d&i *RationalShiftAlgebra

MatricesForHomalg/PackageInfo.g

@@ -11,7 +11,7 @@ SetPackageInfo( rec(
 
 PackageName := "MatricesForHomalg",
 Subtitle := "Matrices for the homalg project",
-Version := "2024.08-05",
+Version := "2024.11-02",
 Date := (function ( ) if IsBound( GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE ) then return GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE; else return Concatenation( ~.Version{[ 1 .. 4 ]}, "-", ~.Version{[ 6, 7 ]}, "-01" ); fi; end)( ),
 License := "GPL-2.0-or-later",
 

MatricesForHomalg/gap/HomalgRing.gd

@@ -316,6 +316,32 @@ DeclareProperty( "IsLocalizedWeylRing",
 DeclareProperty( "IsExteriorRing",
         IsHomalgRing );
 
+##  <#GAPDoc Label="IsShiftAlgebra">
+##  <ManSection>
+##    <Prop Arg="R" Name="IsShiftAlgebra"/>
+##    <Returns><C>true</C> or <C>false</C></Returns>
+##    <Description>
+##      <A>R</A> is a ring for &homalg;.
+##    </Description>
+##  </ManSection>
+##  <#/GAPDoc>
+##
+DeclareProperty( "IsShiftAlgebra",
+        IsHomalgRing );
+
+##  <#GAPDoc Label="IsRationalShiftAlgebra">
+##  <ManSection>
+##    <Prop Arg="R" Name="IsRationalShiftAlgebra"/>
+##    <Returns><C>true</C> or <C>false</C></Returns>
+##    <Description>
+##      <A>R</A> is a ring for &homalg;.
+##    </Description>
+##  </ManSection>
+##  <#/GAPDoc>
+##
+DeclareProperty( "IsRationalShiftAlgebra",
+        IsHomalgRing );
+
 ##  <#GAPDoc Label="IsPseudoDoubleShiftAlgebra">
 ##  <ManSection>
 ##    <Prop Arg="R" Name="IsPseudoDoubleShiftAlgebra"/>
@@ -1246,6 +1272,84 @@ DeclareAttribute( "RelativeIndeterminateAntiCommutingVariablesOfExteriorRing",
 DeclareAttribute( "IndeterminatesOfExteriorRing",
         IsHomalgRing );
 
