| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/cap/tst/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 22.8.2025 mit Größe 19 kB |
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Quelle Simplify.tst Sprache: unbekannt |
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gap> START_TEST( "Simplify" );
# gap> LoadPackage( "CAP", false ); true ############################# ## ## Categories ## ############################# gap> DeclareCategory( "IsStringsAsCategory", IsCapCategory ); gap> DeclareCategory( "IsObjectInStringsAsCategory", IsCapCategoryObject ); gap> DeclareCategory( "IsMorphismInStringsAsCategory", IsCapCategoryMorphism ); ############################# ## ## Attributes ## ############################# gap> DeclareAttribute( "UnderlyingString", IsObjectInStringsAsCategory ); gap> DeclareAttribute( "UnderlyingString", IsMorphismInStringsAsCategory ); ############################# ## ## Constructors ## ############################# gap> BindGlobal( "RemovedCharacters", > function( str, chars ) > > return Filtered( str, c -> not c in chars ); > > end ); gap> BindGlobal( "DeleteVowels", > function( str, n ) > local vowels; > > vowels := "aeiou"; > > return RemovedCharacters( str , vowels{[ 1 .. Minimum( Length( vowels ), n ) ]} ); > > end ); ## gap> BindGlobal( "StringsAsCategoryObject", > function( cat, string ) > > return CreateCapCategoryObjectWithAttributes( cat, > UnderlyingString, string ); > > end ); ## gap> BindGlobal( "StringsAsCategoryMorphism", > function( cat, source, string, range ) > > return CreateCapCategoryMorphismWithAttributes( cat, > source, > range, > UnderlyingString, string ); > > end ); ## gap> BindGlobal( "StringsAsCategory", > function( ) > local category, vowels; > > category := CreateCapCategoryWithDataTypes( "Category of strings up to vowels", > IsStringsAsCategory, > IsObjectInStringsAsCategory, > IsMorphismInStringsAsCategory, > IsCapCategoryTwoCell, > IsStringRep, > IsStringRep, > fail ); > > vowels := "aeiou"; > > ## > AddIsEqualForObjects( category, > function( cat, a, b ) > > return UnderlyingString( a ) = UnderlyingString( b ); > > end ); > > ## > AddIsEqualForMorphisms( category, > function( cat, alpha, beta ) > > return UnderlyingString( alpha ) = UnderlyingString( beta ); > > end ); > > ## > AddIsCongruentForMorphisms( category, > function( cat, alpha, beta ) > > return RemovedCharacters( UnderlyingString( alpha ), vowels ) = RemovedCharacters( Underl > > end ); > > AddIsWellDefinedForObjects( category, > function( cat, a ) > > return true; > > end); > > ## > AddIsWellDefinedForMorphisms( category, > function( cat, alpha ) > > return RemovedCharacters( Concatenation( UnderlyingString( Source( alpha ) ), Underlying > > end ); > > ## > AddPreCompose( category, > function( cat, alpha, beta ) > > return StringsAsCategoryMorphism( cat, > Source( alpha ), > Concatenation( UnderlyingString( alpha ), UnderlyingString( beta ) ), > Range( beta ) ); > > end ); > > ## > AddIdentityMorphism( category, > function( cat, a ) > > return StringsAsCategoryMorphism( cat, a, "", a ); > > end ); > > ## SimplifyObject* > ## > AddSimplifyObject( category, > function( cat, a, n ) > local min; > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > min := Minimum( Length( vowels ), n ); > > return StringsAsCategoryObject( cat, RemovedCharacters( UnderlyingString( a ) , vowels{[ > > end ); > > ## > AddSimplifyObject_IsoFromInputObject( category, > function( cat, a, n ) > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > return StringsAsCategoryMorphism( cat, a, "", SimplifyObject( a, n ) ); > > end ); > > ## > AddSimplifyObject_IsoToInputObject( category, > function( cat, a, n ) > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > return StringsAsCategoryMorphism( cat, SimplifyObject( a, n ), "", a); > > end ); > > ## SimplifyMorphism > ## > AddSimplifyMorphism( category, > function( cat, alpha, n ) > local min; > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > min := Minimum( Length( vowels ), n ); > > return StringsAsCategoryMorphism( cat, > Source( alpha ), > RemovedCharacters( UnderlyingString( alpha ) , vowels{[ 1 .. min ]} ), > Range( alpha ) ); > > end ); > > ## SimplifySource > ## > AddSimplifySource( category, > function( cat, alpha, n ) > local new_source; > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > new_source := StringsAsCategoryObject( cat, DeleteVowels( UnderlyingString( Source( alp > > return StringsAsCategoryMorphism( cat, > new_source, > UnderlyingString( alpha ), > Range( alpha ) ); > > end ); > > ## > AddSimplifySource_IsoToInputObject( category, > function( cat, alpha, n ) > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > return StringsAsCategoryMorphism( cat, > Source( SimplifySource( alpha, n ) ), > "", > Source( alpha ) ); > > end ); > > ## > AddSimplifySource_IsoFromInputObject( category, > function( cat, alpha, n ) > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > return StringsAsCategoryMorphism( cat, > Source( alpha ), > "", > Source( SimplifySource( alpha, n ) ) ); > > end ); > > ## SimplifyRange > ## > AddSimplifyRange( category, > function( cat, alpha, n ) > local new_range; > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > new_range := StringsAsCategoryObject( cat, DeleteVowels( UnderlyingString( Range( alpha > > return StringsAsCategoryMorphism( cat, > Source( alpha ), > UnderlyingString( alpha ), > new_range ); > > end ); > > ## > AddSimplifyRange_IsoToInputObject( category, > function( cat, alpha, n ) > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > return StringsAsCategoryMorphism( cat, > Range( SimplifyRange( alpha, n ) ), > "", > Range( alpha ) ); > > end ); > > ## > AddSimplifyRange_IsoFromInputObject( category, > function( cat, alpha, n ) > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > return StringsAsCategoryMorphism( cat, > Range( alpha ), > "", > Range( SimplifyRange( alpha, n ) ) ); > > end ); > > ## SimplifySourceAndRange > ## > AddSimplifySourceAndRange( category, > function( cat, alpha, n ) > local new_source, new_range; > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > new_source := StringsAsCategoryObject( cat, DeleteVowels( UnderlyingString( Source( alp > > new_range := StringsAsCategoryObject( cat, DeleteVowels( UnderlyingString( Range( alpha > > return StringsAsCategoryMorphism( cat, > new_source, > UnderlyingString( alpha ), > new_range ); > > end ); > > ## > AddSimplifySourceAndRange_IsoToInputSource( category, > function( cat, alpha, n ) > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > return StringsAsCategoryMorphism( cat, > Source( SimplifySourceAndRange( alpha, n ) ), > "", > Source( alpha ) ); > > end ); > > ## > AddSimplifySourceAndRange_IsoFromInputSource( category, > function( cat, alpha, n ) > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > return StringsAsCategoryMorphism( cat, > Source( alpha ), > "", > Source( SimplifySourceAndRange( alpha, n ) ) ); > > end ); > > ## > AddSimplifySourceAndRange_IsoToInputRange( category, > function( cat, alpha, n ) > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > return StringsAsCategoryMorphism( cat, > Range( SimplifySourceAndRange( alpha, n ) ), > "", > Range( alpha ) ); > > end ); > > ## > AddSimplifySourceAndRange_IsoFromInputRange( category, > function( cat, alpha, n ) > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > return StringsAsCategoryMorphism( cat, > Range( alpha ), > "", > Range( SimplifySourceAndRange( alpha, n ) ) ); > > end ); > > ## SimplifyEndo > ## > AddSimplifyEndo( category, > function( cat, endo, n ) > local new_object; > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > new_object := StringsAsCategoryObject( category, DeleteVowels( UnderlyingString( Sourc > > return StringsAsCategoryMorphism( cat, > new_object, > UnderlyingString( endo ), > new_object ); > > end ); > > ## > AddSimplifyEndo_IsoToInputObject( category, > function( cat, endo, n ) > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > return StringsAsCategoryMorphism( cat, > Source( SimplifyEndo( endo, n ) ), > "", > Source( endo ) ); > > end ); > > ## > AddSimplifyEndo_IsoFromInputObject( category, > function( cat, endo, n ) > > if n = 0 then > Print( "this