MethodFunction -- a type of method function
Description
Functions of this type are created by
method.
Protected objects of class MethodFunction:
-
abs -- absolute value function
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accumulate -- apply a binary operator repeatedly
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acos -- arccosine
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acosh -- inverse hyperbolic cosine
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acot -- compute the inverse cotangent
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acoth -- compute the hyperbolic arctangent of a number
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addCone -- adds cones to a Fan
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addPolyhedron -- adds Polyhedra to a PolyhedralComplex
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adjoint' -- see adjoint -- the tensor-Hom adjunction maps
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affineHull -- computes the affine hull of a polyhedron
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affineImage -- computes the affine image of a cone or polyhedron
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affinePreimage -- computes the affine preimage of a cone or polyhedron
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agm -- arithmetic-geometric mean
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all -- whether all elements satisfy a specified condition
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ambDim -- ambient dimension of a Polyhedron, Cone or Fan
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ambient -- ambient free module of a subquotient, or ambient ring
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antipode -- antipode for skew commuting polynomial rings
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apropos -- symbols matching a pattern
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areCompatible -- checks if the intersection of two cones/polyhedra is a face of each
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arXiv -- link to an arXiv article
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asin -- arcsine
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asinh -- inverse hyperbolic sine
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assert -- check whether something is true, raise an error if not
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atan -- compute the arctangent of a number
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atan2 -- compute an angle of a certain triangle
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atanh -- compute the hyperbolic arctangent of a number
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autoload -- arrange for a function to be loaded automatically
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barycentricTriangulation -- computes a triangulation of a polytope
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baseName -- the base name of a generator
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baseRing -- produce the ring from which a ring was formed
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BesselJ -- Bessel function of the first kind
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BesselY -- Bessel function of the second kind
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Beta -- Beta function
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between -- insert something between elements of a list
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binomial -- binomial coefficient
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bipyramid -- computes the bipyramid over a polyhedron
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borel -- see borel(Matrix) -- make a Borel fixed submodule
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ccRefinement -- computes the coarsest common refinement of a set of rays
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ceiling -- ceiling function
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cellDecompose -- Deprecated variant of {\tt regularSubdivision}
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changeBase -- change integer base
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char -- computes the characteristic of the ring or field
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chi
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clean -- Set to zero elements that are approximately zero
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coefficient -- coefficient of a monomial
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coefficientRing -- get the coefficient ring
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coimage -- coimage of a map
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cokernel -- cokernel of a map of modules, graded modules, or chaincomplexes
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columnAdd -- add a multiple of one column to another
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columnMult -- multiply a column by a ring element
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columnPermute -- permute some columns
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columnRankProfile -- find the column rank profile of a mutable matrix
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columnSwap -- interchange columns
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commonFace -- checks if the intersection is a face of both Cones or Polyhedra, or of cones with fans
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commonRing -- find smallest containing ring
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comodule -- submodule to quotient module
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compareExchange -- compares and possibly exchanges the value of an atomic integer
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complement -- see complement(Matrix) -- find the minimal generators for cokernel of a matrix (low level form)
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complete
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components -- list the components of a direct sum
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compositions -- list the compositions of an integer
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compress -- extract nonzero columns from a matrix
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conductor -- the conductor of a finite ring map
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cone -- mapping cone or polyhedral cone
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coneFromHData -- Constructing a polyhedral cone as intersection of halfspaces.