+##  <#GAPDoc Label="IndeterminateCoordinatesOfShiftAlgebra">
+##  <ManSection>
+##    <Attr Arg="R" Name="IndeterminateCoordinatesOfShiftAlgebra"/>
+##    <Returns>a list of &homalg; ring elements</Returns>
+##    <Description>
+##      The list of indeterminate coordinates of the &homalg; shift algebra <A>R</A>.
+##    </Description>
+##  </ManSection>
+##  <#/GAPDoc>
+##
+DeclareAttribute( "IndeterminateCoordinatesOfShiftAlgebra",
+        IsHomalgRing );
+
+##  <#GAPDoc Label="ParametersOfRationalShiftAlgebra">
+##  <ManSection>
+##    <Attr Arg="R" Name="ParametersOfRationalShiftAlgebra"/>
+##    <Returns>a list of &homalg; ring elements</Returns>
+##    <Description>
+##      The list of indeterminate coordinates of the &homalg; shift algebra <A>R</A>.
+##    </Description>
+##  </ManSection>
+##  <#/GAPDoc>
+##
+DeclareAttribute( "ParametersOfRationalShiftAlgebra",
+        IsHomalgRing );
+
+##  <#GAPDoc Label="RelativeIndeterminateCoordinatesOfShiftAlgebra">
+##  <ManSection>
+##    <Attr Arg="R" Name="RelativeIndeterminateCoordinatesOfShiftAlgebra"/>
+##    <Returns>a list of &homalg; ring elements</Returns>
+##    <Description>
+##      The list of relative indeterminate coordinates of the &homalg; shift algebra <A>R</A>.
+##    </Description>
+##  </ManSection>
+##  <#/GAPDoc>
+##
+DeclareAttribute( "RelativeIndeterminateCoordinatesOfShiftAlgebra",
+        IsHomalgRing );
+
+##  <#GAPDoc Label="RelativeParametersOfRationalShiftAlgebra">
+##  <ManSection>
+##    <Attr Arg="R" Name="RelativeParametersOfRationalShiftAlgebra"/>
+##    <Returns>a list of &homalg; ring elements</Returns>
+##    <Description>
+##      The list of relative indeterminate coordinates of the &homalg; shift algebra <A>R</A>.
+##    </Description>
+##  </ManSection>
+##  <#/GAPDoc>
+##
+DeclareAttribute( "RelativeParametersOfRationalShiftAlgebra",
+        IsHomalgRing );
+
+##  <#GAPDoc Label="IndeterminateShiftsOfShiftAlgebra">
+##  <ManSection>
+##    <Attr Arg="R" Name="IndeterminateShiftsOfShiftAlgebra"/>
+##    <Returns>a list of &homalg; ring elements</Returns>
+##    <Description>
+##      The list of indeterminate shifts of the &homalg; shift algebra <A>R</A>.
+##    </Description>
+##  </ManSection>
+##  <#/GAPDoc>
+##
+DeclareAttribute( "IndeterminateShiftsOfShiftAlgebra",
+        IsHomalgRing );
+
+##  <#GAPDoc Label="IndeterminateShiftsOfRationalShiftAlgebra">
+##  <ManSection>
+##    <Attr Arg="R" Name="IndeterminateShiftsOfRationalShiftAlgebra"/>
+##    <Returns>a list of &homalg; ring elements</Returns>
+##    <Description>
+##      The list of indeterminate shifts of the &homalg; shift algebra <A>R</A>.
+##    </Description>
+##  </ManSection>
+##  <#/GAPDoc>
+##
+DeclareAttribute( "IndeterminateShiftsOfRationalShiftAlgebra",
+        IsHomalgRing );
+
 ##  <#GAPDoc Label="IndeterminateCoordinatesOfPseudoDoubleShiftAlgebra">
 ##  <ManSection>
 ##    <Attr Arg="R" Name="IndeterminateCoordinatesOfPseudoDoubleShiftAlgebra"/>
@@ -1706,6 +1810,12 @@ DeclareOperation( "KoszulDualRing",
 DeclareOperation( "KoszulDualRing",
         [ IsHomalgRing ] );
 
+DeclareOperation( "ShiftAlgebra",
+        [ IsHomalgRing, IsList ] );
+
+DeclareOperation( "RationalShiftAlgebra",
+        [ IsHomalgRing, IsList ] );
+
 DeclareOperation( "PseudoDoubleShiftAlgebra",
         [ IsHomalgRing, IsList ] );
 

MatricesForHomalg/gap/HomalgRing.gi

@@ -103,6 +103,20 @@
 
                     brackets := [ "{", "}" ];
 
+                ## the pseudo shift algebra:
+                elif HasIndeterminateShiftsOfShiftAlgebra( R ) then
+
+                    var := IndeterminateShiftsOfShiftAlgebra( R );
+
+                    brackets := [ "<", ">" ];
+
+                ## the pseudo shift algebra:
+                elif HasIndeterminateShiftsOfRationalShiftAlgebra( R ) then
+
+                    var := IndeterminateShiftsOfRationalShiftAlgebra( R );
+
+                    brackets := [ "<", ">" ];
+
                 ## the pseudo double-shift algebra:
                 elif HasIndeterminateShiftsOfPseudoDoubleShiftAlgebra( R ) then
 
@@ -574,6 +588,21 @@
 
 end );
 
