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AddDerivationToCAP( MorphismFromCoimageToImageWithGivenObjects, ... ) #1479

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10 changes: 4 additions & 6 deletions CAP/gap/DerivedMethods.autogen.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -1050,17 +1050,15 @@ end : CategoryFilter := IsCapCategory,

##
AddDerivationToCAP( MorphismFromCoimageToImageWithGivenObjects,
"dualizing the derivation of MorphismFromCoimageToImageWithGivenObjects by MorphismFromCoimageToImageWithGivenObjects using that images are given by kernels of cokernels",
"dualizing the derivation of MorphismFromCoimageToImageWithGivenObjects by MorphismFromCoimageToImageWithGivenObjects using that the image embedding lifts the coimage astriction",
[
[ KernelEmbedding, 1 ],
[ CokernelColift, 1 ],
[ CoimageProjectionWithGivenCoimageObject, 1 ],
[ CoastrictionToImageWithGivenImageObject, 1 ],
[ PostCompose, 1 ],
[ IsomorphismFromCoimageToCokernelOfKernel, 1 ],
[ ColiftAlongEpimorphism, 1 ],
],

function ( cat_1, C_1, alpha_1, I_1 )
return PostCompose( cat_1, CokernelColift( cat_1, KernelEmbedding( cat_1, alpha_1 ), I_1, CoastrictionToImageWithGivenImageObject( cat_1, alpha_1, I_1 ) ), IsomorphismFromCoimageToCokernelOfKernel( cat_1, alpha_1 ) );
return ColiftAlongEpimorphism( cat_1, CoimageProjectionWithGivenCoimageObject( cat_1, alpha_1, C_1 ), CoastrictionToImageWithGivenImageObject( cat_1, alpha_1, I_1 ) );
end : CategoryFilter := IsPreAbelianCategory,
Weight := 1,
is_autogenerated_by_CompilerForCAP := true );
Expand Down
17 changes: 6 additions & 11 deletions CAP/gap/DerivedMethods.gi
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Expand Up @@ -2939,21 +2939,16 @@ AddFinalDerivationBundle( "IsomorphismFromImageObjectToKernelOfCokernel as the i

##
AddDerivationToCAP( MorphismFromCoimageToImageWithGivenObjects,
"MorphismFromCoimageToImageWithGivenObjects using that images are given by kernels of cokernels",
[ [ CokernelProjection, 1 ],
[ KernelLift, 1 ],
"MorphismFromCoimageToImageWithGivenObjects using that the image embedding lifts the coimage astriction",
[ [ ImageEmbeddingWithGivenImageObject, 1 ],
[ AstrictionToCoimageWithGivenCoimageObject, 1 ],
[ PreCompose, 1 ],
[ IsomorphismFromKernelOfCokernelToImageObject, 1 ] ],
[ LiftAlongMonomorphism, 1 ] ],

function( cat, coimage, morphism, image )
local cokernel_projection, kernel_lift;

cokernel_projection := CokernelProjection( cat, morphism );

kernel_lift := KernelLift( cat, cokernel_projection, coimage, AstrictionToCoimageWithGivenCoimageObject( cat, morphism, coimage ) );

return PreCompose( cat, kernel_lift, IsomorphismFromKernelOfCokernelToImageObject( cat, morphism ) );
return LiftAlongMonomorphism( cat,
ImageEmbeddingWithGivenImageObject( cat, morphism, image ),
AstrictionToCoimageWithGivenCoimageObject( cat, morphism, coimage ) );

end : CategoryFilter := IsPreAbelianCategory );

Expand Down
87 changes: 23 additions & 64 deletions LinearAlgebraForCAP/gap/precompiled_categories/MatrixCategory_precompiled.gi
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Expand Up @@ -4154,28 +4154,24 @@ end