case must not be handled here" ); > fi; > > return StringsAsCategoryMorphism( cat, > Source( endo ), > "", > Source( SimplifyEndo( endo, n ) ) ); > > end ); > > Finalize( category ); > > return category; > > end ); ############################# ## ## Test ## ############################# # gap> C := StringsAsCategory();; gap> obj1 := StringsAsCategoryObject( C, "qaeiou" );; gap> obj2 := StringsAsCategoryObject( C, "qxayeziouT" );; gap> mor := StringsAsCategoryMorphism( C, obj1, "xyzaTe", obj2 );; gap> IsWellDefined( mor ); true # ## Test SimplifyObject gap> IsEqualForObjects( SimplifyObject( obj1, 0 ), obj1 ); true gap> IsEqualForObjects( SimplifyObject( obj1, 1 ), obj1 ); false gap> ForAny( [0,1,2,3,4], i -> IsEqualForObjects( SimplifyObject( obj1, i ), SimplifyObject( false gap> ForAll( [5,6,7,8], i -> IsEqualForObjects( SimplifyObject( obj1, i ), SimplifyObject( ob true # ## Test SimplifyMorphism gap> IsEqualForMorphisms( SimplifyMorphism( mor, 0 ), mor ); true gap> IsEqualForMorphisms( SimplifyMorphism( mor, 1 ), mor ); false gap> ForAny( [0,1], i -> IsEqualForMorphisms( SimplifyMorphism( mor, i ), SimplifyMorphism( m false gap> ForAll( [2,3,4,5], i -> IsEqualForMorphisms( SimplifyMorphism( mor, i ), SimplifyMorphi true # ## Test SimplifySource gap> IsEqualForMorphismsOnMor( SimplifySource( mor, 0 ), mor ); true gap> IsEqualForMorphismsOnMor( SimplifySource( mor, 1 ), mor ); false gap> ForAny( [0,1,2,3,4], i -> IsEqualForMorphismsOnMor( SimplifySource( mor, i ), SimplifyS false gap> ForAll( [5,6,7,8,9], i -> IsEqualForMorphismsOnMor( SimplifySource( mor, i ), SimplifyS true gap> IsCongruentForMorphisms( > PreCompose( SimplifySource_IsoFromInputObject( mor, infinity ), SimplifySource( mor, in > ); true gap> IsCongruentForMorphisms( > PreCompose( SimplifySource_IsoToInputObject( mor, infinity ), mor ) , SimplifySource( mor > ); true # ## Test SimplifyRange gap> IsEqualForMorphismsOnMor( SimplifyRange( mor, 0 ), mor ); true gap> IsEqualForMorphismsOnMor( SimplifyRange( mor, 1 ), mor ); false gap> ForAny( [0,1,2,3,4], i -> IsEqualForMorphismsOnMor( SimplifyRange( mor, i ), SimplifyRa false gap> ForAll( [5,6,7,8,9], i -> IsEqualForMorphismsOnMor( SimplifyRange( mor, i ), SimplifyRa true gap> IsCongruentForMorphisms( > PreCompose( SimplifyRange( mor, infinity ), SimplifyRange_IsoToInputObject( mor, infini > ); true gap> IsCongruentForMorphisms( > PreCompose( mor, SimplifyRange_IsoFromInputObject( mor, infinity ) ), SimplifyRange( mor > ); true # ## Test SimplifySourceAndRange gap> IsEqualForMorphismsOnMor( SimplifySourceAndRange( mor, 0 ), mor ); true gap> IsEqualForMorphismsOnMor( SimplifySourceAndRange( mor, 1 ), mor ); false gap> ForAny( [0,1,2,3,4], i -> IsEqualForMorphismsOnMor( SimplifySourceAndRange( mor, i ), S false gap> ForAll( [5,6,7,8,9], i -> IsEqualForMorphismsOnMor( SimplifySourceAndRange( mor, i ), S true gap> IsCongruentForMorphisms( > mor, > PreCompose( [ SimplifySourceAndRange_IsoFromInputSource( mor, infinity ), > SimplifySourceAndRange( mor, infinity ), > SimplifySourceAndRange_IsoToInputRange( mor, infinity ) ] ) > ); true gap> IsCongruentForMorphisms( > SimplifySourceAndRange( mor, infinity ), > PreCompose( [ SimplifySourceAndRange_IsoToInputSource( mor, infinity ), > mor, > SimplifySourceAndRange_IsoFromInputRange( mor, infinity ) ] ) > ); true # ## Test SimplifyEndo gap> endo := StringsAsCategoryMorphism( C, obj1, "uoiea", obj1 );; gap> IsWellDefined( endo ); true gap> IsEqualForMorphismsOnMor( SimplifyEndo( endo, 0 ), endo ); true gap> IsEqualForMorphismsOnMor( SimplifyEndo( endo, 1 ), endo ); false gap> ForAny( [0,1,2,3,4], i -> IsEqualForMorphismsOnMor( SimplifySourceAndRange( endo, i ), false gap> ForAll( [5,6,7,8,9], i -> IsEqualForMorphismsOnMor( SimplifySourceAndRange( endo, i ), true gap> iota := SimplifyEndo_IsoToInputObject( endo, infinity );; gap> iota_inv := SimplifyEndo_IsoFromInputObject( endo, infinity );; gap> IsCongruentForMorphisms( PreCompose( [ iota_inv, SimplifyEndo( endo, infinity ), iota true # gap> STOP_TEST( "Simplify" ); [ Dauer der Verarbeitung: 0.43 Sekunden (vorverarbeitet) ] |
2026-03-28