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