NumericalGodeaux : Index
- allLoci -- compute all exceptional loci at which the dimension of the solution space may rise
- allLoci(Matrix,Matrix,Matrix) -- compute all exceptional loci at which the dimension of the solution space may rise
- allLociTors0 -- compute all exceptional loci for torsion-free numerical Godeaux surfaces
- allLociTors0(Matrix,List) -- compute all exceptional loci for torsion-free numerical Godeaux surfaces
- associatedLineInP11 -- compute the associated line in the P11 of a-variables
- associatedLineInP11(Matrix,Matrix) -- compute the associated line in the P11 of a-variables
- Attempts -- optional argument in randomGodeauxSurface
- bihomogeneousModel -- compute a birational model of a numerical Godeaux surface in P1xP3
- bihomogeneousModel(Ideal) -- compute a birational model of a numerical Godeaux surface in P1xP3
- calculationOfTheUnirationalParametrizationOfTorsZ5Lines -- describe the unirational parametrization of the locus of Z/5-lines
- calculationOfTheUnirationalParametrizationOfTorsZ5Lines(String) -- describe the unirational parametrization of the locus of Z/5-lines
- canonicalRing -- computes the canonical ring of a numerical Godeaux surface
- canonicalRing(Matrix) -- computes the canonical ring of a numerical Godeaux surface
- Certify -- optional argument in randomGodeauxSurface
- collapsingOneCStar -- compute the hypersurface of bidegree (4,6) in P3xP5
- collapsingOneCStar(Ideal) -- compute the hypersurface of bidegree (4,6) in P3xP5
- complexModuloRegularSequence -- set-up for minimal free resolution modulo x0,x1
- complexModuloRegularSequence(Ring,String) -- set-up for minimal free resolution modulo x0,x1
- complexModuloRegularSequence4 -- set-up the minimal free resolution modulo $x_0,x_1$ in the case of a fat base point
- complexModuloRegularSequence4(Ring,List) -- set-up the minimal free resolution modulo $x_0,x_1$ in the case of a fat base point
- complexModuloRegularSequence22 -- set-up the minimal free resolution modulo $x_0,x_1$ in the case of 2 double base points
- complexModuloRegularSequence22(Ring) -- set-up the minimal free resolution modulo $x_0,x_1$ in the case of 2 double base points
- complexModuloRegularSequence211 -- set-up the minimal free resolution modulo $x_0,x_1$ for the configuration "211" of base points
- complexModuloRegularSequence211(Ring) -- set-up the minimal free resolution modulo $x_0,x_1$ for the configuration "211" of base points
- complexModuloRegularSequence1111 -- set-up the minimal free resolution modulo $x_0,x_1$ in the case of 4 distinct base points
- complexModuloRegularSequence1111(Ring) -- set-up the minimal free resolution modulo $x_0,x_1$ in the case of 4 distinct base points
- computeParametrizationOfHypLocus -- print commands which compute the parametrization
- computeParametrizationOfHypLocus(Ring) -- print commands which compute the parametrization
- findPointInP3xP5 -- find a point on the model in P3xP5
- findPointInP3xP5(Ring) -- find a point on the model in P3xP5
- fromLineToGodeauxSurface -- compute a birational model of a numerical Godeaux surface from a given line
- fromLineToGodeauxSurface(Matrix) -- compute a birational model of a numerical Godeaux surface from a given line
- fromLineToStandardResolution -- compute a standard resolution F of an S-module R from a given line
- fromLineToStandardResolution(Matrix) -- compute a standard resolution F of an S-module R from a given line
- fromPointInP3xP3xP3xP3ToLine -- compute a line in Q from a point in the model in P3xP3xP3xP3
- fromPointInP3xP3xP3xP3ToLine(Matrix) -- compute a line in Q from a point in the model in P3xP3xP3xP3
- fromPointInP3xP5ToPointInP3xP3xP3xP3 -- compute a point in the model in P3xP3xP3xP3
- fromPointInP3xP5ToPointInP3xP3xP3xP3(Matrix) -- compute a point in the model in P3xP3xP3xP3
- furtherCollapsing -- computes the 5-dimensional anti-canonical hypersurface in the cox ring of a toric variety
- furtherCollapsing(Ring) -- computes the 5-dimensional anti-canonical hypersurface in the cox ring of a toric variety
- getAMatrix -- compute the a-matrix of a given matrix
- getAMatrix(Matrix) -- compute the a-matrix of a given matrix
- getChainComplexes -- resolve the two linear submatrices of the solution matrices over the coordinate ring of the Pfaffians
- getChainComplexes(Matrix,Matrix) -- resolve the two linear submatrices of the solution matrices over the coordinate ring of the Pfaffians