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coneFromVData -- computes the positive hull of rays, cones, and the cone over a polyhedron
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cones -- computes all cones of a fan of a certain dimension
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conjugate -- complex conjugate
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contains -- checks if the first argument contains the second argument
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content -- the content of a polynomial
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contract -- contract one matrix by another
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contract' -- see contract'(Matrix,Matrix) -- contract a matrix by a matrix, the dual notion
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convexHull -- computing the convex hull of points, rays and polyhedra
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cos -- compute the cosine
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cosh -- compute the hyperbolic cosine
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cot -- cotangent
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coth -- hyperbolic cotangent
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cover -- get the covering free module
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coverMap -- see coverMap(Module) -- the surjective map from a free module to a module corresponding to the generators
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crossPolytope -- computes the d-dimensional crosspolytope with diameter 2s
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csc -- cosecant
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csch -- hyperbolic cosecant
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cyclicPolytope -- computes the d dimensional cyclic polytope with n vertices
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debug -- open the private dictionary of a package
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default -- default member of a family
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degree
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degreeGroup (missing documentation)
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degreeLength -- the length of the degree vector
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degrees -- degrees of generators
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degreesMonoid -- see degreesRing -- the ring or monoid of degrees
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degreesRing -- the ring or monoid of degrees
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delete -- delete some elements of a list
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denominator -- denominator of a fraction
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depth -- depth of a net
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diagonalMatrix -- make a diagonal matrix
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diameter -- diameter of an interval
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dictionary -- determine the dictionary to which a symbol belongs
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diff -- differentiate or take difference
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diff' -- see diff'(Matrix,Matrix) -- differentiate a matrix by a matrix, the dual notion
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Digamma -- Digamma function
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dim -- compute the Krull dimension
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directProduct -- computes the direct product of two convex objects
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dismiss -- dismiss a package
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divideByVariable -- divide all columns by a (power of a) variable
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doc -- a simple documentation function
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dualCone -- computes the dual Cone
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dualFaceRepresentationMap (missing documentation)
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eagonNorthcott -- see eagonNorthcott(Matrix) -- Eagon-Northcott complex of a matrix of linear forms
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effCone (missing documentation)
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effGenerators (missing documentation)
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ehrhart -- calculates the Ehrhart polynomial of a polytope
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eint -- exponential integral
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elements -- list of elements
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eliminate
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emptyPolyhedron -- generates the empty polyhedron in n-space
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endPackage -- end a new package
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entries -- lists the entries of a matrix
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erf -- error function
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erfc -- complementary error function
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euler -- Euler characteristic
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eulers -- list the sectional Euler characteristics
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exchange -- exchange the value of an atomic integer
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exp -- exponential function
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expectedReesIdeal -- symmetric algebra ideal plus jacobian dual
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expm1 -- exponential minus 1
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exponents -- the exponents of a polynomial
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exportFrom -- export symbols from a package's private dictionary
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faceFan -- computes the fan generated by the cones over the faces
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faces -- computes all faces of a certain codimension of a Cone or Polyhedron
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facesAsCones -- Returns the faces of a cone as actual cones.
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facesAsPolyhedra -- Returns the faces of a polyhedron as actual polyhedra.
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facets -- Giving the facet inequalities of a cone or polyhedron.
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fan -- generates a Fan
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fanFromGfan -- Construct a fan from output data of {\tt Gfan}
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Fano -- Fano scheme
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findSynonyms -- see findSynonyms(Symbol) -- find synonyms of symbols
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fittingIdeal -- Fitting ideal of a module
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flip -- isomorphism map of commutativity of tensor product
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floor -- floor function
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fold -- apply a binary operator repeatedly
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formation -- recover the methods used to make a module
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frac -- construct a fraction field
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fraction
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fromDividedPowers -- Translates from divided power monomial basis to ordinary monomial basis
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fVector -- computes the f-vector of a Cone, Polyhedron, Fan or PolyhedralComplex
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Gamma -- Gamma function
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gbRemove -- remove Gröbner basis
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gbSnapshot -- the Gröbner basis matrix as so far computed
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gcdCoefficients -- gcd with coefficients
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genera -- list of the successive linear sectional arithmetic genera
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generateAssertions -- generate assert statements from experimental input
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generator -- provide a single generator
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genericMatrix -- make a generic matrix of variables
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genericSkewMatrix -- make a generic skew symmetric matrix of variables
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genericSymmetricMatrix -- make a generic symmetric matrix
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genus -- arithmetic genus
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getChangeMatrix -- get the change of basis matrix
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getWWW -- get a web page
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gramm (missing documentation)
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halfspaces -- computes the defining half-spaces of a Cone or a Polyhedron
