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Package sage :: Package calculus :: Module calculus :: Class Symbolic_object
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Class Symbolic_object

source code

                      object --+                    
                               |                    
structure.sage_object.SageObject --+                
                                   |                
           structure.element.Element --+            
                                       |            
         structure.element.ModuleElement --+        
                                           |        
               structure.element.RingElement --+    
                                               |    
                              SymbolicExpression --+
                                                   |
                                                  Symbolic_object
Known Subclasses:
SymbolicConstant, SymbolicPolynomial 

A class representing a symbolic expression in terms of a \class{SageObject} (not
necessarily a `constant').


Instance Methods [hide private]
 
__init__(self, obj)
Create a symbolic expression.		 source code
 
__hash__(self)
Returns the hash of this symbolic expression.		 source code
 
obj(self)
EXAMPLES:		 source code
 
_fast_float_(self, *vars)
EXAMPLES: sage: x,y,z = var('x,y,z') sage: f = 1 + sin(x)/x + sqrt(z^2+y^2)/cosh(x) sage: ff = f._fast_float_('x', 'y', 'z') sage: f(1.0,2.0,3.0) 4.1780638977866...		 source code
 
__float__(self)
EXAMPLES:		 source code
 
__complex__(self)
EXAMPLES:		 source code
 
_mpfr_(self, field)
EXAMPLES:		 source code
 
_complex_mpfr_field_(self, C)
EXAMPLES:		 source code
 
_complex_double_(self, C)
EXAMPLES:		 source code
 
_real_double_(self, R)
EXAMPLES:		 source code
 
_real_rqdf_(self, R)
EXAMPLES:		 source code
 
_repr_(self, simplify=True)
EXAMPLES:		 source code
 
_latex_(self)
EXAMPLES:		 source code
 
str(self, bits=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...) source code
 
_maxima_init_(self)
File: sage/structure/sage_object.pyx (starting at line 318)		 source code
 
_sys_init_(self, system) source code
 
number_of_arguments(self)
Returns the number of arguments this object can take.		 source code

Inherited from SymbolicExpression: __abs__, __call__, __cmp__, __eq__, __ge__, __gt__, __int__, __le__, __long__, __lt__, __ne__, __nonzero__, __pow__, __str__, _add_, _axiom_init_, _div_, _gap_init_, _gp_init_, _integer_, _kash_init_, _macaulay2_init_, _magma_init_, _maple_init_, _mathematica_init_, _maxima_, _mul_, _neg_, _octave_init_, _pari_init_, _polynomial_, _rational_, _richcmp_, _singular_init_, _sub_, arguments, coeff, coefficient, coefficients, coeffs, combine, conjugate, default_variable, denominator, derivative, diff, differentiate, display2d, exp_simplify, expand, expand_rational, expand_trig, factor, factor_list, find_maximum_on_interval, find_minimum_on_interval, find_root, full_simplify, function, gradient, hessian, imag, integral, integrate, inverse_laplace, laplace, limit, log_simplify, minpoly, n, nintegral, nintegrate, norm, numerator, numerical_approx, partial_fraction, plot, poly, polynomial, power_series, radical_simplify, rational_expand, rational_simplify, real, roots, show, simplify, simplify_exp, simplify_full, simplify_log, simplify_radical, simplify_rational, simplify_trig, solve, subs, subs_expr, substitute, substitute_over_ring, taylor, trig_expand, trig_simplify, variables

Inherited from SymbolicExpression (private): _declare_simplified, _derivative, _factor_list, _has_been_simplified, _has_op, _recursive_sub, _recursive_sub_over_ring

Inherited from structure.element.RingElement: __div__, __idiv__, __imul__, __invert__, __mul__, __new__, __pos__, __rdiv__, __rmul__, __rpow__, __rtruediv__, __truediv__, _idiv_, _imul_, abs, additive_order, is_nilpotent, is_one, is_unit, multiplicative_order, order

Inherited from structure.element.ModuleElement: __add__, __iadd__, __isub__, __neg__, __radd__, __rsub__, __sub__, _iadd_, _ilmul_, _isub_, _lmul_, _rmul_

