Merge pull request #1408 from kamalsaleh/lincomb

add 'LinearCombinationOfMorphisms' to the method record

CAP/PackageInfo.g

@@ -10,7 +10,7 @@ SetPackageInfo( rec(
 
 PackageName := "CAP",
 Subtitle := "Categories, Algorithms, Programming",
-Version := "2023.08-06",
+Version := "2023.08-07",
 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",
 

CAP/examples/TerminalCategoryWithMultipleObjects.g

@@ -10,7 +10,7 @@ T := TerminalCategoryWithMultipleObjects( );
 Display( T );
 #! A CAP category with name TerminalCategoryWithMultipleObjects( ):
 #! 
-#! 65 primitive operations were used to derive 306 operations for this category \
+#! 65 primitive operations were used to derive 307 operations for this category \
 #! which algorithmically
 #! * IsCategoryWithDecidableColifts
 #! * IsCategoryWithDecidableLifts

CAP/examples/TerminalCategoryWithSingleObject.g

@@ -10,7 +10,7 @@ T := TerminalCategoryWithSingleObject( );
 Display( T );
 #! A CAP category with name TerminalCategoryWithSingleObject( ):
 #! 
-#! 63 primitive operations were used to derive 306 operations for this category \
+#! 63 primitive operations were used to derive 307 operations for this category \
 #! which algorithmically
 #! * IsCategoryWithDecidableColifts
 #! * IsCategoryWithDecidableLifts

CAP/gap/AddFunctions.autogen.gd

@@ -3030,6 +3030,25 @@ DeclareOperation( "AddLiftOrFail",
 DeclareOperation( "AddLiftOrFail",
                   [ IsCapCategory, IsList ] );
 
+#! @Description
+#! The arguments are a category $C$ and a function $F$.
+#! This operation adds the given function $F$
+#! to the category for the basic operation `LinearCombinationOfMorphisms`.
+#! $F: ( source, list_of_ring_elements, list_of_morphisms, range ) \mapsto \mathtt{LinearCombinationOfMorphisms}(source, list_of_ring_elements, list_of_morphisms, range)$.
+#! @Returns nothing
+#! @Arguments C, F
+DeclareOperation( "AddLinearCombinationOfMorphisms",
+                  [ IsCapCategory, IsFunction ] );
+
+DeclareOperation( "AddLinearCombinationOfMorphisms",
+                  [ IsCapCategory, IsFunction, IsInt ] );
+
+DeclareOperation( "AddLinearCombinationOfMorphisms",
+                  [ IsCapCategory, IsList, IsInt ] );
+
+DeclareOperation( "AddLinearCombinationOfMorphisms",
+                  [ IsCapCategory, IsList ] );
+
 #! @Description
 #! The arguments are a category $C$ and a function $F$.
 #! This operation adds the given function $F$

CAP/gap/CategoryMorphisms.gd

@@ -721,6 +721,16 @@ DeclareOperation( "PostComposeList",
 DeclareOperation( "SumOfMorphisms",
                   [ IsCapCategoryObject, IsList, IsCapCategoryObject ] );
 
+#! @Description
+#! The arguments are two objects <A>s</A>, <A>r</A> in some linear category over a ring $R$,
+#! a list <A>coeffs</A> of ring elements in $R$ and a list <A>mors</A> of morphisms from <A>s</A> to <A>r</A>.
+#! The output is the linear combination of the morphisms in <A>mors</A> with respect to the coefficients list <A>coeffs</A>,
+#! or the zero morphism from <A>s</A> to <A>r</A> if <A>coeffs</A> and <A>mors</A> are the empty lists.
+#! @Returns a morphism in $\mathrm{Hom}(s,r)$
+#! @Arguments s, coeffs, mors, r
+DeclareOperation( "LinearCombinationOfMorphisms",
+                  [ IsCapCategoryObject, IsList, IsList, IsCapCategoryObject ] );
+
 ###################################
 ##
 #! @Section Well-Definedness of Morphisms

