <Filt Name="IsFIFO"/>
## <Oper Name="NewFIFO" Arg="[l]"/>
## <Oper Name="Add" Arg="f,i" Label="FIFO"/>
## <Oper Name="Append" Arg="f,l" Label="FIFO"/>
## <Description>
## These functions create and extend FIFOs, i.e. first-in first-out
## data structures.
##
## The first command creates a FIFO, with an optional list
## initializing it.
##
## The second and third commands add an element, or append a list,
## to the FIFO.
##
## Elements are removed via <C>NextIterator(f)</C>, and the
## FIFO is tested for emptyness via <C>IsDoneIterator(f)</C>. Thus,
## a typical use is the following code, which tests in breadth-first
## manner that all numbers in <C>[1..1000]</C> have a successor which is
## prime:
## <Example><![CDATA[
## gap> f := NewFIFO([1..10000]);
## <iterator>
## gap> for i in f do if not IsPrime(i) then Add(f,i+1); fi; od;
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory("IsFIFO",IsIterator and IsList);
DeclareOperation("NewFIFO",[IsList]);
DeclareOperation("NewFIFO",[]);
DeclareOperation("Add",[IsFIFO,IsObject]);
DeclareOperation("Append", [IsFIFO,IsObject]);
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