WeierstrassSemigroups : Index

• appendFamily -- Append a one-parameter smoothing family to a data file
• appendFamily(List,Ideal,String,String) -- 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
• checkFlatnessOfOneParameterFamilies(...,Verbose=>...) -- Check flatness of 1-parameter famiiles
• checkFlatnessOfOneParameterFamilies(List,String) -- Check flatness of 1-parameter famiiles
• checkSmoothnessOfOneParameterFamilies -- Check smoothness of 1-parameter families
• checkSmoothnessOfOneParameterFamilies(...,BaseField=>...) -- Check smoothness of 1-parameter families
• checkSmoothnessOfOneParameterFamilies(...,Verbose=>...) -- Check smoothness of 1-parameter families
• checkSmoothnessOfOneParameterFamilies(List,String) -- Check smoothness of 1-parameter families
• clearDenominators -- Clear denominators
• clearDenominators(...,CoeffBound=>...) -- Clear denominators
• clearDenominators(Matrix) -- 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)
• collectByBound(...,CoeffSize=>...) -- Collect 1-parameter families filtered by bound (or congruences or range)
• collectByBound(...,Verbose=>...) -- Collect 1-parameter families filtered by bound (or congruences or range)
• collectByBound(List,ZZ,String,String) -- Collect 1-parameter families filtered by bound (or congruences or range)
• collectByCongruences -- Collect 1-parameter families filtered by bound (or congruences or range)
• collectByCongruences(...,CoeffSize=>...) -- Collect 1-parameter families filtered by bound (or congruences or range)
• collectByCongruences(List,List,String,String) -- Collect 1-parameter families filtered by bound (or congruences or range)
• collectByRange -- Collect 1-parameter families filtered by bound (or congruences or range)
• collectByRange(...,CoeffSize=>...) -- Collect 1-parameter families filtered by bound (or congruences or range)
• collectByRange(List,List,String,String) -- Collect 1-parameter families filtered by bound (or congruences or range)
• collectWithVersalDeformations -- Collect 1-parameter families the using versal deformations
• collectWithVersalDeformations(...,BaseField=>...) -- Collect 1-parameter families the using versal deformations
• collectWithVersalDeformations(...,Bound=>...) -- Collect 1-parameter families the using versal deformations
• collectWithVersalDeformations(...,CoeffBound=>...) -- Collect 1-parameter families the using versal deformations
• collectWithVersalDeformations(...,CoeffSize=>...) -- Collect 1-parameter families the using versal deformations
• collectWithVersalDeformations(...,HighestOrder1=>...) -- Collect 1-parameter families the using versal deformations
• collectWithVersalDeformations(...,Verbose=>...) -- Collect 1-parameter families the using versal deformations
• collectWithVersalDeformations(List,ZZ,String,String) -- Collect 1-parameter families the using versal deformations
• depthCondition1 -- Check the depth conditions for the exactness of the 1,4,4,1 subcomplex of the 1,6,8,3 subcomplex
• depthCondition1(List) -- Check the depth conditions for the exactness of the 1,4,4,1 subcomplex of the 1,6,8,3 subcomplex
• displaySyzygyMatrices -- Display the syzygy matrices
• displaySyzygyMatrices(...,Verbose=>...) -- Display the syzygy matrices
• displaySyzygyMatrices(List) -- Display the syzygy matrices
• findCompleteIntersection -- Find complete intersection defined by some of the generators
• findCompleteIntersection(...,Strategy=>...) -- Find complete intersection defined by some of the generators
• findCompleteIntersection(Ideal) -- Find complete intersection defined by some of the generators
• findPoint -- Find a kk-rational point in a variety
• findPoint(...,Verbose=>...) -- Find a kk-rational point in a variety
• findPoint(Ideal) -- Find a kk-rational point in a variety
• flatteningRelations -- Compute the flattening relations of an unfolding
• flatteningRelations(Ideal,Ring,Matrix) -- Compute the flattening relations of an unfolding
• getFlatFamily -- Compute the flat family depending on a subset of parameters of the universal unfolding
• getFlatFamily(...,BaseField=>...) -- Compute the flat family depending on a subset of parameters of the universal unfolding
