gap> Q := HomalgFieldOfRationalsInSingular( );
Q
gap> B := Q * "a,b";
Q[a,b]
gap> R := B * "x,y";
Q[a,b][x,y]
gap> gamma := ClosedSubsetOfSpecByRadicalColumn( "[x-a,x*y-b]", R );
V_{Q[a,b][x,y]}( <...> )
gap> im := ConstructibleProjection( gamma );
( V_{Q[a,b]}( I1 ) \ V_{Q[a,b]}( J1_1 ) ) ∪ ( V_{Q[a,b]}( I2 ) \ V_{Q[a,b]}( J2_1 ) )
gap> cim := CanonicalObject( im );
( V_{Q[a,b]}( I1 ) \ V_{Q[a,b]}( J1 ) ) ∪ ( V_{Q[a,b]}( I2 ) \ V_{Q[a,b]}( J2 ) )
gap> IsLocallyClosed( cim );
false
gap> Length( cim );
2
gap> Dimension( cim[1].I );
2
gap> Dimension( cim[1].J );
1
gap> Dimension( cim[2].I );
0

gap> zz := HomalgRingOfIntegersInSingular( );
Z
gap> R := zz * "x";
Z[x]
gap> gamma := ClosedSubsetOfSpecByRadicalColumn( "[2*x+1]", R );
V_{Z[x]}( <...> )
gap> im := ConstructibleProjection( gamma );
( V_{Z}( I1 ) \ V_{Z}( J1_1 ) )
gap> Display( im );
( V( <> )

\ V( <2> ) )
gap> char := -im;
( V_{Z}( I1 ) \ V_{Z}( J1_1 ) \ .. \ V_{Z}( J1_3 ) )
gap> Display( char );
( V( <2> )

\ ∅

\ ∅

\ ∅ )
gap> char := CanonicalObject( char );
V_{Z}( <...> )
gap> Display( char );
V( <2> )

gap> Q := HomalgFieldOfRationalsInSingular( );
Q
gap> B := Q * "a";
Q[a]
gap> R := B * "b";
Q[a][b]
gap> V1 := -ClosedSubsetOfSpec( "a*b", R );
V_{Q[a][b]}( I ) \ V_{Q[a][b]}( J )
gap> Display( V1 );
V( <> )

\ V( <a*b> )
gap> W1 := ConstructibleProjection( V1 );
( V_{Q[a]}( I1 ) \ V_{Q[a]}( J1_1 ) )
gap> Display( W1 );
( V( <> )

\ V( <a> ) )
gap> V2 := ClosedSubsetOfSpec( "a", R ) - ClosedSubsetOfSpec( "b", R );
V_{Q[a][b]}( I ) \ V_{Q[a][b]}( J )
gap> Display( V2 );
V( <a> ) \ V( <b> )
gap> W2 := ConstructibleProjection( V2 );
( V_{Q[a]}( I1 ) \ V_{Q[a]}( J1_1 ) )
gap> Display( W2 );
( V( <a> )

\ ∅ )
gap> V3 := ClosedSubsetOfSpec( "a^2-1", R ) - ClosedSubsetOfSpec( "b", R );
V_{Q[a][b]}( I ) \ V_{Q[a][b]}( J )
gap> Display( V3 );
V( <a^2-1> )

\ V( <b> )
gap> W3 := ConstructibleProjection( V3 );
( V_{Q[a]}( I1 ) \ V_{Q[a]}( J1_1 ) )
gap> Display( W3 );
( V( <a^2-1> )

\ ∅ )
gap> V4 := ClosedSubsetOfSpec( "b-a^2+1", R ) - ClosedSubsetOfSpec( "a*b", R );
V_{Q[a][b]}( I ) \ V_{Q[a][b]}( J )
gap> Display( V4 );
V( <b-a^2+1> )

\ V( <a*b> )
gap> W4 := ConstructibleProjection( V4 );
( V_{Q[a]}( I1 ) \ V_{Q[a]}( J1_1 ) \ .. \ V_{Q[a]}( J1_3 ) )
gap> Display( W4 );
( V( <> )

\ V( <a> )

\ V( <a-1> )

\ V( <a+1> ) )
gap> V5 := (ClosedSubsetOfSpec( "b-a^2+1", R ) + ClosedSubsetOfSpec( "a-1", R ))
>       - ClosedSubsetOfSpec( "a*b", R );
V_{Q[a][b]}( I ) \ V_{Q[a][b]}( J )
gap> Display( V5 );
{ V( <b-a^2+1> ) ∪ V( <a-1> ) }

\ V( <a*b> )
gap> W5 := ConstructibleProjection( V5 );
( V_{Q[a]}( I1 ) \ V_{Q[a]}( J1_1 ) \ V_{Q[a]}( J1_2 ) )
gap> Display( W5 );
( V( <> )

\ V( <a+1> )

\ V( <a> ) )
gap> V6 := (ClosedSubsetOfSpec( "b-a^2+1", R ) + ClosedSubsetOfSpec( "a^2-1", R ))
>       - ClosedSubsetOfSpec( "a*b", R );
V_{Q[a][b]}( I ) \ V_{Q[a][b]}( J )
gap> Display( V6 );
{ V( <b-a^2+1> ) ∪ V( <a^2-1> ) }

\ V( <a*b> )
gap> W6 := ConstructibleProjection( V6 );
( V_{Q[a]}( I1 ) \ V_{Q[a]}( J1_1 ) ) ∪ ( V_{Q[a]}( I2 ) \ V_{Q[a]}( J2_1 ) )
gap> Display( W6 );
( V( <> )

\ V( <a> ) )

∪

( V( <a^2-1> )

\ ∅ )
gap> zz := HomalgRingOfIntegersInSingular( );
Z
gap> S := zz * "a";
Z[a]
gap> V7 := ClosedSubsetOfSpec( "2*a^2-2*a+1", S )
>       - ClosedSubsetOfSpec( "3*a-1", S ) - ClosedSubsetOfSpec( "a+1", S );
V_{Z[a]}( I ) \ V_{Z[a]}( J )
gap> Display( V7 );
V( <2*a^2-2*a+1> )

\ { V( <3*a-1> ) ∪ V( <a+1> ) }
gap> W7 := ConstructibleProjection( V7 );
( V_{Z}( I1 ) \ V_{Z}( J1_1 ) \ V_{Z}( J1_2 ) )
gap> Display( W7 );
( V( <> )

\ V( <2> )

\ V( <5> ) )