‣ IsZariskiFrameOfAProjectiveVariety( object ) | ( filter ) |
Returns: true or false
The GAP category of Zariski frames of a projective variety.
‣ IsObjectInZariskiFrameOfAProjectiveVariety( object ) | ( filter ) |
Returns: true or false
The GAP category of objects in a Zariski frame of a projective variety.
‣ IsMorphismInZariskiFrameOfAProjectiveVariety( morphism ) | ( filter ) |
Returns: true or false
The GAP category of morphisms in a Zariski frame of a projective variety.
‣ ZariskiFrameOfProj( R ) | ( attribute ) |
Returns: a CAP category
Construct the Zariski frame of open sets in a projective variety defined as the complements of vanishing loci of (radical) ideals of a homalg ring R.
‣ OpenSubsetOfProj( mat ) | ( operation ) |
‣ OpenSubsetOfProj( str, R ) | ( operation ) |
‣ OpenSubsetOfProjByListOfColumns( L ) | ( operation ) |
Returns: a CAP object
Construct a Zariski open subset (as an object in the Zariski frame of open subsets in a projective variety) from the homogeneous matrix mat. The result is the projective non-support of the module-theoretic cokernel \(M\) of the matrix mat viewed as a morphism in the Freyd category of the associated category of graded rows, i.e., the result is the complement of the projective vanishing locus of the (homogeneous) annihilator of \(M\).
‣ OpenSubsetOfProjByRadicalColumn( I ) | ( operation ) |
‣ OpenSubsetOfProjByRadicalColumn( str, R ) | ( operation ) |
OpenSubsetOfProjByRadicalColumn assumes that the image is a radical ideal.
‣ OpenSubsetOfProjByStandardColumn( I ) | ( operation ) |
‣ OpenSubsetOfProjByStandardColumn( str, R ) | ( operation ) |
OpenSubsetOfProjByStandardColumn assumes that the image is a radical ideal given by some sort of a standard
basis.
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