+##
+InstallMethod( Indeterminates,
+        "for homalg rings",
+        [ IsHomalgRing and HasIndeterminateCoordinatesOfShiftAlgebra ],
+
+  function( R )
+
+    return
+      Concatenation(
+              IndeterminateCoordinatesOfShiftAlgebra( R ),
+              IndeterminateShiftsOfShiftAlgebra( R )
+              );
+
+end );
+
 ##
 InstallMethod( Indeterminates,
         "for homalg rings",
@@ -1364,6 +1393,144 @@
 
 end );
 
+##
+InstallMethod( SetRingProperties,
+        "for homalg rings",
+        [ IsHomalgRing and IsShiftAlgebra, IsHomalgRing and IsFreePolynomialRing, IsList ],
+
+  function( S, R, shift )
+    local r, b, param, paramS, var, d;
+
+    r := CoefficientsRing( R );
+
+    if HasBaseRing( R ) then
+        b := BaseRing( R );
+    else
+        b := r;
+    fi;
+
+    var := IndeterminatesOfPolynomialRing( R );
+    var := List( var, a -> a / S );
+
+    d := Length( var );
+
+    if d > 0 then
+        SetIsFinite( S, false );
+    fi;
+
+    SetCoefficientsRing( S, r );
+
+    if HasRationalParameters( r ) then
+        param := RationalParameters( r );
+        paramS := List( param, a -> a / S );
+        Perform( [ 1 .. Length( param ) ], function( i ) SetName( paramS[i], Name( param[i] ) ); end );
+        SetRationalParameters( S, paramS );
+    fi;
+
+    SetCharacteristic( S, Characteristic( R ) );
+
+    SetIsCommutative( S, shift = [ ] );
+
+    SetIndeterminateCoordinatesOfShiftAlgebra( S, var );
+
+    if HasRelativeIndeterminatesOfPolynomialRing( R ) then
+        SetRelativeIndeterminateCoordinatesOfShiftAlgebra(
+                S, RelativeIndeterminatesOfPolynomialRing( R ) );
+    fi;
+
+    SetIndeterminateShiftsOfShiftAlgebra( S, shift );
+
+    if d > 0 then
+        SetIsLeftArtinian( S, false );
+        SetIsRightArtinian( S, false );
+    fi;
+
+    SetIsLeftNoetherian( S, true );
+    SetIsRightNoetherian( S, true );
+
+    if HasIsIntegralDomain( r ) and IsIntegralDomain( r ) then
+        SetIsIntegralDomain( S, true );
+    fi;
+
+    if d > 0 then
+        SetIsLeftPrincipalIdealRing( S, false );
+        SetIsRightPrincipalIdealRing( S, false );
+        SetIsPrincipalIdealRing( S, false );
+    fi;
+
+    SetBasisAlgorithmRespectsPrincipalIdeals( S, true );
+
+end );
+
+##
+InstallMethod( SetRingProperties,
+        "for homalg rings",
+        [ IsHomalgRing and IsRationalShiftAlgebra, IsHomalgRing and IsFreePolynomialRing, IsList ],
+
+  function( S, R, shift )
+    local r, b, param, paramS, var, d;
+
+    r := CoefficientsRing( R );
+
+    if HasBaseRing( R ) then
+        b := BaseRing( R );
+    else
+        b := r;
+    fi;
+
+    var := IndeterminatesOfPolynomialRing( R );
+    var := List( var, a -> a / S );
+
+    d := Length( var );
+
+    if d > 0 then
+        SetIsFinite( S, false );
+    fi;
+
+    SetCoefficientsRing( S, r );
+
+    if HasRationalParameters( r ) then
+        param := RationalParameters( r );
+        paramS := List( param, a -> a / S );
+        Perform( [ 1 .. Length( param ) ], function( i ) SetName( paramS[i], Name( param[i] ) ); end );
+        SetRationalParameters( S, paramS );
+    fi;
+
+    SetCharacteristic( S, Characteristic( R ) );
+
+    SetIsCommutative( S, shift = [ ] );
+
+    SetParametersOfRationalShiftAlgebra( S, var );
+
+    if HasRelativeIndeterminatesOfPolynomialRing( R ) then
+        SetRelativeParametersOfRationalShiftAlgebra(
+                S, RelativeIndeterminatesOfPolynomialRing( R ) );
+    fi;
+
+    SetIndeterminateShiftsOfRationalShiftAlgebra( S, shift );
+
+    if d > 0 then
+        SetIsLeftArtinian( S, false );
+        SetIsRightArtinian( S, false );
+    fi;
+
+    SetIsLeftNoetherian( S, true );
+    SetIsRightNoetherian( S, true );
+
+    if HasIsIntegralDomain( r ) and IsIntegralDomain( r ) then
+        SetIsIntegralDomain( S, true );
+    fi;
+
+    if d > 0 then
+        SetIsLeftPrincipalIdealRing( S, false );
+        SetIsRightPrincipalIdealRing( S, false );
+        SetIsPrincipalIdealRing( S, false );
+    fi;
+
+    SetBasisAlgorithmRespectsPrincipalIdeals( S, true );
+
+end );
+
 ##
 InstallMethod( SetRingProperties,
         "for homalg rings",