- getEMatrix -- compute the e-matrix of a given matrix
- getEMatrix(Matrix) -- compute the e-matrix of a given matrix
- getP11 -- the polynomial ring which depends only on the a-variables
- getP11(Matrix) -- the polynomial ring which depends only on the a-variables
- getRelationsAndNormalForm -- compute a minimal set of the relations and a normal form for d1' and d2
- getRelationsAndNormalForm(Matrix,Matrix,Matrix) -- compute a minimal set of the relations and a normal form for d1' and d2
- globalVariables -- introduce the main variables for the construction
- globalVariables(Ring,String) -- introduce the main variables for the construction
- globalVariables4 -- introduce the main variables in the case of a fat base point
- globalVariables4(Ring) -- introduce the main variables in the case of a fat base point
- globalVariables22 -- introduce the main variables in the case of 2 double base points
- globalVariables22(Ring) -- introduce the main variables in the case of 2 double base points
- globalVariables211 -- introduce the main variables for the configuration "211" of the base points
- globalVariables211(Ring) -- introduce the main variables for the configuration "211" of the base points
- globalVariables1111 -- introduce the main variables in the case of 4 distinct base points
- globalVariables1111(Ring) -- introduce the main variables in the case of 4 distinct base points
- homologyLocus -- compute the homology of the two chain complexes C1 and C2
- homologyLocus(Matrix,Matrix) -- compute the homology of the two chain complexes C1 and C2
- isSmoothBihomModel -- check whether the model in P1xP3 is smooth or not
- isSmoothBihomModel(Ideal) -- check whether the model in P1xP3 is smooth or not
- isSmoothModelInP5 -- check whether the model in the weighted P5 is smooth or not
- isSmoothModelInP5(Ideal) -- check whether the model in the weighted P5 is smooth or not
- jacobianQ -- compute the Jacobian matrix of the quadratic relations
- jacobianQ(Matrix) -- compute the Jacobian matrix of the quadratic relations
- lineConditionsTorsZ2 -- compute a list of possible loci for Z/2Z-Godeaux surfaces
- lineConditionsTorsZ2(Matrix,Matrix) -- compute a list of possible loci for Z/2Z-Godeaux surfaces
- lineConditionsTorsZ4 -- compute a list of possible loci for Z/4Z-Godeaux surfaces
- lineConditionsTorsZ4(Ideal,Ideal,Matrix,Matrix) -- compute a list of possible loci for Z/4Z-Godeaux surfaces
- lineConditionsTorsZ5 -- compute a list of possible loci for Z/5Z-Godeaux surfaces
- lineConditionsTorsZ5(Ideal,Ideal,Matrix,Matrix) -- compute a list of possible loci for Z/5Z-Godeaux surfaces
- lowerRankLociA -- compute the loci at which the rank of the a-matrix drops
- lowerRankLociA(Matrix,Matrix) -- compute the loci at which the rank of the a-matrix drops
- lowerRankLociA(Matrix,Matrix,Ring) -- compute the loci at which the rank of the a-matrix drops
- lowerRankLociE -- compute the loci at which the rank of the e-matrix drops
- lowerRankLociE(Matrix,Matrix) -- compute the loci at which the rank of the e-matrix drops
- modelInP1BundleOverP2xP5 -- compute the projection from a double point of H_{4,6}
- modelInP1BundleOverP2xP5(Matrix) -- compute the projection from a double point of H_{4,6}
- modelInP3xP3xP3xP3 -- compute the model of the Fano variety F(Q) in P3xP3xP3xP3
- modelInP3xP3xP3xP3(Ring) -- compute the model of the Fano variety F(Q) in P3xP3xP3xP3
- modelInP13 -- compute the image of a variety in P(2,2,3,3,3,3) under a embedding to P13
- modelInP13(Ideal) -- compute the image of a variety in P(2,2,3,3,3,3) under a embedding to P13
- normalBundleLineInQ -- compute the normal bundle of a line in Q
- normalBundleLineInQ(Matrix,Matrix) -- compute the normal bundle of a line in Q
- NumericalGodeaux -- Construction of numerical Godeaux surfaces
- pointOnARationalCodim1Hypersurface -- choose a QQ-rational point on a codimension 1 rational subvariety of the model in P3xP5
- pointOnARationalCodim1Hypersurface(ZZ) -- choose a QQ-rational point on a codimension 1 rational subvariety of the model in P3xP5
- precomputedCoxModel -- load the equation of the 5-dimensional hypersurface in a Cox ring of a toric variety
- precomputedCoxModel(Ring) -- load the equation of the 5-dimensional hypersurface in a Cox ring of a toric variety
- precomputedHyperellipticLocus -- get the ideal of the hyperelliptic locus
- precomputedHyperellipticLocus(Ring) -- get the ideal of the hyperelliptic locus