########
function ( cat_1, alpha_1 )
local morphism_attr_1_1, deduped_2_1, deduped_3_1, deduped_4_1;
deduped_4_1 := UnderlyingRing( cat_1 );
deduped_3_1 := AsHomalgMatrix( alpha_1 );
deduped_2_1 := SyzygiesOfRows( SyzygiesOfColumns( deduped_3_1 ) );
morphism_attr_1_1 := UniqueRightDivide( HomalgIdentityMatrix( RowRankOfMatrix( deduped_3_1 ), deduped_4_1 ), UniqueRightDivide( UniqueLeftDivide( BasisOfColumns( deduped_3_1 ), deduped_3_1 ), deduped_2_1 ) * UniqueRightDivide( HomalgIdentityMatrix( NumberRows( deduped_2_1 ), deduped_4_1 ), UniqueRightDivide( BasisOfRows( deduped_3_1 ), deduped_2_1 ) ) );
local morphism_attr_1_1, deduped_2_1;
deduped_2_1 := AsHomalgMatrix( alpha_1 );
morphism_attr_1_1 := UniqueRightDivide( HomalgIdentityMatrix( RowRankOfMatrix( deduped_2_1 ), UnderlyingRing( cat_1 ) ), UniqueRightDivide( UniqueLeftDivide( BasisOfColumns( deduped_2_1 ), deduped_2_1 ), BasisOfRows( deduped_2_1 ) ) );
return AsCapCategoryMorphism( cat_1, AsCapCategoryObject( cat_1, NumberRows( morphism_attr_1_1 ) ), morphism_attr_1_1, AsCapCategoryObject( cat_1, NumberColumns( morphism_attr_1_1 ) ) );
end
########

, 1811 : IsPrecompiledDerivation := true );
, 805 : IsPrecompiledDerivation := true );

##
cat!.cached_precompiled_functions.InverseOfMorphismFromCoimageToImage :=

########
function ( cat_1, alpha_1 )
local deduped_1_1, deduped_2_1, deduped_3_1, deduped_4_1;
deduped_4_1 := UnderlyingRing( cat_1 );
deduped_3_1 := AsHomalgMatrix( alpha_1 );
deduped_2_1 := RowRankOfMatrix( deduped_3_1 );
deduped_1_1 := SyzygiesOfRows( SyzygiesOfColumns( deduped_3_1 ) );
return AsCapCategoryMorphism( cat_1, AsCapCategoryObject( cat_1, deduped_2_1 ), UniqueRightDivide( HomalgIdentityMatrix( deduped_2_1, deduped_4_1 ), UniqueRightDivide( UniqueLeftDivide( BasisOfColumns( deduped_3_1 ), deduped_3_1 ), deduped_1_1 ) * UniqueRightDivide( HomalgIdentityMatrix( NumberRows( deduped_1_1 ), deduped_4_1 ), UniqueRightDivide( BasisOfRows( deduped_3_1 ), deduped_1_1 ) ) ), AsCapCategoryObject( cat_1, ColumnRankOfMatrix( deduped_3_1 ) ) );
local deduped_1_1, deduped_2_1;
deduped_2_1 := AsHomalgMatrix( alpha_1 );
deduped_1_1 := RowRankOfMatrix( deduped_2_1 );
return AsCapCategoryMorphism( cat_1, AsCapCategoryObject( cat_1, deduped_1_1 ), UniqueRightDivide( HomalgIdentityMatrix( deduped_1_1, UnderlyingRing( cat_1 ) ), UniqueRightDivide( UniqueLeftDivide( BasisOfColumns( deduped_2_1 ), deduped_2_1 ), BasisOfRows( deduped_2_1 ) ) ), AsCapCategoryObject( cat_1, ColumnRankOfMatrix( deduped_2_1 ) ) );
end
########