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headlines -- display a table of documentation headlines
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heft -- heft vector of ring or monoid
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height -- height of a net
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hilbertFunction -- the Hilbert function
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hirzebruch -- computes the fan of the r-th Hirzebruch surface
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homogenize -- homogenize with respect to a variable
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homomorphism -- get the homomorphism from element of Hom
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httpHeaders -- see httpHeaders(String) -- prepend http headers to a string
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hypercube -- Returns the d-dimensional hypercube
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hyperplanes -- computes the defining hyperplanes of a Cone or a Polyhedron
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icFractions -- fractions integral over an affine domain
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icMap -- natural map from an affine domain into its integral closure
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icPIdeal -- compute the integral closure in prime characteristic of a principal ideal
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image -- image of a map
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imageFan -- computes the fan of the image
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imaginaryPart -- imaginary part
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importFrom -- import symbols to the current private dictionary
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incompCones -- returns the pairs of incompatible cones
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incompPolyhedra -- returns the pairs of incompatible polyhedra
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index -- numeric index of a ring variable
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indices -- indices of a polynomial; also components for a direct sum
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inducesWellDefinedMap -- whether a map is well defined
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inInterior -- checks if a point lies in the relative interior of a Cone/Polyhedron
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insert -- copy a list, inserting an element
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installAssignmentMethod -- install methods assignment to the value of an operator
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instances -- see instances(Type)
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integrate -- numerical integration
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interiorLatticePoints -- computes the lattice points in the relative interior of a polytope
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interiorPoint -- computes a point in the relative interior of the Polyhedron
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interiorVector -- computes a vector in the relative interior of a Cone
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inverse -- compute the inverse
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inverseErf -- inverse error function
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inverseRegularizedBeta -- inverse of the regularized beta function
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inverseRegularizedGamma -- inverse of the upper regularized gamma function
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irreducibleCharacteristicSeries -- irreducible characteristic series of an ideal
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irreducibleDecomposition -- express a monomial ideal as an intersection of irreducible monomial ideals
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isAffineRing -- whether something is an affine ring
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isBorel -- whether an ideal is fixed by upper triangular changes of coordinates
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isc -- ISC lookup
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isCommutative -- whether a ring is commutative
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isCompact -- checks compactness of a Polyhedron
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isComplete -- checks completeness of a Fan or PolyhedralComplex
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isConstant -- whether a ring element is constant
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isDirectSum -- whether something is a direct sum
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isEmpty
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isFace -- tests if the first argument is a face of the second
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isField -- whether something is a field
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isFinite -- whether a number is finite
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isFreeModule -- whether something is a free module
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isFullDimensional -- Determine whether a polyhedral object is full-dimensional
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isHomogeneous -- whether something is homogeneous (graded)
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isIdeal -- whether something is an ideal
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isInfinite -- whether a number is infinite
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isInjective -- whether a map is injective
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isIsomorphism -- whether a map is an isomorphism
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isLatticePolytope -- checks if a polyhedron is a lattice polytope
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isLiftable (missing documentation)
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isMember -- test membership in a list or set
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isModule -- whether something is a module
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isMonomialIdeal -- whether something is a monomial ideal
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isNormal
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isPointed -- checks if a Cone or Fan is pointed
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isPolynomialRing -- whether something is a polynomial ring
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isPolytopal -- checks if a Fan is polytopal
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isProjective (missing documentation)
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isPure -- checks if a Fan or PolyhedralComplex is of pure dimension
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isQuotientModule -- whether something is evidently a quotient of a free module
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isQuotientOf -- whether one thing is a quotient of another
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isQuotientRing -- whether something is a quotient ring
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isReal -- whether a number is real
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isRing -- whether something is a ring
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isSimplicial -- checks if a polyhedral object is simplicial
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isSkewCommutative -- whether a ring has skew commuting variables
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isSquareFree -- whether something is square free monomial ideal
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isStandardGradedPolynomialRing -- Checks whether a ring is a polynomial ring over a field with variables of degree 1
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isSubmodule -- whether a module is evidently a submodule of a free module
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isSubquotient -- see isSubquotient(Module,Module) -- check whether a module is a subquotient of another
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isSubset -- whether one object is a subset of another
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isSupportedInZeroLocus -- whether support of a module is contained in the zero locus of the (irrelevant) ideal
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isSurjective -- whether a map is surjective
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isUnit -- whether a ring element is a unit
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isWellDefined -- whether a map is well defined
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jacobian -- the Jacobian matrix of partial derivatives
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kernelOfLocalization -- the kernel of the localization map
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koszul -- Koszul complex or specific matrix in the Koszul complex
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latticePoints -- computes the lattice points of a polytope
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latticeVolume -- Returning the lattice volume of a polyhedron.