• getFlatFamily(...,Verbose=>...) -- Compute the flat family depending on a subset of parameters of the universal unfolding
• getFlatFamily(Ideal,Ring,Matrix) -- Compute the flat family depending on a subset of parameters of the universal unfolding
• getFlatFamily(Ideal,Ring,Matrix,List) -- Compute the flat family depending on a subset of parameters of the universal unfolding
• getFromDisk -- Read a file from the hard disk
• getFromDisk(String) -- Read a file from the hard disk
• getListOfIdeals -- Read a list of ideals from a dataBase
• getListOfIdeals(...,Verbose=>...) -- Read a list of ideals from a dataBase
• getListOfIdeals(List,String) -- Read a list of ideals from a dataBase
• getOneParameterFamily -- Compute a one parameter smoothing family
• getOneParameterFamily(...,CoeffSize=>...) -- Compute a one parameter smoothing family
• getOneParameterFamily(...,Verbose=>...) -- Compute a one parameter smoothing family
• getOneParameterFamily(Ideal,Ideal,Matrix,ZZ) -- Compute a one parameter smoothing family
• getParameterFamily -- Compute the parametric family which uses the same terms as J
• getParameterFamily(Ideal) -- Compute the parametric family which uses the same terms as J
• getRangeOfOneParameterFamily -- Compute the range of degrees of a one parameter family
• getRangeOfOneParameterFamily(Ideal) -- Compute the range of degrees of a one parameter family
• getSmoothingFamily -- Get a smoothing family for the semigroup L
• getSmoothingFamily(...,BaseField=>...) -- Get a smoothing family for the semigroup L
• getSmoothingFamily(...,CoeffBound=>...) -- Get a smoothing family for the semigroup L
• getSmoothingFamily(...,CoeffSize=>...) -- Get a smoothing family for the semigroup L
• getSmoothingFamily(...,Verbose=>...) -- Get a smoothing family for the semigroup L
• getSmoothingFamily(List,List) -- Get a smoothing family for the semigroup L
• getSmoothingFamily(List,ZZ) -- Get a smoothing family for the semigroup L
• getSmoothingFamilyWithVersalDeformation -- Get a smoothing family using versal deformations
• getSmoothingFamilyWithVersalDeformation(...,BaseField=>...) -- Get a smoothing family using versal deformations
• getSmoothingFamilyWithVersalDeformation(...,Bound=>...) -- Get a smoothing family using versal deformations
• getSmoothingFamilyWithVersalDeformation(...,CoeffBound=>...) -- Get a smoothing family using versal deformations
• getSmoothingFamilyWithVersalDeformation(...,CoeffSize=>...) -- Get a smoothing family using versal deformations
• getSmoothingFamilyWithVersalDeformation(...,HighestOrder1=>...) -- Get a smoothing family using versal deformations
• getSmoothingFamilyWithVersalDeformation(...,Verbose=>...) -- Get a smoothing family using versal deformations
• getSmoothingFamilyWithVersalDeformation(List) -- 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?
• give1683Format(List) -- Does the semigroup ideal of L has a resolution with total betti numbers 1,6,8,3?
• give1683Format(List,List,List,List) -- Does the semigroup ideal of L has a resolution with total betti numbers 1,6,8,3?
• give1683Format(ZZ,ZZ,ZZ,ZZ) -- Does the semigroup ideal of L has a resolution with total betti numbers 1,6,8,3?
• hasExactSubcomplex -- Check the depth conditions for the exactness of the 1,4,4,1 subcomplex of the 1,6,8,3 subcomplex
• hasExactSubcomplex(List) -- Check the depth conditions for the exactness of the 1,4,4,1 subcomplex of the 1,6,8,3 subcomplex
• HighestOrder1 -- Option keys for various functions
• hilbertBurchConditions -- Check the depth conditions for the exactness of the 1,4,4,1 subcomplex of the 1,6,8,3 subcomplex
• hilbertBurchConditions(List) -- Check the depth conditions for the exactness of the 1,4,4,1 subcomplex of the 1,6,8,3 subcomplex
• hilbertBurchMatrices -- Check the depth conditions for the exactness of the 1,4,4,1 subcomplex of the 1,6,8,3 subcomplex
• hilbertBurchMatrices(List) -- 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
• improveFamily(...,Verbose=>...) -- Find a 1-parameter smoothing family with perhaps smaller number of terms and coefficients
• improveFamily(Ideal) -- Find a 1-parameter smoothing family with perhaps smaller number of terms and coefficients
• isSmoothingFamily -- Is the family a smoothing family?