Expand All @@ -4186,32 +4182,13 @@ end

########
function ( cat_1, I_1, alpha_1, C_1 )
local morphism_attr_1_1, deduped_2_1, deduped_3_1, deduped_4_1;
deduped_4_1 := UnderlyingRing( cat_1 );
deduped_3_1 := AsHomalgMatrix( alpha_1 );
deduped_2_1 := SyzygiesOfRows( SyzygiesOfColumns( deduped_3_1 ) );
morphism_attr_1_1 := UniqueRightDivide( HomalgIdentityMatrix( RowRankOfMatrix( deduped_3_1 ), deduped_4_1 ), UniqueRightDivide( UniqueLeftDivide( BasisOfColumns( deduped_3_1 ), deduped_3_1 ), deduped_2_1 ) * UniqueRightDivide( HomalgIdentityMatrix( NumberRows( deduped_2_1 ), deduped_4_1 ), UniqueRightDivide( BasisOfRows( deduped_3_1 ), deduped_2_1 ) ) );
return AsCapCategoryMorphism( cat_1, AsCapCategoryObject( cat_1, NumberRows( morphism_attr_1_1 ) ), morphism_attr_1_1, C_1 );
end
########

, 1610 : IsPrecompiledDerivation := true );

##
cat!.cached_precompiled_functions.InverseOfMorphismFromCoimageToImageWithGivenObjects :=

########
function ( cat_1, I_1, alpha_1, C_1 )
local deduped_1_1, deduped_2_1, deduped_3_1, deduped_4_1;
deduped_4_1 := UnderlyingRing( cat_1 );
deduped_3_1 := AsHomalgMatrix( alpha_1 );
deduped_2_1 := RowRankOfMatrix( deduped_3_1 );
deduped_1_1 := SyzygiesOfRows( SyzygiesOfColumns( deduped_3_1 ) );
return AsCapCategoryMorphism( cat_1, AsCapCategoryObject( cat_1, deduped_2_1 ), UniqueRightDivide( HomalgIdentityMatrix( deduped_2_1, deduped_4_1 ), UniqueRightDivide( UniqueLeftDivide( BasisOfColumns( deduped_3_1 ), deduped_3_1 ), deduped_1_1 ) * UniqueRightDivide( HomalgIdentityMatrix( NumberRows( deduped_1_1 ), deduped_4_1 ), UniqueRightDivide( BasisOfRows( deduped_3_1 ), deduped_1_1 ) ) ), C_1 );
local deduped_1_1;
deduped_1_1 := AsHomalgMatrix( alpha_1 );
return AsCapCategoryMorphism( cat_1, I_1, UniqueRightDivide( HomalgIdentityMatrix( AsInteger( I_1 ), UnderlyingRing( cat_1 ) ), UniqueRightDivide( UniqueLeftDivide( BasisOfColumns( deduped_1_1 ), deduped_1_1 ), BasisOfRows( deduped_1_1 ) ) ), C_1 );
end
########

;
, 604 : IsPrecompiledDerivation := true );

##
AddIsAutomorphism( cat,
Expand Down Expand Up @@ -7094,25 +7071,23 @@ end

########
function ( cat_1, alpha_1 )
local morphism_attr_1_1, deduped_2_1, deduped_3_1;
deduped_3_1 := AsHomalgMatrix( alpha_1 );
deduped_2_1 := SyzygiesOfRows( SyzygiesOfColumns( deduped_3_1 ) );
morphism_attr_1_1 := UniqueRightDivide( UniqueLeftDivide( BasisOfColumns( deduped_3_1 ), deduped_3_1 ), deduped_2_1 ) * UniqueRightDivide( HomalgIdentityMatrix( NumberRows( deduped_2_1 ), UnderlyingRing( cat_1 ) ), UniqueRightDivide( BasisOfRows( deduped_3_1 ), deduped_2_1 ) );
local morphism_attr_1_1, deduped_2_1;
deduped_2_1 := AsHomalgMatrix( alpha_1 );
morphism_attr_1_1 := UniqueRightDivide( UniqueLeftDivide( BasisOfColumns( deduped_2_1 ), deduped_2_1 ), BasisOfRows( deduped_2_1 ) );
return AsCapCategoryMorphism( cat_1, AsCapCategoryObject( cat_1, NumberRows( morphism_attr_1_1 ) ), morphism_attr_1_1, AsCapCategoryObject( cat_1, NumberColumns( morphism_attr_1_1 ) ) );
end
########

, 1609 : IsPrecompiledDerivation := true );
, 603 : IsPrecompiledDerivation := true );