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leadCoefficient -- the coefficient of the leading term
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leadComponent -- the leading component(s) of a vector or matrix
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leadMonomial -- the leading monomial of a ring element
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leadTerm -- get the greatest term
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liftable -- whether lifting to another ring is possible
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linealitySpace -- computes a basis of the lineality space
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linearTransform (missing documentation)
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linSpace -- Deprecated version of @TO "linealitySpace"@
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listForm -- convert to list form
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listSymbols -- compact display of symbols and their values
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lngamma -- logarithm of the Gamma function
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log -- logarithm function
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log1p -- logarithm of 1+x
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LUdecomposition -- LU decomposition
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makeDirectory -- see makeDirectory(String) -- make a directory
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maxCones -- displays the generating Cones of a Fan
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maxFace -- computes the face of a Polyhedron or Cone where a weight attains its maximum
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maxPolyhedra -- displays the generating Polyhedra of a PolyhedralComplex
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memoize -- record results of function evaluation for future use
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methodOptions -- see methodOptions(Function) -- recover the options used when a method function was created
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minFace -- computes the face of a Polyhedron or Cone where a weight attains its minimum
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minimalNonFaces (missing documentation)
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minimize
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minkowskiSum -- computes the Minkowski sum of two convex objects
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minkSummandCone -- computes the Cone of all Minkowski summands and the minimal decompositions
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mixedVolume -- computes the mixed volume of a list of polytope
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module -- make or get a module
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monomialSubideal -- find the largest monomial ideal in an ideal
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multidegree -- multidegree
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multigraded -- convert a Betti tally into a multigraded Betti tally
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nefCone (missing documentation)
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nefGenerators (missing documentation)
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newCoordinateSystem -- change variables
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newtonPolytope -- computes the Newton polytope of a polynomial
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next -- get the next object from an iterator
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nextPrime -- compute the smallest prime greater than or equal to a given number
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norm
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normalFan -- computes the normalFan of a polyhedron
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nullhomotopy -- make a null homotopy
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nullSpace -- find the null space of a mutable matrix
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numColumns -- see numColumns(Matrix) -- number of columns in a matrix or mutable matrix
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numerator -- numerator of a fraction
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numeric -- convert to floating point
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numericInterval -- converts to an interval
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numgens -- the number of generators
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numRows -- see numRows(Matrix) -- number of rows in a matrix or mutable matrix
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nVertices -- Returns the number of vertices of a polyhedron
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objectiveVector -- computes an objective vector of a face of a polyhedron
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ofClass -- English phrases for types
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pack -- pack elements of a list or string into several shorter lists or strings
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packageTemplate -- a template for a package
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pad -- pad a string or net with spaces
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part -- select terms of a polynomial by degree(s) or weight(s)
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partition -- partition a set or list by values of a function
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partitions -- list the partitions of an integer
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parts -- display terms of a polynomial degree by degree
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pdim -- calculate the projective dimension
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peek' -- examine contents of an object
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permanents -- ideal generated by square permanents of a matrix
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permutations -- produce all permutations of a list
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pfaffians -- ideal generated by Pfaffians
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pivots -- see pivots(Matrix) -- list of pivot locations of a matrix
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installHilbertFunction -- see poincare -- assemble degrees of a ring, module, or ideal into a polynomial
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poincare -- assemble degrees of a ring, module, or ideal into a polynomial
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poincareN -- assemble degrees into polynomial
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polar -- computes the polar of a polyhedron
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polarFace -- computes the dual face of the polar polyhedron