CAP/gap/DerivedMethods.gi

@@ -1952,6 +1952,21 @@ AddDerivationToCAP( SumOfMorphisms,
 
 end : CategoryFilter := IsAbCategory );
 
+##
+AddDerivationToCAP( LinearCombinationOfMorphisms,
+                    "LinearCombinationOfMorphisms using SumOfMorphisms and MultiplyWithElementOfCommutativeRingForMorphisms",
+                    [ [ MultiplyWithElementOfCommutativeRingForMorphisms, 2 ],
+                      [ SumOfMorphisms, 1 ] ],
+
+  function( cat, obj1, coeffs, mors, obj2 )
+    local morphisms;
+
+    morphisms := ListN( coeffs, mors, { r, alpha } -> MultiplyWithElementOfCommutativeRingForMorphisms( cat, r, alpha ) );
+
+    return SumOfMorphisms( cat, obj1, morphisms, obj2 );
+
+end : CategoryFilter := IsLinearCategoryOverCommutativeRing );
+
 ##
 AddDerivationToCAP( LiftAlongMonomorphism,
                     "LiftAlongMonomorphism using Lift",

CAP/gap/MethodRecord.gi

@@ -576,6 +576,43 @@ SumOfMorphisms := rec(
   compatible_with_congruence_of_morphisms := true,
 ),
 
+LinearCombinationOfMorphisms := rec(
+  filter_list := [ "category", "object", "list_of_elements_of_commutative_ring_of_linear_structure", "list_of_morphisms", "object" ],
+  input_arguments_names := [ "cat", "source", "list_of_ring_elements", "list_of_morphisms", "range" ],
+  pre_function := function( cat, source, list_of_ring_elements, list_of_morphisms, range )
+    local m;
+
+    if not Length( list_of_ring_elements ) = Length( list_of_morphisms ) then
+
+        return [ false, "the length of the lists of coefficients and morphisms must be the same" ];
+
+    fi;
+
+    for m in list_of_morphisms do
+
+        if not IsEqualForObjects( cat, source, Source( m ) ) or not IsEqualForObjects( cat, range, Range( m ) ) then
+
+            return [ false, "some of the morphisms are not compatible with the provided source and range objects" ];
+
+        fi;
+
+    od;
+
+    return [ true ];
+
+  end,
+  return_type := "morphism",
+  output_source_getter_string := "source",
+  output_range_getter_string := "range",
+  dual_operation := "LinearCombinationOfMorphisms",
+  dual_preprocessor_func := function( arg )
+      local list;
+      list := CAP_INTERNAL_OPPOSITE_RECURSIVE( arg );
+      return NTuple( 5, list[1], list[5], list[3], list[4], list[2] );
+  end,
+  compatible_with_congruence_of_morphisms := true,
+),
+
 PreComposeList := rec(
   filter_list := [ "category", "list_of_morphisms" ],
   input_arguments_names := [ "cat", "list_of_morphisms" ],

CAP/gap/OppositeCategory.gi

@@ -224,7 +224,7 @@ BindGlobal( "CAP_INTERNAL_INSTALL_OPPOSITE_ADDS_FROM_CATEGORY",
 
                     return Concatenation( "MorphismDatum( cat, ", argument_name, " )" );
 
-                elif filter = "integer" or filter = "element_of_commutative_ring_of_linear_structure" or filter = "nonneg_integer_or_infinity" then
+                elif filter in [ "integer", "element_of_commutative_ring_of_linear_structure", "nonneg_integer_or_infinity", "list_of_elements_of_commutative_ring_of_linear_structure" ] then
 
                     return argument_name;
 

FreydCategoriesForCAP/PackageInfo.g

@@ -10,7 +10,7 @@ SetPackageInfo( rec(
 
 PackageName := "FreydCategoriesForCAP",
 Subtitle := "Freyd categories - Formal (co)kernels for additive categories",
-Version := "2023.08-01",
+Version := "2023.08-02",
 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",
 
