@@ -9,8 +9,9 @@ The following examples tests the functionality of the software projects
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``` @meta
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DocTestSetup = quote
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using HomalgProject
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+ GAP.Globals.SizeScreen( GAP.julia_to_gap( [ 4096 ] ) )
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+ LoadPackageAndExposeGlobals( "IO_ForHomalg", Main, all_globals = true )
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LoadPackageAndExposeGlobals( "GradedModules", Main, all_globals = true )
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- LoadPackageAndExposeGlobals( "GradedModulePresentationsForCAP", Main, all_globals = true )
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GAP.Globals.HOMALG_IO.show_banners = false
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HomalgFieldOfRationalsInSingular = GAP.Globals.HomalgFieldOfRationalsInSingular
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LeftPresentation = GAP.Globals.LeftPresentation
@@ -20,33 +21,12 @@ DocTestSetup = quote
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FilteredByPurity = GAP.Globals.FilteredByPurity
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OnFirstStoredPresentation = GAP.Globals.OnFirstStoredPresentation
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OnLastStoredPresentation = GAP.Globals.OnLastStoredPresentation
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- GradedRing = GAP.Globals.GradedRing
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- GradedLeftPresentations = GAP.Globals.GradedLeftPresentations
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- InfoOfInstalledOperationsOfCategory = GAP.Globals.InfoOfInstalledOperationsOfCategory
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- ListPrimitivelyInstalledOperationsOfCategory = GAP.Globals.ListPrimitivelyInstalledOperationsOfCategory
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- GradedFreeLeftPresentation = GAP.Globals.GradedFreeLeftPresentation
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- GradedPresentationMorphism = GAP.Globals.GradedPresentationMorphism
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- IsWellDefined = GAP.Globals.IsWellDefined
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- IsMonomorphism = GAP.Globals.IsMonomorphism
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- IsEpimorphism = GAP.Globals.IsEpimorphism
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- ImageEmbedding = GAP.Globals.ImageEmbedding
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- CokernelObject = GAP.Globals.CokernelObject
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- IsZero = GAP.Globals.IsZero
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- AffineDimension = GAP.Globals.AffineDimension
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- FullSubcategoryByMembershipFunction = GAP.Globals.FullSubcategoryByMembershipFunction
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- / = GAP.Globals.QUO
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- CanonicalProjection = GAP.Globals.CanonicalProjection
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- InstallFunctor = GAP.Globals.InstallFunctor
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- ApplyFunctor = GAP.Globals.ApplyFunctor
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- IsIsomorphism = GAP.Globals.IsIsomorphism
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end
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```
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``` jldoctest
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julia> using HomalgProject
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- julia> LoadPackageAndExposeGlobals( "OscarForHomalg", Main, all_globals = true )
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-
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julia> LoadPackageAndExposeGlobals( "GradedModules", Main, all_globals = true )
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julia> ℚ = HomalgFieldOfRationalsInSingular( )
@@ -255,120 +235,6 @@ currently represented by the above matrix
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```
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- ``` jldoctest
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- julia> using HomalgProject
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-
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- julia> LoadPackageAndExposeGlobals( "GradedModulePresentationsForCAP", Main, all_globals = true )
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-
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- julia> ℚ = HomalgFieldOfRationalsInSingular( )
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- GAP: Q
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-
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- julia> S = GradedRing( ℚ["x,y"] )
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- GAP: Q[x,y]
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- (weights: yet unset)
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-
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- julia> Sgrmod = GradedLeftPresentations( S )
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- GAP: The category of graded left f.p. modules over Q[x,y] (with weights [ 1, 1 ])
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-
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- julia> InfoOfInstalledOperationsOfCategory( Sgrmod )
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- 40 primitive operations were used to derive 179 operations for this category which
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- * IsAbCategory
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- * IsMonoidalCategory
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- * IsAbelianCategoryWithEnoughProjectives
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-
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- julia> #ListPrimitivelyInstalledOperationsOfCategory( Sgrmod )
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-
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- julia> M = GradedFreeLeftPresentation( 2, S, @gap([ 1, 1 ]) )
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- GAP: <An object in The category of graded left f.p. modules over Q[x,y] (with weights [ 1, 1 ])>
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-
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- julia> N = GradedFreeLeftPresentation( 1, S, @gap([ 0 ]) )
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- GAP: <An object in The category of graded left f.p. modules over Q[x,y] (with weights [ 1, 1 ])>
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-
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- julia> mat = HomalgMatrix( "[x,y]", 2, 1, S )
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- GAP: <A 2 x 1 matrix over a graded ring>