##
cat!.cached_precompiled_functions.MorphismFromCoimageToImage :=

########
function ( cat_1, alpha_1 )
local deduped_1_1, deduped_2_1;
deduped_2_1 := AsHomalgMatrix( alpha_1 );
deduped_1_1 := SyzygiesOfRows( SyzygiesOfColumns( deduped_2_1 ) );
return AsCapCategoryMorphism( cat_1, AsCapCategoryObject( cat_1, ColumnRankOfMatrix( deduped_2_1 ) ), UniqueRightDivide( UniqueLeftDivide( BasisOfColumns( deduped_2_1 ), deduped_2_1 ), deduped_1_1 ) * UniqueRightDivide( HomalgIdentityMatrix( NumberRows( deduped_1_1 ), UnderlyingRing( cat_1 ) ), UniqueRightDivide( BasisOfRows( deduped_2_1 ), deduped_1_1 ) ), AsCapCategoryObject( cat_1, RowRankOfMatrix( deduped_2_1 ) ) );
local deduped_1_1;
deduped_1_1 := AsHomalgMatrix( alpha_1 );
return AsCapCategoryMorphism( cat_1, AsCapCategoryObject( cat_1, ColumnRankOfMatrix( deduped_1_1 ) ), UniqueRightDivide( UniqueLeftDivide( BasisOfColumns( deduped_1_1 ), deduped_1_1 ), BasisOfRows( deduped_1_1 ) ), AsCapCategoryObject( cat_1, RowRankOfMatrix( deduped_1_1 ) ) );
end
########

Expand All @@ -7123,29 +7098,13 @@ end

########
function ( cat_1, C_1, alpha_1, I_1 )
local morphism_attr_1_1, deduped_2_1, deduped_3_1;
deduped_3_1 := AsHomalgMatrix( alpha_1 );
deduped_2_1 := SyzygiesOfRows( SyzygiesOfColumns( deduped_3_1 ) );
morphism_attr_1_1 := UniqueRightDivide( UniqueLeftDivide( BasisOfColumns( deduped_3_1 ), deduped_3_1 ), deduped_2_1 ) * UniqueRightDivide( HomalgIdentityMatrix( NumberRows( deduped_2_1 ), UnderlyingRing( cat_1 ) ), UniqueRightDivide( BasisOfRows( deduped_3_1 ), deduped_2_1 ) );
return AsCapCategoryMorphism( cat_1, C_1, morphism_attr_1_1, AsCapCategoryObject( cat_1, NumberColumns( morphism_attr_1_1 ) ) );
end
########

, 1408 : IsPrecompiledDerivation := true );

##
cat!.cached_precompiled_functions.MorphismFromCoimageToImageWithGivenObjects :=

########
function ( cat_1, C_1, alpha_1, I_1 )
local deduped_1_1, deduped_2_1;
deduped_2_1 := AsHomalgMatrix( alpha_1 );
deduped_1_1 := SyzygiesOfRows( SyzygiesOfColumns( deduped_2_1 ) );
return AsCapCategoryMorphism( cat_1, C_1, UniqueRightDivide( UniqueLeftDivide( BasisOfColumns( deduped_2_1 ), deduped_2_1 ), deduped_1_1 ) * UniqueRightDivide( HomalgIdentityMatrix( NumberRows( deduped_1_1 ), UnderlyingRing( cat_1 ) ), UniqueRightDivide( BasisOfRows( deduped_2_1 ), deduped_1_1 ) ), AsCapCategoryObject( cat_1, RowRankOfMatrix( deduped_2_1 ) ) );
local deduped_1_1;
deduped_1_1 := AsHomalgMatrix( alpha_1 );
return AsCapCategoryMorphism( cat_1, C_1, UniqueRightDivide( UniqueLeftDivide( BasisOfColumns( deduped_1_1 ), deduped_1_1 ), BasisOfRows( deduped_1_1 ) ), I_1 );
end
########

;
, 402 : IsPrecompiledDerivation := true );

##
AddMorphismFromEqualizerToSink( cat,
Expand Down
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