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bd103f1
start of my comments
cdwensley Apr 1, 2026
801da3c
possible addition to the manual
cdwensley Apr 2, 2026
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37 changes: 32 additions & 5 deletions doc/gslp.xml
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Expand Up @@ -14,7 +14,7 @@
The functions described in this chapter have been written by Thomas Breuer,
they are available since <Package>Utils</Package> 0.94.
<P/>
<E>Generalized straight line programs</E> (in the following abbreviated
<E>Generalized straight line programs</E> (abbreviated
as <E>gslps</E>) are a generalization of the straight line programs
that are described in the &GAP; library,
see <Ref Sect="Straight Line Programs" BookName="ref"/>.
Expand Down Expand Up @@ -43,7 +43,34 @@ are that
</Item>
</List>
<P/>
A gslp in &GAP; is represented by an object in the category

Recall, from the main library, that the simplest form of a straight line program
defines a way of evaluating a word in a group. For example, <M>a^4b^7a^5b^6</M>
may be evaluated as <M>cbac</M> where <M>c=a^4b^6</M>.
The following listing shows how this may be encoded, where <M>1,2,3</M>
denote the three variables; <M>[1,4,2,6]</M> encodes <M>a^4b^6</M>,
defining the new variable <M>3</M>;
<M>[3,1,2,1,1,1,3,1]</M> encodes <M>cabc</M>;
and <M>2</M> is the number of generators.
The result of this program is then evaluated using generators <M>[x,y]</M>
and <M>[(1,2,3),(2,3,4)]</M>.
<P/>
<Example><![CDATA[
gap> f2 := FreeGroup( "x", "y" );;
gap> genf2 := GeneratorsOfGroup( f2 );;
gap> slp := StraightLineProgram( [ [[1,4,2,6],3], [3,1,2,1,1,1,3,1] ], 2 );;
gap> ResultOfStraightLineProgram( slp, genf2 );
x^4*y^7*x^5*y^6
gap> ResultOfStraightLineProgram( slp, [(1,2,3),(2,3,4)] );
(1,2,4)
gap> LinesOfStraightLineProgram( slp );
[ [ [ 1, 4, 2, 6 ], 3 ], [ 3, 1, 2, 1, 1, 1, 3, 1 ] ]
]]></Example>
It is generalisations of these operations which this chapter describes.

<P/>
A generalized straight line program gslp in &GAP;
is represented by an object in the category
<Ref Filt="IsGeneralizedStraightLineProgram"/>.
This object has exactly one of the following forms.
<P/>
Expand Down Expand Up @@ -117,7 +144,7 @@ Label="for kind and list"/>.
Defining attributes for gslps are
<Ref Attr="NrInputsOfGeneralizedStraightLineProgram"/>
and <Ref Attr="DataOfGeneralizedStraightLineProgram"/>.
The probably most interesting operation for gslps is
Probably the most interesting operation for gslps is
<Ref Oper="ResultOfGeneralizedStraightLineProgram"/>.
<P/>
Currently we do not intend to provide methods applicable to
Expand All @@ -136,12 +163,12 @@ and <Ref Oper="String" BookName="ref"/>.
<Section Label="sec-gslp">
<Heading>Functions for Generalized Straight Line Programs</Heading>

<#Include Label="IsGeneralizedStraightLineProgram">
<#Include Label="GeneralizedStraightLineProgram">
<#Include Label="IsGeneralizedStraightLineProgram">
<#Include Label="ResultOfGeneralizedStraightLineProgram">
<#Include Label="DataOfGeneralizedStraightLineProgram">
<#Include Label="NrInputsOfGeneralizedStraightLineProgram">
<#Include Label="NrOutputsOfGeneralizedStraightLineProgram">
<#Include Label="ResultOfGeneralizedStraightLineProgram">
<#Include Label="EquivalentStraightLineProgram">
<#Include Label="IsInternallyConsistent_gslp">

Expand Down
98 changes: 53 additions & 45 deletions lib/gslp.gd
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Expand Up @@ -32,13 +32,11 @@