@@ -87,7 +87,7 @@ PackageDoc := rec(
 
 Dependencies := rec(
   GAP := ">= 4.12.1",
-  NeededOtherPackages := [ [ "CAP", ">= 2023.06-04" ],
+  NeededOtherPackages := [ [ "CAP", ">= 2023.08-07" ],
                            [ "MatricesForHomalg", ">= 2023.01-01" ],
                            [ "GradedRingForHomalg", ">=2019.08.07" ],
                            [ "MonoidalCategories", ">= 2023.02-04" ],

FreydCategoriesForCAP/examples/RingsAsAbCats.g

@@ -40,7 +40,7 @@ BasisOfExternalHom( u, u );
 #! [ <1> ]
 CoefficientsOfMorphism( alpha );
 #! [ 2 ]
-IsCongruentForMorphisms( alpha, SumOfMorphisms( u, ListN( CoefficientsOfMorphism( alpha ), BasisOfExternalHom( u, u ), { x, y } -> MultiplyWithElementOfCommutativeRingForMorphisms( x, y ) ), u ) );
+IsCongruentForMorphisms( alpha, LinearCombinationOfMorphisms( u, CoefficientsOfMorphism( alpha ), BasisOfExternalHom( u, u ), u ) );
 #! true
 
 EEE := KoszulDualRing( HomalgFieldOfRationalsInSingular( ) * "x,y" );;
@@ -72,11 +72,19 @@ Lift( alpha * alpha, alpha );
 #! <5*e0*e1+3*e0+4*e1+2>
 Colift( alpha, alpha * alpha );
 #! <5*e0*e1+3*e0+4*e1+2>
-BasisOfExternalHom( u, u );
+basis := BasisOfExternalHom( u, u );
 #! [ <1>, <e0>, <e1>, <e0*e1> ]
-CoefficientsOfMorphism( alpha );
+coeffs := CoefficientsOfMorphism( alpha );
 #! [ 2, 3, 4, 5 ]
-IsCongruentForMorphisms( alpha, SumOfMorphisms( u, ListN( CoefficientsOfMorphism( alpha ), BasisOfExternalHom( u, u ), { x, y } -> MultiplyWithElementOfCommutativeRingForMorphisms( x, y ) ), u ) );
+IsCongruentForMorphisms( alpha, LinearCombinationOfMorphisms( u, coeffs, basis, u ) );
+#! true
+u_op := Opposite( u );
+#! <An object in Opposite( Ring as category( Q{e0,e1} ) )>
+alpha_op := Opposite( alpha );
+#! <A morphism in Opposite( Ring as category( Q{e0,e1} ) )>
+basis := BasisOfExternalHom( u_op, u_op );;
+coeffs := CoefficientsOfMorphism( alpha_op );
+#! [ 2, 3, 4, 5 ]
+IsCongruentForMorphisms( alpha_op, LinearCombinationOfMorphisms( u_op, coeffs, basis, u_op ) );
 #! true
-
 #! @EndExample

FreydCategoriesForCAP/gap/CategoryOfRows.autogen.gd

@@ -198,6 +198,7 @@
 #! * <Ref BookName="CAP" Func="InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure" Label="for Is" />
 #! * <Ref BookName="CAP" Func="InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructureWithGivenObjects" Label="for Is" />
 #! * <Ref BookName="CAP" Func="InterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism" Label="for Is" />
+#! * <Ref BookName="CAP" Func="LinearCombinationOfMorphisms" Label="for Is" />
 #! * <Ref BookName="CAP" Func="MereExistenceOfSolutionOfLinearSystemInAbCategory" Label="for Is" />
 #! * <Ref BookName="CAP" Func="MultiplyWithElementOfCommutativeRingForMorphisms" Label="for Is" />
 #! * <Ref BookName="CAP" Func="SolveLinearSystemInAbCategory" Label="for Is" />