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poly -- see poly(String) -- make a polynomial using classic Macaulay syntax
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polyhedra -- computes all polyhedra of a polyhedral complex of a certain dimension
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polyhedralComplex -- generates a PolyhedralComplex
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polyhedron -- Turn a cone into a polyhedron
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polyhedronFromHData -- Constructing a polyhedron from its H-representation, i.e. inequalities and equations
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polytope -- returns a polytope of which the fan is the normal fan if it is polytopal
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positions -- which elements of a list satisfy a condition
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posOrthant -- generates the positive orthant in n-space
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precision
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preimage -- preimage of a map
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presentation -- presentation of a module or ring
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product
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profile -- profile a function
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Proj -- make a projective variety
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projectiveHilbertPolynomial -- Hilbert polynomial of projective space
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promote -- promote to another ring
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proximum -- computes the proximum of the Polyhedron/Cone to a point in euclidean metric
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pseudoRemainder -- compute the pseudo-remainder
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pushout -- compute the pushout morphism
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pyramid -- computes the pyramid over a polyhedron
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QRDecomposition -- compute a QR decomposition of a real matrix
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quotient' -- matrix quotient (opposite)
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quotientRemainder -- matrix quotient and remainder
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quotientRemainder' -- matrix quotient and remainder (opposite)
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randomKRationalPoint -- Pick a random K rational point on the scheme X defined by I
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rank -- compute the rank
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realPart -- real part
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reducedRowEchelonForm -- compute the reduced row echelon form of a matrix or mutable matrix over a field
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reduceHilbert -- reduce a Hilbert series expression
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reductionNumber -- Reduction number of one ideal with respect to another
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registerFinalizer -- register a string that will be displayed when an object is garbage collected
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regularizedBeta -- regularized beta function
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regularizedGamma -- upper regularized gamma function
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regularSubdivision -- Computes the regular cell decomposition
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regularTriangulation -- Computes a regular triangulation of a given polytope.
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relations -- the defining relations
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remainder -- matrix remainder
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remainder' -- matrix quotient and remainder (opposite)
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removeLowestDimension -- remove components of lowest dimension
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reshape -- reshape a matrix
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ring -- get the associated ring of an object
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rotate -- see rotate(ZZ,VisibleList) -- rotate a list
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round -- round a number
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rowAdd -- add a multiple of one row to another
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rowMult -- multiply a row by a ring element
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rowPermute -- permute some rows
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rowRankProfile -- find the row rank profile of a mutable matrix
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rowSwap -- interchange rows
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saveSession -- save the actual Polyhedra session to a file
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scanKeys -- apply a function to each key in a hash table or database
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scanLines -- apply a function to each line of a file
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scanValues -- apply a function to each value in a hash table or database
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schreyerOrder -- create or obtain free modules with Schreyer monomial orders
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searchPath -- see searchPath(List,String) -- search a path for a file
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sec -- secant
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sech -- hyperbolic secant
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secondaryPolytope -- computes the secondary polytope of a compact polyhedron
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selectValues -- see select(HashTable,Function) -- select part of a hash table
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selectInSubring -- select columns in a subring
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selectKeys -- select a part of a hash table by keys
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selectVariables -- see selectVariables(List,PolynomialRing) -- make a subring of a polynomial ring generated by selected variables
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setup
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setupEmacs
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setupLift -- set up lift from one ring to another
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setupPromote -- set up promote from one ring to another
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sheaf -- make a coherent sheaf
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sheafMap (missing documentation)
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show -- display various objects in an external viewer
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simplex -- Produces a full-dimensional simplex
