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products/Sources/formale Sprachen/GAP/pkg/hap/doc/ (GAP Algebra Version 4.15.1^©) Datei vom 19.6.2025 mit Größe 32 kB

Impressum smallestImage.gd Sprache: Shell

#############################################################################
##
##
#W files.gd images Package Chris Jefferson
##
## Declaration file for types for MinimalImage and CanonicalImage.
##
#Y Copyright (C) 2014 University of St. Andrews, North Haugh,
#Y St. Andrews, Fife KY16 9SS, Scotland
##

#############################################################################
##
## Two transformations of a group used when calculating MinimialImages of
## Transformations, Permutations and PartialPermutations
##

DeclareAttribute( "rowcolsquareGroup", IsPermGroup );
DeclareAttribute( "rowcolsquareGroup2", IsPermGroup );

DeclareAttribute( "MinOrbitPerm", IsPermGroup );
DeclareAttribute( "MaxOrbitPerm", IsPermGroup );

#############################################################################
##
#F MinimialImage
##

#############################################################################
## <#GAPDoc Label="MinimalImage">
## <ManSection>
## <Func Name="MinimalImage" Arg="G, pnt[, act][, Config]"/>
## <Func Name="IsMinimalImage" Arg="G, pnt[, act][, Config]"/>
## <Func Name="MinimalImagePerm" Arg="G, pnt[, act][, Config]"/>
## <Description>
## <Ref Func="MinimalImage"/> returns the minimal image of <A>pnt</A> under
## the group <A>G</A>. <Ref Func="IsMinimalImage"/> returns a boolean which
## is <K>true</K> if <Ref Func="MinimalImage"/> would return <A>pnt</A> (so
## the value is it's own minimal image).
## 
## <Ref Func="MinimalImagePerm"/> returns the permutation which maps
## <A>pnt</A> to its minimal image.
## 
## The option <A>Config</A> defines a number of advanced configuration
## options, which are described in 'ImagesAdvancedConfig'.
## </Description>
## </ManSection>
## <#/GAPDoc>
DeclareGlobalFunction("MinimalImage");
DeclareGlobalFunction("IsMinimalImage");
DeclareGlobalFunction("MinimalImagePerm");

#############################################################################
## <#GAPDoc Label="IsMinimalImageLessThan">
## <ManSection>
## <Func Name="IsMinimalImageLessThan" Arg="G, A, B[, act][, config]"/>
## <Description>
## <Ref Func="IsMinimalImageLessThan"/> checks if the minimal image of
## <A>A</A> under the group <A>G</A> is smaller than <A>B</A>.
## 
## It returns MinImage.Smaller, MinImage.Equal or MinImage.Larger, if the
## minimal image of <A>A</A> is smaller, equal or larger than <A>B</A>.
## 
## The option <A>Config</A> defines a number of advanced configuration
## options, which are described in 'ImagesAdvancedConfig'.
## </Description>
## </ManSection>
## <#/GAPDoc>
DeclareGlobalFunction("IsMinimalImageLessThan");

#############################################################################
## <#GAPDoc Label="CanonicalImage">
## <ManSection>
## <Func Name="CanonicalImage" Arg="G[, pnt][, act][, Config]"/>
## <Func Name="IsCanonicalImage" Arg="G[, pnt][, act][, Config]"/>
## <Func Name="CanonicalImagePerm" Arg="G, [, pnt][, act][, Config]"/>

## <Description>
## <Ref Func="CanonicalImage"/> returns a canonical image of <A>pnt</A> under
## the group <A>G</A>. <Ref Func="IsCanonicalImage"/> returns a boolean which
## is <K>true</K> if <Ref Func="CanonicalImage"/> would return <A>pnt</A> (so
## the value is it's own minimal image).
## 
## <Ref Func="CanonicalImagePerm"/> returns the permutation which maps
## <A>pnt</A> to its minimal image.
## 
## By default, these functions use the fastest algorithm for calculating
## canonical images, which is often changed in new versions of the package.
## The option <A>Config</A> defines a number of advanced configuration
## options, which are described in 'ImagesAdvancedConfig'. These include the ability
## to choose the canonicalising algorithm used.
## </Description>
## </ManSection>
## <#/GAPDoc>
DeclareGlobalFunction("CanonicalImage");
DeclareGlobalFunction("IsCanonicalImage");
DeclareGlobalFunction("CanonicalImagePerm");

DeclareGlobalFunction("_CanonicalImageParse");

DeclareOperation( "CanonicalImageOp", [IsPermGroup, IsObject, IsFunction, IsObject] );

DeclareOperation( "MinimalImageUnorderedPair", [IsPermGroup, IsObject]);
DeclareOperation( "MinimalImageUnorderedPair", [IsPermGroup, IsObject, IsFunction]);
DeclareOperation( "MinimalImageOrderedPair", [IsPermGroup, IsObject]);
DeclareOperation( "MinimalImageOrderedPair", [IsPermGroup, IsObject, IsFunction]);