- precomputedHyperellipticPoint -- compute a point in the hyperelliptic locus using the unirational parametrization
- precomputedHyperellipticPoint(Ring) -- compute a point in the hyperelliptic locus using the unirational parametrization
- precomputedModelInP3xP3xP3xP3 -- load the precomputed ideal of the model of F(Q) in P3xP3xP3xP3
- precomputedModelInP3xP3xP3xP3(Ring) -- load the precomputed ideal of the model of F(Q) in P3xP3xP3xP3
- precomputedModelInP3xP5 -- load the precomputed model
- precomputedModelInP3xP5(Ring) -- load the precomputed model
- PrecomputedParametrization -- optional argument for using a precomputed unirational parametrization
- precomputedTorsZ2Line -- compute a line leading generically to a Z/2-Godeaux surface using a unirational parametrization
- precomputedTorsZ2Line(Ring) -- compute a line leading generically to a Z/2-Godeaux surface using a unirational parametrization
- precomputedTorsZ3Line -- compute a line leading generically to a Z/3-Godeaux surface using a unirational parametrization
- precomputedTorsZ3Line(Ring) -- compute a line leading generically to a Z/3-Godeaux surface using a unirational parametrization
- precomputedTorsZ4Line -- compute a line leading generically to a Z/4-Godeaux surface using a unirational parametrization
- precomputedTorsZ4Line(Ring) -- compute a line leading generically to a Z/4-Godeaux surface using a unirational parametrization
- precomputedTorsZ5Line -- compute a line leading generically to a Z/5-Godeaux surface using a unirational parametrization
- precomputedTorsZ5Line(Ring) -- compute a line leading generically to a Z/5-Godeaux surface using a unirational parametrization
- randomGodeauxSurface -- compute a birational model of a numerical Godeaux surface
- randomGodeauxSurface(..., Attempts => ...) -- optional argument in randomGodeauxSurface
- randomGodeauxSurface(..., Certify => ...) -- optional argument in randomGodeauxSurface
- randomGodeauxSurface(..., Height => ...) -- optional argument for the random computations
- randomGodeauxSurface(..., PrecomputedParametrization => ...) -- optional argument for using a precomputed unirational parametrization
- randomGodeauxSurface(Ring) -- compute a birational model of a numerical Godeaux surface
- randomGodeauxSurface(Ring,String) -- compute a birational model of a numerical Godeaux surface
- randomGodeauxSurface(Ring,String,ZZ) -- compute a birational model of a numerical Godeaux surface
- randomGodeauxSurface(Ring,String,ZZ,ZZ) -- compute a birational model of a numerical Godeaux surface
- randomLine -- compute a line through a given point which is completely contained in the Pfaffian variety
- randomLine(Ideal,Ideal,Matrix,Ring) -- compute a line through a given point which is completely contained in the Pfaffian variety
- randomLine(Ideal,Matrix,Ring) -- compute a line through a given point which is completely contained in the Pfaffian variety
- randomLineTors0 -- compute a line for a torsion-free numerical Godeaux surface
- randomLineTors0(Matrix,Matrix) -- compute a line for a torsion-free numerical Godeaux surface
- randomLineTors0(Matrix,Matrix,List,ZZ) -- compute a line for a torsion-free numerical Godeaux surface
- randomLineTorsZ2 -- compute a line for a numerical Godeaux surface with a cyclic torsion group of order 2
- randomLineTorsZ2(..., Height => ...) -- optional argument for the random computations
- randomLineTorsZ2(..., PrecomputedParametrization => ...) -- optional argument for using a precomputed unirational parametrization
- randomLineTorsZ2(Matrix,Matrix) -- compute a line for a numerical Godeaux surface with a cyclic torsion group of order 2
- randomLineTorsZ3 -- compute a line for a numerical Godeaux surface with a cyclic torsion group of order 3
- randomLineTorsZ3(..., Height => ...) -- optional argument for the random computations
- randomLineTorsZ3(..., PrecomputedParametrization => ...) -- optional argument for using a precomputed unirational parametrization
- randomLineTorsZ3(Matrix,Matrix) -- compute a line for a numerical Godeaux surface with a cyclic torsion group of order 3
- randomLineTorsZ4 -- compute a line for a numerical Godeaux surface with a cyclic torsion group of order 4
- randomLineTorsZ4(..., Height => ...) -- optional argument for the random computations
- randomLineTorsZ4(..., PrecomputedParametrization => ...) -- optional argument for using a precomputed unirational parametrization
