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Package sage :: Package calculus :: Module calculus :: Class SymbolicFunctionEvaluation
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Class SymbolicFunctionEvaluation

source code

                      object --+                    
                               |                    
structure.sage_object.SageObject --+                
                                   |                
           structure.element.Element --+            
                                       |            
         structure.element.ModuleElement --+        
                                           |        
               structure.element.RingElement --+    
                                               |    
                              SymbolicExpression --+
                                                   |
                                                  SymbolicFunctionEvaluation
Known Subclasses:
SymbolicFunctionEvaluation_delayed 

The result of evaluating a formal symbolic function.

EXAMPLES:
    sage: h = function('gfun', x); h
    gfun(x)
    sage: k = h.integral(x); k
    integrate(gfun(x), x)
    sage: k(gfun=sin)
    -cos(x)
    sage: k(gfun=cos)
    sin(x)
    sage: k.diff(x)
    gfun(x)


Instance Methods [hide private]
 
__init__(self, f, args=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...)
INPUT: f -- symbolic function args -- a tuple or list of symbolic expressions, at which f is formally evaluated.		 source code
 
__float__(self) source code
 
_is_atomic(self)
File: sage/structure/element.pyx (starting at line 497) Return True if and only if parenthesis are not required when *printing* out any of $x - s$, $x + s$, $x^s$ and $x/s$.		 source code
 
arguments(self)
Return arguments of self.		 source code
 
_repr_(self, simplify=True)
File: sage/structure/element.pyx (starting at line 291)		 source code
 
_latex_(self) source code
 
_maxima_init_(self)
Return string that in Maxima evaluates to something equivalent to \code{self}.		 source code
 
_mathematica_init_(self)
Return string that in Mathematica evaluates to something equivalent to \code{self}.		 source code
 
_recursive_sub(self, kwds)
EXAMPLES:...		 source code
 
_recursive_sub_over_ring(self, kwds, ring) source code
 
variables(self)
Return the variables appearing in the simplified form of \code{self}.		 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_, _maxima_, _mpfr_, _mul_, _neg_, _octave_init_, _pari_init_, _polynomial_, _rational_, _real_double_, _real_rqdf_, _richcmp_, _singular_init_, _sub_, _sys_init_, 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, number_of_arguments, 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

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, _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, f, args=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...)
(Constructor)

source code  

INPUT:
    f -- symbolic function
    args -- a tuple or list of symbolic expressions, at which
            f is formally evaluated.
Overrides: SymbolicExpression.__init__

_is_atomic(self)

source code  
File: sage/structure/element.pyx (starting at line 497)

Return True if and only if parenthesis are not required when
*printing* out any of $x - s$, $x + s$, $x^s$ and $x/s$.

EXAMPLES:
    sage: n = 5; n._is_atomic()
    True
    sage: n = x+1; n._is_atomic()
    False
Overrides: structure.element.Element._is_atomic
(inherited documentation)

arguments(self)

source code  

Return arguments of self.

EXAMPLES:
    sage: f = function('Gamma', var('z'), var('w'))
    sage: f.arguments()
    (z, w)
Overrides: SymbolicExpression.arguments

_repr_(self, simplify=True)

source code  
File: sage/structure/element.pyx (starting at line 291)
Overrides: structure.element.Element._repr_
(inherited documentation)

_maxima_init_(self)

source code  

Return string that in Maxima evaluates to something
equivalent to \code{self}.

EXAMPLES:
    sage: f = function('Gamma', var('w'), var('theta')); f
    Gamma(w, theta)
    sage: f._maxima_init_()
    "'Gamma(w, theta)"
    sage: maxima(f(sqrt(2), theta+3))
    'Gamma(sqrt(2),theta+3)
Overrides: SymbolicExpression._maxima_init_

_mathematica_init_(self)

source code  

Return string that in Mathematica evaluates to something
equivalent to \code{self}.

EXAMPLES:
    sage: f = function('Gamma', var('z'))
    sage: mathematica(f) # optional
    Gamma[z]
    sage: f = function('Gamma', var('w'), var('z')); f
    Gamma(w, z)
    sage: f._mathematica_init_()
    'Gamma[w, z]'
    sage: mathematica(f(sqrt(2), z+1)) # optional
    Gamma[Sqrt[2], 1 + z]
Overrides: SymbolicExpression._mathematica_init_

_recursive_sub(self, kwds)

source code  

EXAMPLES:
    sage: y = var('y')
    sage: f = function('foo',x); f
    foo(x)
    sage: f(foo=sin)
    sin(x)
    sage: f(x+y)
    foo(y + x)
    sage: a = f(pi)
    sage: a.substitute(foo = sin)
    0
    sage: a = f(pi/2)
    sage: a.substitute(foo = sin)
    1
    
    sage: b = f(pi/3) + x + y
    sage: b
    y + x + foo(pi/3)
    sage: b(foo = sin)
    y + x + sqrt(3)/2
    sage: b(foo = cos)
    y + x + 1/2
    sage: b(foo = cos, x=y)
    2*y + 1/2
Overrides: SymbolicExpression._recursive_sub

_recursive_sub_over_ring(self, kwds, ring)

source code 
Overrides: SymbolicExpression._recursive_sub_over_ring

variables(self)

source code  

Return the variables appearing in the simplified form of \code{self}.

EXAMPLES:
    sage: foo = function('foo')
    sage: var('x,y,a,b,z,t')
    (x, y, a, b, z, t)
    sage: w = foo(x,y,a,b,z) + t
    sage: w
    foo(x, y, a, b, z) + t
    sage: w.variables()
    (a, b, t, x, y, z)
Overrides: SymbolicExpression.variables

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