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-
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- julia> Display( mat )
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- x,
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- y
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-
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- (over a graded ring)
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-
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- julia> ϕ = GradedPresentationMorphism( M, mat, N )
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- GAP: <A morphism in The category of graded left f.p. modules over Q[x,y] (with weights [ 1, 1 ])>
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-
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- julia> IsWellDefined( ϕ )
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- true
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-
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- julia> IsMonomorphism( ϕ )
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- false
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-
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- julia> IsEpimorphism( ϕ )
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- false
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-
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- julia> ι = ImageEmbedding( ϕ )
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- GAP: <A monomorphism in The category of graded left f.p. modules over Q[x,y] (with weights [ 1, 1 ])>
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-
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- julia> IsMonomorphism( ι )
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- true
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-
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- julia> IsIsomorphism( ι )
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- false
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-
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- julia> coker_mod = CokernelObject( ϕ )
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- GAP: <An object in The category of graded left f.p. modules over Q[x,y] (with weights [ 1, 1 ])>
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-
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- julia> Display( coker_mod )
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- x,
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- y
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- (over a graded ring)
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-
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- An object in The category of graded left f.p. modules over Q[x,y] (with weights [ 1, 1 ])
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-
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- (graded, degree of generator:[ 0 ])
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-
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- julia> IsZero( coker_mod )
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- false
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-
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- julia> is_artinian = GAP.julia_to_gap( M -> AffineDimension( M ) <= 0 );
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-
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- julia> C = FullSubcategoryByMembershipFunction( Sgrmod, is_artinian );
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-
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- julia> CohP1 = Sgrmod / C
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- GAP: The Serre quotient category of The category of graded left f.p. modules over Q[x,y] (with weights [ 1, 1 ]) by test function with name: #1
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-
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- julia> InfoOfInstalledOperationsOfCategory( CohP1 )
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- 21 primitive operations were used to derive 146 operations for this category which
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- * IsAbCategory
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- * IsAbelianCategory
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-
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- julia> Sh = CanonicalProjection( CohP1 )
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- GAP: Embedding in The Serre quotient category of The category of graded left f.p. modules over Q[x,y] (with weights [ 1, 1 ]) by test function with name: #1
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-
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- julia> InstallFunctor( Sh, g"Sheafification" )
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-
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- julia> ψ = ApplyFunctor( Sh, ϕ )
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- GAP: <A morphism in The Serre quotient category of The category of graded left f.p. modules over Q[x,y] (with weights [ 1, 1 ]) by test function with name: #1>
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-
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- julia> IsMonomorphism( ψ )
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- false
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-
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- julia> IsEpimorphism( ψ )
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- true
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-
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- julia> coker_shv = CokernelObject( ψ )
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- GAP: <A zero object in The Serre quotient category of The category of graded left f.p. modules over Q[x,y] (with weights [ 1, 1 ]) by test function with name: #1>
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-
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- julia> IsZero( coker_shv )
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- true
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-
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- julia> ϵ = ApplyFunctor( Sh, ι )
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- GAP: <A morphism in The Serre quotient category of The category of graded left f.p. modules over Q[x,y] (with weights [ 1, 1 ]) by test function with name: #1>
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-
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- julia> IsIsomorphism( ϵ )
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- true
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-
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- ```
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-
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``` @meta
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DocTestSetup = nothing
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```
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