Package sage :: Package calculus :: Module calculus :: Class SymbolicOperation

Class SymbolicOperation

                      object --+                    
                               |                    
structure.sage_object.SageObject --+                
                                   |                
           structure.element.Element --+            
                                       |            
         structure.element.ModuleElement --+        
                                           |        
               structure.element.RingElement --+    
                                               |    
                              SymbolicExpression --+
                                                   |
                                                  SymbolicOperation

Known Subclasses:: SymbolicArithmetic, SymbolicComposition


A parent class representing any operation on \class{SymbolicExpression} objects.

Instance Methods

[hide private]

__init__(self, operands)
Create a symbolic expression.

source code

variables(self, vars=())
Return sorted list of variables that occur in the simplified form of \code{self}. 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__, __hash__, __int__, __le__, __long__, __lt__, __ne__, __nonzero__, __pow__, __str__, _add_, _axiom_init_, _complex_double_, _complex_mpfr_field_, _div_, _fast_float_, _gap_init_, _gp_init_, _integer_, _kash_init_, _macaulay2_init_, _magma_init_, _maple_init_, _mathematica_init_, _maxima_, _maxima_init_, _mpfr_, _mul_, _neg_, _octave_init_, _pari_init_, _polynomial_, _rational_, _real_double_, _real_rqdf_, _richcmp_, _singular_init_, _sub_, _sys_init_, 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

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_, _repr_, 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, operands)
(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)

variables(self, vars=`()`)

source code


Return sorted list of variables that occur in the simplified
form of \code{self}.  The ordering is alphabetic.

EXAMPLES:
    sage: var('x,y,z,w,a,b,c')
    (x, y, z, w, a, b, c)
    sage: f = (x - x) + y^2 - z/z + (w^2-1)/(w+1); f
    y^2 + (w^2 - 1)/(w + 1) - 1
    sage: f.variables()
    (w, y)

    sage: (x + y + z + a + b + c).variables()
    (a, b, c, x, y, z)

    sage: (x^2 + x).variables()
    (x,)

Overrides: SymbolicExpression.variables

number_of_arguments(self)

source code


Returns the number of arguments this object can take.

EXAMPLES:
    sage: x,y,z = var('x,y,z')
    sage: (x+y).number_of_arguments()
    2
    sage: (x+1).number_of_arguments()
    1
    sage: (sin+1).number_of_arguments()
    1
    sage: (sin+x).number_of_arguments()
    1
    sage: (sin+x+y).number_of_arguments()
    2
    sage: (sin(z)+x+y).number_of_arguments()
    3
    sage: (sin+cos).number_of_arguments()
    1
    sage: (sin(x+y)).number_of_arguments()
    2
    
    sage: ( 2^(8/9) - 2^(1/9) )(x-1)
    Traceback (most recent call last):
    ...
    ValueError: the number of arguments must be less than or equal to 0

Note that \code{self} is simplified first:
    sage: f = x + pi - x; f
    pi
    sage: f.number_of_arguments()
    0

Overrides: SymbolicExpression.number_of_arguments

Class SymbolicOperation

__init__(self, operands) (Constructor)

variables(self, vars=())

number_of_arguments(self)

init(self, operands)
(Constructor)

variables(self, vars=`()`)