MatricesForHomalg/gap/Tools.gi

@@ -3726,6 +3726,8 @@
         indets := RelativeIndeterminateAntiCommutingVariablesOfExteriorRing( R );
     elif HasIndeterminateAntiCommutingVariablesOfExteriorRing( R ) then
         indets := IndeterminateAntiCommutingVariablesOfExteriorRing( R );
+    elif HasIndeterminateShiftsOfShiftAlgebra( R ) then
+        indets := IndeterminateShiftsOfShiftAlgebra( R );
     elif HasIndeterminateShiftsOfPseudoDoubleShiftAlgebra( R ) then
         indets := IndeterminateShiftsOfPseudoDoubleShiftAlgebra( R );
     elif HasIndeterminateShiftsOfDoubleShiftAlgebra( R ) then
@@ -3804,6 +3806,8 @@
         indets := RelativeIndeterminateAntiCommutingVariablesOfExteriorRing( R );
     elif HasIndeterminateAntiCommutingVariablesOfExteriorRing( R ) then
         indets := IndeterminateAntiCommutingVariablesOfExteriorRing( R );
+    elif HasIndeterminateShiftsOfShiftAlgebra( R ) then
+        indets := IndeterminateShiftsOfShiftAlgebra( R );
     elif HasIndeterminateShiftsOfPseudoDoubleShiftAlgebra( R ) then
         indets := IndeterminateShiftsOfPseudoDoubleShiftAlgebra( R );
     elif HasIndeterminateShiftsOfDoubleShiftAlgebra( R ) then

RingsForHomalg/PackageInfo.g

@@ -11,7 +11,7 @@ SetPackageInfo( rec(
 
 PackageName := "RingsForHomalg",
 Subtitle := "Dictionaries of external rings",
-Version := "2024.06-01",
+Version := "2024.11-02",
 Date := (function ( ) if IsBound( GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE ) then return GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE; else return Concatenation( ~.Version{[ 1 .. 4 ]}, "-", ~.Version{[ 6, 7 ]}, "-01" ); fi; end)( ),
 License := "GPL-2.0-or-later",
 
@@ -207,7 +207,7 @@ PackageDoc := rec(
 Dependencies := rec(
   GAP := ">= 4.12.1",
   NeededOtherPackages := [
-                   [ "MatricesForHomalg", ">= 2023.08-01" ],
+                   [ "MatricesForHomalg", ">= 2024.11-02" ],
                    [ "HomalgToCAS", ">= 2023.08-01" ],
                    [ "GaussForHomalg", ">= 2023.08-01" ],
                    [ "GAPDoc", ">= 1.0" ]