## <Ref Filt="IsStraightLineProgram" BookName="ref"/>.
## <P/>
## <Example><![CDATA[
## gap> gslp:= GeneralizedStraightLineProgram( "union",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );
## <generalized straight line program>
## gap> IsGeneralizedStraightLineProgram( gslp );
## gap> gslp3 := GeneralizedStraightLineProgram( "compose",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );;
## gap> IsGeneralizedStraightLineProgram( gslp3 );
## true
## gap> slp:= StraightLineProgram( [[[1,2]]], 1 );
## <straight line program>
## gap> slp := StraightLineProgram( [[[1,2]]], 1 );;
## gap> IsGeneralizedStraightLineProgram( slp );
## true
## gap> IsGeneralizedStraightLineProgram( [ slp, slp ] );
Expand Down Expand Up @@ -75,10 +73,9 @@ InstallTrueMethod( IsGeneralizedStraightLineProgram, IsStraightLineProgram );
## There is no default method to compute the value if it is not stored.
## <P/>
## <Example><![CDATA[
## gap> gslp:= GeneralizedStraightLineProgram( "union",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );
## <generalized straight line program>
## gap> DataOfGeneralizedStraightLineProgram( gslp );
## gap> gslp2 := GeneralizedStraightLineProgram( "union",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );;
## gap> DataOfGeneralizedStraightLineProgram( gslp2 );
## [ "union", [ <straight line program>, <straight line program> ] ]
## ]]></Example>
## </Description>
Expand Down Expand Up @@ -109,9 +106,9 @@ DeclareAttribute( "DataOfGeneralizedStraightLineProgram",
## <A>gslp</A> is constructed.
## <P/>
## <Example><![CDATA[
## gap> NrInputsOfGeneralizedStraightLineProgram(
## > GeneralizedStraightLineProgram( "union",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] ) );
## gap> gslp2 := GeneralizedStraightLineProgram( "union",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );;
## gap> NrInputsOfGeneralizedStraightLineProgram( gslp2 );
## 1
## ]]></Example>
## <P/>
Expand Down Expand Up @@ -143,14 +140,16 @@ DeclareSynonymAttr( "NrInputsOfGeneralizedStraightLineProgram",
## Note that the &GAP; library does not define a corresponding attribute
## for straight line programs.
## <P/>
## In the examples, glsp2 outputs <M>[p^2,p^3]</M>,
## while glsp3 outputs <M>p^6</M>.
## <Example><![CDATA[
## gap> NrOutputsOfGeneralizedStraightLineProgram(
## > GeneralizedStraightLineProgram( "union",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] ) );
## gap> gslp2 := GeneralizedStraightLineProgram( "union",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );;
## gap> NrOutputsOfGeneralizedStraightLineProgram( gslp2 );
## 2
## gap> NrOutputsOfGeneralizedStraightLineProgram(
## > GeneralizedStraightLineProgram( "compose",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] ) );
## gap> gslp3 := GeneralizedStraightLineProgram( "compose",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );;
## gap> NrOutputsOfGeneralizedStraightLineProgram( gslp3 );
## 1
## ]]></Example>
## </Description>
Expand Down Expand Up @@ -191,15 +190,23 @@ DeclareAttribute( "NrOutputsOfGeneralizedStraightLineProgram",
## Label="for a list of lines (and the number of generators)"/> and
## <C>l</C> returns a gslp.
## <P/>
## In the examples <M>p^2, [p^2,p^3]</M> and <M>(p^2)^3</M>
## are computed, with <M>p=(1,2,3,4,5,6)</M>.
## <P/>
## <Example><![CDATA[
## gap> GeneralizedStraightLineProgram( [[[1,2]]], 1 );
## gap> gslp1 := GeneralizedStraightLineProgram( [[[1,2]]], 1 );
## <straight line program>
## gap> GeneralizedStraightLineProgram( "union",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );
## <generalized straight line program>
## gap> GeneralizedStraightLineProgram( "compose",
## gap> ResultOfStraightLineProgram( gslp1, [(1,2,3,4,5,6)] );
## [ (1,3,5)(2,4,6) ]
## gap> gslp2 := GeneralizedStraightLineProgram( "union",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );
## <generalized straight line program>
## gap> ResultOfStraightLineProgram( gslp2, [(1,2,3,4,5,6)] );
## [ (1,3,5)(2,4,6), (1,4)(2,5)(3,6) ]
## gap> gslp3 := GeneralizedStraightLineProgram( "compose",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );;
## gap> ResultOfStraightLineProgram( gslp3, [(1,2,3,4,5,6)] );
## [ () ]
## ]]></Example>
## </Description>
## </ManSection>
Expand Down Expand Up @@ -245,23 +252,24 @@ DeclareGlobalFunction( "GeneralizedStraightLineProgram" );