Inherited from structure.element.ModuleElement (private): _lmul_nonscalar, _rmul_nonscalar

Inherited from structure.element.Element: __reduce__, __rxor__, __xor__, _cmp_, _im_gens_, base_base_extend, base_base_extend_canonical_sym, base_extend, base_extend_canonical, base_extend_canonical_sym, base_extend_recursive, base_ring, category, is_zero, parent

Inherited from structure.element.Element (private): _coeff_repr, _is_atomic, _latex_coeff_repr, _make_new_with_parent_c, _set_parent

Inherited from structure.sage_object.SageObject: __repr__, _axiom_, _gap_, _gp_, _interface_, _interface_init_, _interface_is_cached_, _kash_, _macaulay2_, _magma_, _maple_, _mathematica_, _octave_, _pari_, _r_init_, _sage_, _singular_, db, dump, dumps, rename, reset_name, save, version

Inherited from object: __delattr__, __getattribute__, __reduce_ex__, __setattr__

Properties [hide private]

Inherited from object: __class__

Method Details [hide private]

__init__(self, obj)
(Constructor)

source code  

Create a symbolic expression.

EXAMPLES:
This example is mainly for testing purposes.

We explicitly import the SymbolicExpression class.
    sage: from sage.calculus.calculus import SymbolicExpression

Then we make an instance of it.  Note that it prints as a
``generic element'', since it doesn't even have a specific
value!
    sage: a = SymbolicExpression(); a
    Generic element of a structure

It's of the right type.
    sage: type(a)
    <class 'sage.calculus.calculus.SymbolicExpression'>

And it has the right parent. 
    sage: a.parent()
    Symbolic Ring
Overrides: SymbolicExpression.__init__
(inherited documentation)

__hash__(self)
(Hashing function)

source code  

Returns the hash of this symbolic expression.

EXAMPLES:
We hash a symbolic polynomial:
    sage: hash(x^2 + 1) #random due to architecture dependence
    -832266011

The default hashing strategy is to simply hash
the string representation of an object.
    sage: hash(repr(x^2+1)) #random due to architecture dependence
    -832266011

In some cases a better hashing strategy is used.
    sage: hash(SR(3/1)) 
    3
    sage: hash(repr(SR(3/1))) #random due to architecture dependence
    -2061914958
Overrides: SymbolicExpression.__hash__
(inherited documentation)

_fast_float_(self, *vars)

source code  

EXAMPLES: 
    sage: x,y,z = var('x,y,z')
    sage: f = 1 + sin(x)/x + sqrt(z^2+y^2)/cosh(x)
    sage: ff = f._fast_float_('x', 'y', 'z')
    sage: f(1.0,2.0,3.0)
    4.1780638977866...
    sage: ff(1.0,2.0,3.0)
    4.17806389778660...
Overrides: SymbolicExpression._fast_float_
(inherited documentation)

_mpfr_(self, field)

source code  

EXAMPLES:
Overrides: SymbolicExpression._mpfr_

_complex_mpfr_field_(self, C)

source code  

EXAMPLES:
Overrides: SymbolicExpression._complex_mpfr_field_

_complex_double_(self, C)

source code  

EXAMPLES:
Overrides: SymbolicExpression._complex_double_

_real_double_(self, R)

source code  

EXAMPLES:
Overrides: SymbolicExpression._real_double_

_real_rqdf_(self, R)

source code  

EXAMPLES:
Overrides: SymbolicExpression._real_rqdf_

_repr_(self, simplify=True)

source code  

EXAMPLES:
Overrides: structure.element.Element._repr_

_maxima_init_(self)

source code  
File: sage/structure/sage_object.pyx (starting at line 318)
Overrides: SymbolicExpression._maxima_init_

_sys_init_(self, system)

source code 
Overrides: SymbolicExpression._sys_init_

number_of_arguments(self)

source code  

Returns the number of arguments this object can take.

EXAMPLES:
    sage: SR = SymbolicExpressionRing()
    sage: a = SR(e)
    sage: a.number_of_arguments()
    0
Overrides: SymbolicExpression.number_of_arguments

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