Package sage :: Package calculus :: Module calculus :: Class CallableSymbolicExpressionRing_class

Class CallableSymbolicExpressionRing_class

                      object --+                        
                               |                        
structure.sage_object.SageObject --+                    
                                   |                    
             structure.parent.Parent --+                
                                       |                
    structure.parent_base.ParentWithBase --+            
                                           |            
        structure.parent_gens.ParentWithGens --+        
                                               |        
                                 rings.ring.Ring --+    
                                                   |    
                          rings.ring.CommutativeRing --+
                                                       |
                                                      CallableSymbolicExpressionRing_class

Instance Methods

[hide private]

__init__(self, args)
x.__init__(...) initializes x; see x.__class__.__doc__ for signature

source code

__call__(self, x)
TESTS:...

source code

_coerce_impl(self, x)
File: sage/structure/parent.pyx (starting at line 373) Canonically coerce x in assuming that the parent of x is not equal to self.

source code

_repr_(self)
String representation of ring of callable symbolic expressions.

source code

args(self)
Returns the arguments of \code{self}.

source code

arguments(self)
Returns the arguments of \code{self}.

source code

zero_element(self)
Return the zero element of the ring of callable symbolic expressions.

source code

_an_element_impl(self)
Return an element of the ring of callabel symbolic expressions.

source code

Inherited from rings.ring.CommutativeRing: __div__, __new__, __pow__, __rdiv__, __rpow__, extension, fraction_field, ideal_monoid, is_commutative, krull_dimension, quo, quotient, quotient_ring

Inherited from rings.ring.Ring: __getitem__, __hash__, __iter__, __len__, __mul__, __rmul__, __rxor__, __xor__, _ideal_class_, base_extend, category, characteristic, ideal, is_atomic_repr, is_exact, is_field, is_finite, is_integral_domain, is_noetherian, is_prime_field, is_ring, is_subring, one_element, order, principal_ideal, random_element, unit_ideal, zero_ideal, zeta, zeta_order

Inherited from rings.ring.Ring (private): _r_action

Inherited from structure.parent_gens.ParentWithGens: __getslice__, __getstate__, __setstate__, _is_valid_homomorphism_, gen, gens, gens_dict, hom, inject_variables, injvar, latex_name, latex_variable_names, list, ngens, 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, base_ring

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, _coerce_self, _coerce_try

Inherited from structure.sage_object.SageObject: __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 rings.ring.Ring (private): _one_element, _unit_ideal, _zero_element, _zero_ideal

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, args)
(Constructor)

source code

x.__init__(...) initializes x; see x.__class__.__doc__ for signature

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

call(self, x)
(Call operator)

source code



TESTS:
    sage: f(x) = x+1; g(y) = y+1
    sage: f.parent()(g)
    x |--> y + 1
    sage: g.parent()(f)
    y |--> x + 1
    sage: f(x) = x+2*y; g(y) = y+3*x
    sage: f.parent()(g)
    x |--> y + 3*x
    sage: g.parent()(f)
    y |--> 2*y + x

Overrides: rings.ring.Ring.__call__

_coerce_impl(self, x)

source code

File: sage/structure/parent.pyx (starting at line 373)

Canonically coerce x in assuming that the parent of x is not
equal to self.

Overrides: structure.parent.Parent._coerce_impl: (inherited documentation)

_repr_(self)

source code


String representation of ring of callable symbolic expressions.

EXAMPLES:
    sage: R = CallableSymbolicExpressionRing(var('x,y,theta'))
    sage: R._repr_()
    'Callable function ring with arguments (x, y, theta)'

args(self)

source code


Returns the arguments of \code{self}.  The order that the variables appear
in \code{self.args()} is the order that is used in evaluating the elements
of \code{self}.

EXAMPLES:
    sage: x,y = var('x,y')
    sage: f(x,y) = 2*x+y
    sage: f.parent().args()
    (x, y)
    sage: f(y,x) = 2*x+y
    sage: f.parent().args()
    (y, x)

arguments(self)

source code


Returns the arguments of \code{self}.  The order that the variables appear
in \code{self.args()} is the order that is used in evaluating the elements
of \code{self}.

EXAMPLES:
    sage: x,y = var('x,y')
    sage: f(x,y) = 2*x+y
    sage: f.parent().args()
    (x, y)
    sage: f(y,x) = 2*x+y
    sage: f.parent().args()
    (y, x)

zero_element(self)

source code


Return the zero element of the ring of callable symbolic expressions.

EXAMPLES:
    sage: R = CallableSymbolicExpressionRing(var('x,y,theta'))
    sage: f = R.zero_element(); f
    (x, y, theta) |--> 0
    sage: f(2,3,4)
    0

Overrides: rings.ring.Ring.zero_element

_an_element_impl(self)

source code


Return an element of the ring of callabel symbolic expressions.
This is used by the coercion model.

EXAMPLES:
    sage: R = CallableSymbolicExpressionRing(var('x,y,theta'))
    sage: R._an_element_impl()
    (x, y, theta) |--> 0

Overrides: structure.parent.Parent._an_element_impl

Class CallableSymbolicExpressionRing_class

__init__(self, args) (Constructor)

__call__(self, x) (Call operator)

_coerce_impl(self, x)

_repr_(self)

args(self)

arguments(self)

zero_element(self)

_an_element_impl(self)

init(self, args)
(Constructor)

call(self, x)
(Call operator)