SpaceCurves : Table of Contents

• SpaceCurves -- generation of space curves
• allACMBetti -- lists all Betti tables of ACM curves with a given Hilbert function
• BlowUpPoints -- key for CubicSurface and QuarticSurfaceRational
• CanonicalClass -- key for QuadricSurface, CubicSurface and QuarticSurfaceRational
• Coordinate -- key of Divisor
• CubicSurface -- type of HashTable
• cubicSurface -- creates a cubicSurface
• Curve -- type of HashTable
• curve -- generates a random curve
• degree(Curve) -- computes the degree of a Curve
• degree(Divisor) -- computes the degree of a Divisor
• degreeMatrix -- computes the Hilbert-Burch degree matrix from a Betti table of ACM curves
• dgTable -- prints the table of (degree,genus) pairs
• Divisor -- type of HashTable
• divisor -- creates a Divisor
• Divisor * Divisor -- intersection number of two Divisors
• Divisor + Divisor -- sum of two Divisors
• Divisor - Divisor -- difference of two Divisors
• divisor(Curve) -- extracts the Divisor of a Curve
• generalACMBetti -- the most general Betti table of an ACM curve with a given Hilbert function
• genus(Curve) -- computes the genus of a Curve
• genus(Divisor) -- computes the genus of a Divisor
• HyperplaneClass -- key for QuadricSurface, CubicSurface and QuarticSurfaceRational
• ideal(Curve) -- extracts the ideal of a Curve
• ideal(QuadricSurface) -- extracts the ideal of a surface
• IntersectionPairing -- key for QuadricSurface, CubicSurface and QuarticSurfaceRational
• isACMBetti -- checks whether a Betti table is that of an ACM curve
• isPrime(Curve) -- checks if the ideal of a Curve is prime
• isSmooth -- checks smoothness of an ideal or of a Curve
• isSmoothACMBetti -- checks whether a Betti table is that of a smooth ACM curve
• MapToP3 -- key for CubicSurface and QuarticSurfaceRational
• minimalCurve -- generates a minimal curve in the biliaison class
• minimalCurveBetti -- computes the Betti diagram of the minimal curve
• net(CubicSurface) -- displays the ideal of the CubicSurface
• net(Curve) -- displays the ideal of the curve
• net(Divisor) -- displays the coordinates of the Divisor
• net(QuadricSurface) -- displays the ideal of the QuadricSurface
• net(QuarticSurfaceRational) -- displays the ideal of the QuarticSurfaceRational
• positiveChars -- generates all positive characters of a given degree
• QuadricSurface -- type of HashTable
• quadricSurface -- creates a QuadricSurface
• QuarticSurfaceRational -- type of HashTable
• quarticSurfaceRational -- creates a QuarticSurfaceRational
• randomDeterminantalIdeal -- produces a random determinantal ideal
• raoModule -- computes the Rao module of a curve
• smoothDivisors -- produces a list of smooth divisors of a given degree on a surface
• smoothDivisors(ZZ,ZZ) -- produces a list of smooth divisors of given degree and genus
• specializeACMBetti -- lists all 1-specialization of a Betti table of an ACM curve
• Surface -- key of Divisor
• surface -- the surface key of a Divisor or a Curve
• ZZ * Divisor -- multiply a Divisor by an integer