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Package sage :: Package rings :: Package polynomial :: Module groebner_fan :: Class PolyhedralCone
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Class PolyhedralCone

source code

                      object --+    
                               |    
structure.sage_object.SageObject --+
                                   |
                                  PolyhedralCone
Instance Methods [hide private]
 
__init__(self, gfan_polyhedral_cone, ring=Rational Field)
Converts polymake/gfan data on a polyhedral cone into a sage class.		 source code
 
_repr_(self)
Returns a basic description of the polyhedral cone.		 source code
 
facets(self)
Returns the inward facet normals of the Groebner cone.		 source code
 
ambient_dim(self)
Returns the ambient dimension of the Groebner cone.		 source code
 
dim(self)
Returns the dimension of the Groebner cone.		 source code
 
lineality_dim(self)
Returns the lineality dimension of the Groebner cone.		 source code
 
relative_interior_point(self)
Returns a point in the relative interior of the Groebner cone.		 source code

Inherited from structure.sage_object.SageObject: __hash__, __new__, __repr__, _axiom_, _axiom_init_, _gap_, _gap_init_, _gp_, _gp_init_, _interface_, _interface_init_, _interface_is_cached_, _kash_, _kash_init_, _macaulay2_, _macaulay2_init_, _magma_, _magma_init_, _maple_, _maple_init_, _mathematica_, _mathematica_init_, _maxima_, _maxima_init_, _octave_, _octave_init_, _pari_, _pari_init_, _r_init_, _sage_, _singular_, _singular_init_, category, db, dump, dumps, plot, rename, reset_name, save, version

Inherited from object: __delattr__, __getattribute__, __reduce__, __reduce_ex__, __setattr__, __str__

Properties [hide private]

Inherited from object: __class__

Method Details [hide private]

__init__(self, gfan_polyhedral_cone, ring=Rational Field)
(Constructor)

source code  

Converts polymake/gfan data on a polyhedral cone into a sage
class.  Currently (18-03-2008) needs a lot of work.

EXAMPLES:
    sage: R3.<x,y,z> = PolynomialRing(QQ,3)
    sage: gf = R3.ideal([x^8-y^4,y^4-z^2,z^2-2]).groebner_fan()
    sage: a = gf[0].groebner_cone()
    sage: a.facets()
    [[0, 0, 1], [0, 1, 0], [1, 0, 0]]
Overrides: object.__init__

_repr_(self)

source code  

Returns a basic description of the polyhedral cone.

EXAMPLES:
    sage: R3.<x,y,z> = PolynomialRing(QQ,3)
    sage: gf = R3.ideal([x^8-y^4,y^4-z^2,z^2-2]).groebner_fan()
    sage: a = gf[0].groebner_cone()
    sage: a # indirect doctests
    Polyhedral cone in 3 dimensions of dimension 3

facets(self)

source code  

Returns the inward facet normals of the Groebner cone.

EXAMPLES:
    sage: R3.<x,y,z> = PolynomialRing(QQ,3)
    sage: gf = R3.ideal([x^8-y^4,y^4-z^2,z^2-2]).groebner_fan()
    sage: a = gf[0].groebner_cone()
    sage: a.facets()
    [[0, 0, 1], [0, 1, 0], [1, 0, 0]]

ambient_dim(self)

source code  

Returns the ambient dimension of the Groebner cone.

EXAMPLES:
    sage: R3.<x,y,z> = PolynomialRing(QQ,3)
    sage: gf = R3.ideal([x^8-y^4,y^4-z^2,z^2-2]).groebner_fan()
    sage: a = gf[0].groebner_cone()
    sage: a.ambient_dim()
    3

dim(self)

source code  

Returns the dimension of the Groebner cone.

EXAMPLES:
    sage: R3.<x,y,z> = PolynomialRing(QQ,3)
    sage: gf = R3.ideal([x^8-y^4,y^4-z^2,z^2-2]).groebner_fan()
    sage: a = gf[0].groebner_cone()
    sage: a.dim()
    3

lineality_dim(self)

source code  

Returns the lineality dimension of the Groebner cone.  This is
the just the difference between the ambient dimension and the
dimension of the cone.

EXAMPLES:
    sage: R3.<x,y,z> = PolynomialRing(QQ,3)
    sage: gf = R3.ideal([x^8-y^4,y^4-z^2,z^2-2]).groebner_fan()
    sage: a = gf[0].groebner_cone()
    sage: a.lineality_dim()
    0

relative_interior_point(self)

source code  

Returns a point in the relative interior of the Groebner cone.

EXAMPLES:
    sage: R3.<x,y,z> = PolynomialRing(QQ,3)
    sage: gf = R3.ideal([x^8-y^4,y^4-z^2,z^2-2]).groebner_fan()
    sage: a = gf[0].groebner_cone()
    sage: a.relative_interior_point()
    [1, 1, 1]

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