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sin -- compute the sine
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singularLocus -- singular locus
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sinh -- compute the hyperbolic sine
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size -- the size of an object
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skeleton -- computes the k-skeleton of a Fan or PolyhedralComplex
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smallestFace -- determines the smallest face of the Cone/Polyhedron containing a point
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smoothSubfan -- computes the subfan of all smooth cones
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someTerms -- select some terms of a polynomial
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source -- source of a map
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Spec -- make an affine variety
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splitWWW -- separate an http response into header and body
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sqrt -- square root function
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stacksProject -- link to a Stacks Project tag
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standardForm -- convert to standard form
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standardPairs -- find the standard pairs of a monomial ideal
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stanleyReisnerRing (missing documentation)
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statePolytope -- computes the state polytope of a homogeneous ideal
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stdSimplex -- generates the d-dimensional standard simplex
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stellarSubdivision -- computes the stellar subdivision of the fan by a ray
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store -- store the value of an atomic integer
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sublatticeBasis -- computes a basis for the sublattice generated by integral vectors or lattice points of a polytope
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sublists -- process interspersed subsequences of a visible list
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submatrix
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submatrix' -- exclude rows and/or columns of a matrix
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submatrixByDegrees -- submatrix consisting of rows and columns in an interval or box of degrees
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subquotient -- make a subquotient module
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subsets -- produce the subsets of a set or list
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substitute -- substituting values for variables
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sum -- compute the sum
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super -- get the ambient module
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support -- list of variables occurring in a polynomial or matrix
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switch -- copy a list, switching two elements
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sylvesterMatrix -- see sylvesterMatrix(RingElement,RingElement,RingElement)
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symmetricPower -- symmetric power
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tailCone -- computes the tail/recession cone of a polyhedron
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tan -- compute the tangent
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tanh -- compute the hyperbolic tangent
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target -- target of a map
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tensorAssociativity -- associativity isomorphisms for tensor products
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terms -- provide a list of terms of a polynomial
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testHunekeQuestion -- tests a conjecture on integral closures strengthening the Eisenbud-Mazur conjecture
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tests -- locate a package's tests
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toDividedPowers -- Translates to divided power monomial basis from ordinary monomial basis
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toField -- see toField(Ring) -- declare that a ring is a field
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topCoefficients -- first variable and its coefficient of a polynomial or matrix
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topComponents -- compute top dimensional component of an ideal or module
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toSublattice -- calculates the preimage of a polytope in the sublattice generated by its lattice points
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trace -- see trace(Matrix) -- trace of a matrix
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triangulate -- Deprecated name for {\tt barycentricTriangulation}
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truncateOutput
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ultimate -- ultimate value for an iteration
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unbag -- see unbag(Bag)
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uniquePermutations -- produce all unique permutations of a list
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urlEncode -- URL encoding
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value -- evaluate
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variety -- get the variety
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vector -- make a vector
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versalEmbedding -- Compute a versal embedding
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vertexEdgeMatrix -- computes the vertex-edge-relations matrix
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vertexFacetMatrix -- computes the vertex-facet-relations matrix
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vertices -- displays the vertices of a Polyhedron or a PolyhedralComplex
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volume -- computes the volume of a polytope
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wedgeProduct -- see wedgeProduct(ZZ,ZZ,Module) -- the exterior multiplication map
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weightRange -- the pair of lowest and highest weights of the monomials
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isWeylAlgebra -- see Weyl algebras
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whichGm -- Largest Gm satisfied by an ideal
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width -- width of a file or net
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wikipedia -- link to a Wikipedia article
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zeta -- Riemann zeta function