- randomLineTorsZ4(Matrix,Matrix) -- compute a line for a numerical Godeaux surface with a cyclic torsion group of order 4
- randomLineTorsZ5 -- compute a line for a numerical Godeaux surface with a cyclic torsion group of order 5
- randomLineTorsZ5(..., Height => ...) -- optional argument for the random computations
- randomLineTorsZ5(..., PrecomputedParametrization => ...) -- optional argument for using a precomputed unirational parametrization
- randomLineTorsZ5(Matrix,Matrix) -- compute a line for a numerical Godeaux surface with a cyclic torsion group of order 5
- randomPoint -- compute a rational point in a variety
- randomPoint(Ideal) -- compute a rational point in a variety
- randomPoint(Ideal,List) -- compute a rational point in a variety
- randomPoint(Ideal,Ring) -- compute a rational point in a variety
- randomSection -- choose a point in the solution space defined by the linear relations
- randomSection(Matrix,Matrix,Matrix) -- choose a point in the solution space defined by the linear relations
- randomStandardResolution -- compute a random standard resolution of an S-module R
- randomStandardResolution(..., Height => ...) -- optional argument for the random computations
- randomStandardResolution(..., PrecomputedParametrization => ...) -- optional argument for using a precomputed unirational parametrization
- randomStandardResolution(Ring) -- compute a random standard resolution of an S-module R
- randomStandardResolution(Ring,String) -- compute a random standard resolution of an S-module R
- randomStandardResolution(Ring,String,ZZ) -- compute a random standard resolution of an S-module R
- randomStandardResolution(Ring,String,ZZ,ZZ) -- compute a random standard resolution of an S-module R
- setupGeneralMatrices -- compute the general set-up for the construction
- setupGeneralMatrices(ChainComplex,Matrix,Matrix) -- compute the general set-up for the construction
- setupGodeaux -- summarize the single steps for the general set-up of the construction
- setupGodeaux(Ring,String) -- summarize the single steps for the general set-up of the construction
- setupSkewMatrices -- compute four skew-symmetric matrices whose Pfaffians are among the quadratic relations
- setupSkewMatrices(Matrix,String) -- compute four skew-symmetric matrices whose Pfaffians are among the quadratic relations
- singleSolutionMatricesLine -- evaluate the single solution matrices at a line
- singleSolutionMatricesLine(Matrix,Matrix) -- evaluate the single solution matrices at a line
- singleSolutionMatricesOverP11 -- display the single solution matrices over the P^n of a-variables
- singleSolutionMatricesOverP11(Matrix) -- display the single solution matrices over the P^n of a-variables
- singularLocusQ -- compute the minimal primes of the singular locus of the Pfaffian relations
- singularLocusQ(Matrix) -- compute the minimal primes of the singular locus of the Pfaffian relations
- solutionMatrix -- display the relations linear in the c- and o-variables as a matrix
- solutionMatrix(Matrix) -- display the relations linear in the c- and o-variables as a matrix
- standardResolution -- compute a standard resolution of an S-module R obtained from the given input
- standardResolution(Matrix,Matrix,Matrix,String) -- compute a standard resolution of an S-module R obtained from the given input
- surfaceInWeightedP5 -- compute the surface in P(2,2,3,3,3,3)
- surfaceInWeightedP5(ChainComplex) -- compute the surface in P(2,2,3,3,3,3)
- surfaceInWeightedP5(Matrix) -- compute the surface in P(2,2,3,3,3,3)
- tangentSpacePoint -- compute the complete intersection of quadrics in the tangent space at a given point
- tangentSpacePoint(Ideal,Ideal,Matrix) -- compute the complete intersection of quadrics in the tangent space at a given point
- tangentSpacePoint(Ideal,Matrix) -- compute the complete intersection of quadrics in the tangent space at a given point
- tricanonicalModelInP3 -- computes the tricanonical model of a numerical Godeaux surface in P3
- tricanonicalModelInP3(Ideal) -- computes the tricanonical model of a numerical Godeaux surface in P3
- verifyAssertions -- verify the ring condition
- verifyAssertions(Matrix) -- verify the ring condition
- verifyThmHypLocus -- print commands which verify the assertions on the hyperelliptic locus
- verifyThmHypLocus(Ring) -- print commands which verify the assertions on the hyperelliptic locus