WeierstrassSemigroups : Table of Contents

• WeierstrassSemigroups -- Compute smoothing families for Weierstrass semigroups
• appendFamily -- Append a one-parameter smoothing family to a data file
• BaseField -- Option keys for various functions
• Bound -- Option keys for various functions
• checkFlatnessOfOneParameterFamilies -- Check flatness of 1-parameter famiiles
• checkSmoothnessOfOneParameterFamilies -- Check smoothness of 1-parameter families
• clearDenominators -- Clear denominators
• CoeffBound -- Option keys for various functions
• CoeffSize -- Option keys for various functions
• collectByBound -- Collect 1-parameter families filtered by bound (or congruences or range)
• collectWithVersalDeformations -- Collect 1-parameter families the using versal deformations
• displaySyzygyMatrices -- Display the syzygy matrices
• findCompleteIntersection -- Find complete intersection defined by some of the generators
• findPoint -- Find a kk-rational point in a variety
• flatteningRelations -- Compute the flattening relations of an unfolding
• getFlatFamily -- Compute the flat family depending on a subset of parameters of the universal unfolding
• getFromDisk -- Read a file from the hard disk
• getListOfIdeals -- Read a list of ideals from a dataBase
• getOneParameterFamily -- Compute a one parameter smoothing family
• getParameterFamily -- Compute the parametric family which uses the same terms as J
• getRangeOfOneParameterFamily -- Compute the range of degrees of a one parameter family
• getSmoothingFamily -- Get a smoothing family for the semigroup L
• getSmoothingFamilyWithVersalDeformation -- Get a smoothing family using versal deformations
• give1683Format -- Does the semigroup ideal of L has a resolution with total betti numbers 1,6,8,3?
• HighestOrder1 -- Option keys for various functions
• hilbertBurchMatrices -- Check the depth conditions for the exactness of the 1,4,4,1 subcomplex of the 1,6,8,3 subcomplex
• HowToStartCollecting -- How to start collecting
• improveFamily -- Find a 1-parameter smoothing family with perhaps smaller number of terms and coefficients
• isSmoothingFamily -- Is the family a smoothing family?
• makeRange -- Make a range of degrees for getSmoothingFamily
• makeUnfolding -- Makes the universal homogeneous unfolding of an ideal with positive degree parameters
• pruneFamily -- Present the family with fewest number of variables
• restrictedUnfolding -- Compute a restricted unfolding
• satisfiesDegreeCondition1 -- Does the semigroup ideal of L satisfies the degree condition for the 3rd respectively 2nd syzgy matrix?
• smoothnessWithReductions -- Check smoothness by using reductions to points
• solvingFlatteningRelations -- Solving the flatttening relations over QQ
• testBound -- Test whether b is bound for the semigroup L and compute a 1-parameter smoothing family if yes
• toDoList -- Make a list of semigroups not previously known to be Weierstrass