#############################################################################
## <#GAPDoc Label="ImagesAdvancedConfig">
## <ManSection>
## <Var Name="ImagesAdvancedConfig" />
## <Description>
## This section describes the advanced configuration options for both
## <Ref Func="MinimalImage"/> and <Ref Func="CanonicalImage"/>. Assume
## we have called <Ref Func="MinimalImage"/> or <Ref Func="CanonicalImage"/>
## with arguments <C>(<A>G</A>,<A>O</A>,<A>A</A>)</C>.
## 
##
## <List>
## <C>order</C>
## <Item> The search ordering used while building the image. There are many
## configuration options available. We shall list here just the three
## most useful ones. A full list is in the paper "Minimal and Canonical Images" by
## the authors of this package.
## <List>
## <C>CanonicalConfig_Minimum</C>
## <Item>
## Lexicographically smallest set -- same as using MinimalImage.
## </Item>
## <C>CanonicalConfig_FixedMinOrbit</C>
## <Item>
## Lexicographically smallest set under the ordering of the integers
## given by the MinOrbitPerm function.
## </Item>
## <C>CanonicalConfig_RareRatioOrbitFixPlusMin</C>
## <Item>
## The current best algorithm (default)
## </Item>
## </List>
## </Item>
## <C>stabilizer</C>
## <Item>The group <C>Stabilizer(<A>G</A>,<A>O</A>,<A>A</A>)</C>,
## or a subgroup of this group; see <Ref Func="Stabilizer" BookName="ref"/>.
## If this group is large, it is more efficient to pre-calculate it.
## Default behaviour is to calculate the group, pass <C>Group(())</C> to disable
## this behaviour. This is not checked, and passing an incorrect group will
## produce incorrect answers.
## </Item>
## <C>disableStabilizerCheck</C> (default <K>false</K>)
## <Item> By default, during search we perform cheap checks to try to find
## extra elements of the stabilizer. Pass true to disable this check, this
## will make the algorithm MUCH slower if the stabilizer argument is a
## subgroup.
## </Item>
## <C>getStab</C> (default <K>false</K>)
## <Item> Return the calculated value of <C>Stabilizer(<A>G</A>,<A>O</A>,<A>A</A>)</C>.
## This may return a subgroup rather than the whole stabilizer.
## </Item>
## </List>
## </Description>
## </ManSection>
## <#/GAPDoc>

BindGlobal("GetPerm", 1);
BindGlobal("GetImage", 2);
BindGlobal("GetBool", 3);

BindGlobal("MinImage", rec(Smaller := -1, Equal := 0, Larger := 1));

BindGlobal("CanonicalConfig_Minimum", MakeImmutable(rec(
 branch := "minimum"
)));

BindGlobal("CanonicalConfig_FixedMinOrbit", MakeImmutable(rec(
 branch := "static", order := "MinOrbit"
)));

BindGlobal("CanonicalConfig_FixedMaxOrbit", MakeImmutable(rec(
 branch := "static", order := "MaxOrbit"
)));

BindGlobal("CanonicalConfig_MinOrbit", MakeImmutable(rec(
 branch := "dynamic", order := "MinOrbit"
)));

BindGlobal("CanonicalConfig_MaxOrbit", MakeImmutable(rec(
 branch := "dynamic", order := "MaxOrbit"
)));

BindGlobal("CanonicalConfig_SingleMaxOrbit", MakeImmutable(rec(
 branch := "dynamic", order := "SingleMaxOrbit"
)));

BindGlobal("CanonicalConfig_RareOrbit", MakeImmutable(rec(
 branch := "dynamic", order := "RareOrbit"
)));

BindGlobal("CanonicalConfig_CommonOrbit", MakeImmutable(rec(
 branch := "dynamic", order := "CommonOrbit"
)));

BindGlobal("CanonicalConfig_RareRatioOrbit", MakeImmutable(rec(
 branch := "dynamic", order := "RareRatioOrbit"
)));

BindGlobal("CanonicalConfig_CommonRatioOrbit", MakeImmutable(rec(
 branch := "dynamic", order := "CommonRatioOrbit"
)));

BindGlobal("CanonicalConfig_RareRatioOrbitFix", MakeImmutable(rec(
 branch := "dynamic", order := "RareRatioOrbitFix"
)));

BindGlobal("CanonicalConfig_CommonRatioOrbitFix", MakeImmutable(rec(
 branch := "dynamic", order := "CommonRatioOrbitFix"
)));

BindGlobal("CanonicalConfig_RareRatioOrbitFixPlusMin", MakeImmutable(rec(
 branch := "dynamic", order := "RareRatioOrbitFix",
 orbfilt := "Min"
)));

BindGlobal("CanonicalConfig_RareRatioOrbitFixPlusRare", MakeImmutable(rec(
 branch := "dynamic", order := "RareRatioOrbitFix",
 orbfilt := "Rare"
)));

BindGlobal("CanonicalConfig_RareRatioOrbitFixPlusCommon", MakeImmutable(rec(
 branch := "dynamic", order := "RareRatioOrbitFix",
 orbfilt := "Common"
)));

BindGlobal("CanonicalConfig_RareOrbitPlusMin", MakeImmutable(rec(
 branch := "dynamic", order := "RareOrbit",
 orbfilt := "Min"
)));

BindGlobal("CanonicalConfig_RareOrbitPlusRare", MakeImmutable(rec(
 branch := "dynamic", order := "RareOrbit",
 orbfilt := "Rare"
)));

BindGlobal("CanonicalConfig_RareOrbitPlusCommon", MakeImmutable(rec(
 branch := "dynamic", order := "RareOrbit",
 orbfilt := "Common"
)));

BindGlobal("CanonicalConfig_Fast", CanonicalConfig_RareRatioOrbitFixPlusMin);

#E files.gd . . . . . . . . . . . . . . . . . . . . . . . . . . . ends here

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