FreydCategoriesForCAP/gap/CategoryOfRows.gi

@@ -1326,9 +1326,8 @@ AddFinalDerivationBundle( "Using BasisOfExternalHom and CoefficientsOfMorphism t
                     [
                       [ BasisOfExternalHom, 1 ],
                       [ CoefficientsOfMorphism, 2 ],
-                      [ MultiplyWithElementOfCommutativeRingForMorphisms, 2 ],
-                      [ PreComposeList, 2 ],
-                      [ SumOfMorphisms, 1 ]
+                      [ LinearCombinationOfMorphisms, 1 ],
+                      [ PreComposeList, 2 ]
                     ],
                     [
                       HomomorphismStructureOnObjects,
@@ -1405,8 +1404,7 @@ AddFinalDerivationBundle( "Using BasisOfExternalHom and CoefficientsOfMorphism t
   InterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism,
   [
     [ BasisOfExternalHom, 1 ],
-    [ MultiplyWithElementOfCommutativeRingForMorphisms, 2 ],
-    [ SumOfMorphisms, 1 ]
+    [ LinearCombinationOfMorphisms, 1 ],
   ],
   function ( cat, a, b, iota )
     local coeffs, basis;
@@ -1415,7 +1413,7 @@ AddFinalDerivationBundle( "Using BasisOfExternalHom and CoefficientsOfMorphism t
 
     basis := BasisOfExternalHom( cat, a, b );
 
-    return SumOfMorphisms( cat, a, ListN( coeffs, basis, { c, m } -> MultiplyWithElementOfCommutativeRingForMorphisms( cat, c, m ) ), b );
+    return LinearCombinationOfMorphisms( cat, a, coeffs, basis, b );
 
   end
 ] :

FreydCategoriesForCAP/gap/LinearClosure.gi

@@ -854,7 +854,7 @@ InstallMethodWithCache( ExtendFunctorToLinearClosureOfSource,
 
         supp := List( supp, m -> ApplyFunctor( F, m ) );
 
-        return Sum( ListN( coeffs, supp, MultiplyWithElementOfCommutativeRingForMorphisms ) );
+        return LinearCombinationOfMorphisms( s, coeffs, supp, r );
 
     end );
 

LinearAlgebraForCAP/PackageInfo.g

@@ -10,7 +10,7 @@ SetPackageInfo( rec(
 
 PackageName := "LinearAlgebraForCAP",
 Subtitle := "Category of Matrices over a Field for CAP",
-Version := "2023.08-01",
+Version := "2023.08-02",
 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",
 
@@ -89,7 +89,7 @@ Dependencies := rec(
   NeededOtherPackages := [ [ "ToolsForHomalg", ">= 2015.09.18" ],
                            [ "MatricesForHomalg", ">= 2023.01-01" ],
                            [ "GaussForHomalg", ">= 2021.04-02" ],
-                           [ "CAP", ">= 2023.05-03" ],
+                           [ "CAP", ">= 2023.08-07" ],
                            [ "MonoidalCategories", ">= 2023.02-04" ],
                            ],
   SuggestedOtherPackages := [

LinearAlgebraForCAP/gap/precompiled_categories/MatrixCategoryPrecompiled.gi

@@ -3501,6 +3501,21 @@ end
 
     , 100 );
 
+    ##
+    AddLinearCombinationOfMorphisms( cat,
+
+########
+function ( cat_1, source_1, list_of_ring_elements_1, list_of_morphisms_1, range_1 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, source_1, range_1, UnderlyingMatrix, Iterated( ListN( list_of_ring_elements_1, list_of_morphisms_1, function ( r_2, alpha_2 )
+                return r_2 * UnderlyingMatrix( alpha_2 );
+            end ), function ( alpha_2, beta_2 )
+              return alpha_2 + beta_2;
+          end, HomalgZeroMatrix( Dimension( source_1 ), Dimension( range_1 ), UnderlyingRing( cat_1 ) ) ) );
+end
+########
+
+    , 502 : IsPrecompiledDerivation := true );
+
     ##
     AddMereExistenceOfSolutionOfLinearSystemInAbCategory( cat,