## </Item>
## </List>
## <P/>
## In order to avoid the introduction of unnecessary operations,
## we define <Ref Oper="ResultOfGeneralizedStraightLineProgram"/> just as
## a synonym of <Ref Oper="ResultOfStraightLineProgram" BookName="ref"/>.
## <P/>
## <Example><![CDATA[
## gap> gens:= [ (1,2,3,4,5,6) ];;
## gap> gslp:= GeneralizedStraightLineProgram( "union",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );
## <generalized straight line program>
## gap> ResultOfGeneralizedStraightLineProgram( gslp, gens );
## gap> gens := [ (1,2,3,4,5,6) ];;
## gap> gslp := StraightLineProgram( [ [ [1,2] ] ], 1 );;
## gap> ResultOfGeneralizedStraightLineProgram( gslp, gens );
## [ (1,3,5)(2,4,6) ]
## gap> gslp2 := GeneralizedStraightLineProgram( "union",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );;
## gap> ResultOfGeneralizedStraightLineProgram( gslp2, gens );
## [ (1,3,5)(2,4,6), (1,4)(2,5)(3,6) ]
## gap> gslp:= GeneralizedStraightLineProgram( "compose",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );
## <generalized straight line program>
## gap> ResultOfGeneralizedStraightLineProgram( gslp, gens );
## gap> gslp3 := GeneralizedStraightLineProgram( "compose",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );;
## gap> ResultOfGeneralizedStraightLineProgram( gslp3, gens );
## [ () ]
## ]]></Example>
## <P/>
## In order to avoid the introduction of unnecessary operations,
## we define <Ref Oper="ResultOfGeneralizedStraightLineProgram"/> just as
## a synonym of <Ref Oper="ResultOfStraightLineProgram" BookName="ref"/>.
## </Description>
## </ManSection>
## <#/GAPDoc>
Expand Down Expand Up @@ -290,23 +298,23 @@ DeclareOperation( "ResultOfGeneralizedStraightLineProgram",
## output, for any list of input elements.
## <P/>
## <Example><![CDATA[
## gap> gslp:= GeneralizedStraightLineProgram( "union",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );
## gap> gslp2 := GeneralizedStraightLineProgram( "union",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );
## <generalized straight line program>
## gap> slp:= EquivalentStraightLineProgram( gslp );
## gap> slp2 := EquivalentStraightLineProgram( gslp2 );
## <straight line program>
## gap> Display( slp );
## gap> Display( slp2 );
## # input:
## r:= [ g1 ];
## # program:
## # return values:
## [ r[1]^2, r[1]^3 ]
## gap> gslp:= GeneralizedStraightLineProgram( "compose",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );
## gap> gslp3 := GeneralizedStraightLineProgram( "compose",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );
## <generalized straight line program>
## gap> slp:= EquivalentStraightLineProgram( gslp );
## gap> slp3 := EquivalentStraightLineProgram( gslp3 );
## <straight line program>
## gap> Display( slp );
## gap> Display( slp3 );
## # input:
## r:= [ g1 ];
## # program:
Expand Down
12 changes: 6 additions & 6 deletions lib/gslp.gi
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Expand Up @@ -218,13 +218,13 @@ InstallMethod( String,
## compatible with the numbers of inputs and outputs of <A>gslp</A>.
## <P/>
## <Example><![CDATA[
## gap> gslp:= GeneralizedStraightLineProgram( "union",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );;
## gap> IsInternallyConsistent( gslp );
## gap> gslp2 := GeneralizedStraightLineProgram( "union",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );;
## gap> IsInternallyConsistent( gslp2 );
## true
## gap> gslp:= GeneralizedStraightLineProgram( "compose",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );;
## gap> IsInternallyConsistent( gslp );
## gap> gslp3 := GeneralizedStraightLineProgram( "compose",
## > [ [ [[[1,2]]], 1 ], [ [[[1,3]]], 1 ] ] );;
## gap> IsInternallyConsistent( gslp3 );
## true
## ]]></Example>
## </Description>
Expand Down