using CapAndHomalgt
CapAndHomalg v1.0.0
Imported OSCAR's components GAP and Singular_jll
Type: ?CapAndHomalg for more information
LoadPackage( "ZariskiFrames" )
ℚ = HomalgFieldOfRationalsInSingular( )
GAP: Q
R = ℚ["x,y"]
GAP: Q[x,y]
x = ClosedSubsetOfSpec( "y", R )
GAP: V_{Q[x,y]}( <...> )
Display( x )
V( <y> )
IsClosed( x )
true
y = ClosedSubsetOfSpec( "x", R )
GAP: V_{Q[x,y]}( <...> )
d = ClosedSubsetOfSpec( "x+y-1", R )
GAP: V_{Q[x,y]}( <...> )
xuy = x + y
GAP: V_{Q[x,y]}( <...> )
Display( xuy )
{ V( <y> ) ∪ V( <x> ) }
IsClosed( xuy )
true
#mxuy = -xuy
mxuy = AdditiveInverse( xuy )
GAP: V_{Q[x,y]}( I ) \ V_{Q[x,y]}( J )
Display( mxuy )
V( <> ) \ { V( <y> ) ∪ V( <x> ) }
IsClosed( mxuy )
false
IsOpen( mxuy )
true
xmy = x - y
GAP: V_{Q[x,y]}( I ) \ V_{Q[x,y]}( J )
Display( xmy )
V( <y> ) \ V( <x> )
xmy2 = xmy - y
GAP: V_{Q[x,y]}( I ) \ V_{Q[x,y]}( J )
Display( xmy2 )
V( <y> ) \ V( <x> )
lc = xuy - d
GAP: V_{Q[x,y]}( I ) \ V_{Q[x,y]}( J )
lc0 = lc - 0
GAP: V_{Q[x,y]}( I ) \ V_{Q[x,y]}( J )
IsIdenticalObj( lc, lc0 )
true
IsLocallyClosed( lc )
true
IsClosed( lc )
false
Dimension( lc )
1
tp = d * xuy
GAP: V_{Q[x,y]}( <...> )
Dimension( tp )
0
c = lc + tp
GAP: ( V_{Q[x,y]}( I1 ) \ V_{Q[x,y]}( J1 ) ) ∪ ( V_{Q[x,y]}( I2 ) \ V_{Q[x,y]}( J\ 2 ) )
c0 = c - 0
GAP: ( V_{Q[x,y]}( I1 ) \ V_{Q[x,y]}( J1 ) ) ∪ ( V_{Q[x,y]}( I2 ) \ V_{Q[x,y]}( J\ 2 ) )
IsIdenticalObj( c, c0 )
true
c[1]
GAP: V_{Q[x,y]}( I ) \ V_{Q[x,y]}( J )
c[2]
GAP: V_{Q[x,y]}( I ) \ V_{Q[x,y]}( J )
Dimension( c )
1
c == xuy
true
cc = CanonicalObject( c )
GAP: V_{Q[x,y]}( <...> )
Display( cc )
V( <x*y> )
cc == xuy
true
t = c - lc
GAP: ( V_{Q[x,y]}( I1 ) \ V_{Q[x,y]}( J1 ) )
Display( t )
V( <x+y-1,y^2-y> ) \ ∅
IsClosed( t )
true
t == tp
true
z = c - c
GAP: ( V_{Q[x,y]}( I1 ) \ V_{Q[x,y]}( J1 ) )
Display( z )
V( <x*y> ) \ V( <x*y> )
z = StandardizedObject( z )
GAP: ( V_{Q[x,y]}( I1 ) \ V_{Q[x,y]}( J1 ) )
Display( z )
∅ \ ∅