Package sage :: Package schemes :: Package generic :: Module ambient_space :: Class AmbientSpace

Class AmbientSpace

                      object --+                
                               |                
structure.sage_object.SageObject --+            
                                   |            
             structure.parent.Parent --+        
                                       |        
    structure.parent_base.ParentWithBase --+    
                                           |    
                               scheme.Scheme --+
                                               |
                      object --+               |
                               |               |
structure.sage_object.SageObject --+           |
                                   |           |
             structure.parent.Parent --+       |
                                       |       |
    structure.parent_base.ParentWithBase --+   |
                                           |   |
        structure.parent_gens.ParentWithGens --+
                                               |
                                              AmbientSpace

Known Subclasses:: affine_space.AffineSpace_generic, projective_space.ProjectiveSpace_ring


Base class for ambient spaces over a ring.

INPUT:
    n -- dimension
    R -- ring

Instance Methods

[hide private]

__init__(self, n, R=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...) source code

__cmp__(self, right)

source code

_constructor(self)

source code

_latex_(self)

source code

_repr_(self)

source code

_repr_generic_point(self, coords=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...) source code

_latex_generic_point(self, coords=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...) source code

_check_satisfies_equations(self, v)
Verify that the coordinates of v define a point on this scheme, or raise a TypeError.

source code

base_extend(self, S, check=True)
Y is either a scheme in the same category as self or a ring.

source code

ambient_space(self)

source code

defining_polynomials(self)

source code

gen(self, n=0)
File: sage/structure/parent_gens.pyx (starting at line 206)

source code

gens(self)
File: sage/structure/parent_gens.pyx (starting at line 269) Return a tuple whose entries are the generators for this object, in order.

source code

ngens(self)
File: sage/structure/parent_gens.pyx (starting at line 202)

source code

dimension(self)
Return the relative dimension of this scheme over its base.

source code

Inherited from scheme.Scheme: _Hom_, __add__, __call__, __div__, base_morphism, base_ring, base_scheme, category, coordinate_ring, count_points, hom, identity_morphism, point, point_homset, point_set, structure_morphism, zeta_series

Inherited from scheme.Scheme (private): _homset_class, _point_class, _point_morphism_class

Inherited from structure.parent_gens.ParentWithGens: __getitem__, __getslice__, __getstate__, __len__, __new__, __setstate__, _is_valid_homomorphism_, gens_dict, inject_variables, injvar, latex_name, latex_variable_names, list, objgen, objgens, variable_name, variable_names

Inherited from structure.parent_gens.ParentWithGens (private): _assign_names, _first_ngens

Inherited from structure.parent_base.ParentWithBase: Hom, base, base_extend_canonical, base_extend_canonical_sym, base_extend_recursive

Inherited from structure.parent.Parent: __contains__, _coerce_, coerce_map_from, coerce_map_from_impl, construction, get_action, get_action_impl, has_coerce_map_from, has_coerce_map_from_impl, init_coerce

Inherited from structure.parent.Parent (private): _an_element, _an_element_impl, _coerce_impl, _coerce_self, _coerce_try

Inherited from structure.sage_object.SageObject: __hash__, __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_, db, dump, dumps, plot, rename, reset_name, save, version

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

Properties

[hide private]

Inherited from structure.parent_gens.ParentWithGens (private): _gens, _gens_dict, _latex_names, _list, _names

Inherited from structure.parent.Parent (private): _has_coerce_map_from

Inherited from object: __class__

Method Details

[hide private]

init(self, n, R=`['4ti2-20061025',` `'R-2.6.0',` `'atlas-3.7.37',` `'atlas-3.8.1',` `'a...`)
(Constructor)

source code

Overrides: scheme.Scheme.__init__

cmp(self, right)
(Comparison operator)

source code

Overrides: scheme.Scheme.__cmp__

base_extend(self, S, check=True)

source code


Y is either a scheme in the same category as self or a ring.

Overrides: scheme.Scheme.base_extend: (inherited documentation)

gen(self, n=0)

source code

File: sage/structure/parent_gens.pyx (starting at line 206)

Overrides: structure.parent_gens.ParentWithGens.gen: (inherited documentation)

gens(self)

source code

File: sage/structure/parent_gens.pyx (starting at line 269)

Return a tuple whose entries are the generators for this
object, in order.

Overrides: structure.parent_gens.ParentWithGens.gens: (inherited documentation)

ngens(self)

source code

File: sage/structure/parent_gens.pyx (starting at line 202)

Overrides: structure.parent_gens.ParentWithGens.ngens: (inherited documentation)

dimension(self)

source code


Return the relative dimension of this scheme over its base.

Overrides: scheme.Scheme.dimension

Class AmbientSpace

__init__(self, n, R=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...) (Constructor)

__cmp__(self, right) (Comparison operator)

base_extend(self, S, check=True)

gen(self, n=0)

gens(self)

ngens(self)

dimension(self)

init(self, n, R=`['4ti2-20061025',` `'R-2.6.0',` `'atlas-3.7.37',` `'atlas-3.8.1',` `'a...`)
(Constructor)

cmp(self, right)
(Comparison operator)