• isSmoothingFamily(...,Verbose=>...) -- Is the family a smoothing family?
• isSmoothingFamily(List,Ideal,Matrix,Ideal) -- Is the family a smoothing family?
• makeRange -- Make a range of degrees for getSmoothingFamily
• makeRange(...,Verbose=>...) -- Make a range of degrees for getSmoothingFamily
• makeRange(List,List) -- Make a range of degrees for getSmoothingFamily
• makeUnfolding -- Makes the universal homogeneous unfolding of an ideal with positive degree parameters
• makeUnfolding(...,BaseField=>...) -- Makes the universal homogeneous unfolding of an ideal with positive degree parameters
• makeUnfolding(...,Verbose=>...) -- Makes the universal homogeneous unfolding of an ideal with positive degree parameters
• makeUnfolding(Ideal) -- Makes the universal homogeneous unfolding of an ideal with positive degree parameters
• makeUnfolding(List) -- Makes the universal homogeneous unfolding of an ideal with positive degree parameters
• prepareInitialPositionList -- Compute the flat family depending on a subset of parameters of the universal unfolding
• prepareInitialPositionList(...,Verbose=>...) -- Compute the flat family depending on a subset of parameters of the universal unfolding
• prepareInitialPositionList(List,ZZ) -- Compute the flat family depending on a subset of parameters of the universal unfolding
• pruneFamily -- Present the family with fewest number of variables
• pruneFamily(...,Verbose=>...) -- Present the family with fewest number of variables
• pruneFamily(Ideal,Ideal,Matrix) -- Present the family with fewest number of variables
• restrictedUnfolding -- Compute a restricted unfolding
• restrictedUnfolding(Ideal,List) -- Compute a restricted unfolding
• satisfiesDegreeCondition1 -- Does the semigroup ideal of L satisfies the degree condition for the 3rd respectively 2nd syzgy matrix?
• satisfiesDegreeCondition1(List) -- Does the semigroup ideal of L satisfies the degree condition for the 3rd respectively 2nd syzgy matrix?
• satisfiesDegreeCondition2 -- Does the semigroup ideal of L satisfies the degree condition for the 3rd respectively 2nd syzgy matrix?
• satisfiesDegreeCondition2(List) -- 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
• smoothnessWithReductions(...,BaseField=>...) -- Check smoothness by using reductions to points
• smoothnessWithReductions(...,Verbose=>...) -- Check smoothness by using reductions to points
• smoothnessWithReductions(Ideal) -- Check smoothness by using reductions to points
• solvingFlatteningRelations -- Solving the flatttening relations over QQ
• solvingFlatteningRelations(...,BaseField=>...) -- Solving the flatttening relations over QQ
• solvingFlatteningRelations(...,CoeffBound=>...) -- Solving the flatttening relations over QQ
• solvingFlatteningRelations(...,CoeffSize=>...) -- Solving the flatttening relations over QQ
• solvingFlatteningRelations(...,Verbose=>...) -- Solving the flatttening relations over QQ
• solvingFlatteningRelations(Ideal,Matrix,Ideal) -- 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
• testBound(...,CoeffSize=>...) -- Test whether b is bound for the semigroup L and compute a 1-parameter smoothing family if yes
• testBound(...,Verbose=>...) -- Test whether b is bound for the semigroup L and compute a 1-parameter smoothing family if yes
• testBound(List,ZZ) -- Test whether b is bound for the semigroup L and compute a 1-parameter smoothing family if yes
• testCongruences -- Test whether b is bound for the semigroup L and compute a 1-parameter smoothing family if yes
• testCongruences(...,CoeffSize=>...) -- Test whether b is bound for the semigroup L and compute a 1-parameter smoothing family if yes
• testCongruences(List,List) -- Test whether b is bound for the semigroup L and compute a 1-parameter smoothing family if yes
• testRange -- Test whether b is bound for the semigroup L and compute a 1-parameter smoothing family if yes
• testRange(...,CoeffSize=>...) -- Test whether b is bound for the semigroup L and compute a 1-parameter smoothing family if yes
• testRange(List,List) -- 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
• toDoList(ZZ) -- Make a list of semigroups not previously known to be Weierstrass
• toDoList(ZZ,ZZ) -- Make a list of semigroups not previously known to be Weierstrass
• WeierstrassSemigroups -- Compute smoothing families for Weierstrass semigroups