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### 4 (Co)frames/Locales of Zariski closed/open subsets in affine varieties

#### 4.1 GAP Categories

##### 4.1-1 IsObjectInZariskiFrameOrCoframeOfAnAffineVariety
 ‣ IsObjectInZariskiFrameOrCoframeOfAnAffineVariety( object ) ( filter )

Returns: true or false

The GAP category of objects in a Zariski frame or coframe of an affine variety.

##### 4.1-2 IsMorphismInZariskiFrameOrCoframeOfAnAffineVariety
 ‣ IsMorphismInZariskiFrameOrCoframeOfAnAffineVariety( morphism ) ( filter )

Returns: true or false

The GAP category of morphisms in a Zariski frame or coframe of an affine variety.

#### 4.2 Operatoins

##### 4.2-1 DistinguishedQuasiAffineSet
 ‣ DistinguishedQuasiAffineSet( eqs, ineqs, R, point_emb ) ( operation )
 ‣ DistinguishedQuasiAffineSet( eqs, ineqs, point_emb ) ( operation )
 ‣ DistinguishedQuasiAffineSet( eqs, ineqs ) ( operation )
 ‣ DistinguishedQuasiAffineSet( eqs_ineqs ) ( operation )

Returns: an object in a meet-semilattice of formal multiple differences

Construct a distinguished quasi-affine set A defined by the set eqs of equations and the set ineqs of inequations over the commutative unital ring R. A quasi-affine set is called distinguished if it is a difference of an affine set and a hypersurface (or, equivalently, hypersurfaces). The optional object point_emb is an object parametrized by A and giving an embedding/realization of the abstract points of A in some context.

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